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43,401
Which binomial confidence interval is correct?
You need to report the back-transformed ones. This is because the original proportions are very small, you need to transform them and then transform them back into proportions.
Which binomial confidence interval is correct?
You need to report the back-transformed ones. This is because the original proportions are very small, you need to transform them and then transform them back into proportions.
Which binomial confidence interval is correct? You need to report the back-transformed ones. This is because the original proportions are very small, you need to transform them and then transform them back into proportions.
Which binomial confidence interval is correct? You need to report the back-transformed ones. This is because the original proportions are very small, you need to transform them and then transform them back into proportions.
43,402
Bias and variance properties of $L^1$ vs $L^2$ normalization
The variance will increase, the problem with L1 regularisation is some of the coefficients are highly unpredictable. The answer depends on how severe is your regularisation($\lambda$ value). I generated sin wave with gaussian noise with different seeds and what is observed is as lower $\lambda$ value the l1 norm has a ...
Bias and variance properties of $L^1$ vs $L^2$ normalization
The variance will increase, the problem with L1 regularisation is some of the coefficients are highly unpredictable. The answer depends on how severe is your regularisation($\lambda$ value). I generat
Bias and variance properties of $L^1$ vs $L^2$ normalization The variance will increase, the problem with L1 regularisation is some of the coefficients are highly unpredictable. The answer depends on how severe is your regularisation($\lambda$ value). I generated sin wave with gaussian noise with different seeds and wh...
Bias and variance properties of $L^1$ vs $L^2$ normalization The variance will increase, the problem with L1 regularisation is some of the coefficients are highly unpredictable. The answer depends on how severe is your regularisation($\lambda$ value). I generat
43,403
Use Importance Sampling and Monte carlo for estimating a summation
As stated your question does not make complete sense: if you are only interested in$$\mathfrak{A} =\sum_{c=1}^{C} a(c)$$and if $C$ is too large for the computation to be done, then representing $\mathfrak{A}$ as an expectation$$\mathfrak{A}=\mathbb{E}[\mathscr{A}(X)]$$can be a way to approximate $\mathfrak{A}$ by a Mon...
Use Importance Sampling and Monte carlo for estimating a summation
As stated your question does not make complete sense: if you are only interested in$$\mathfrak{A} =\sum_{c=1}^{C} a(c)$$and if $C$ is too large for the computation to be done, then representing $\math
Use Importance Sampling and Monte carlo for estimating a summation As stated your question does not make complete sense: if you are only interested in$$\mathfrak{A} =\sum_{c=1}^{C} a(c)$$and if $C$ is too large for the computation to be done, then representing $\mathfrak{A}$ as an expectation$$\mathfrak{A}=\mathbb{E}[\...
Use Importance Sampling and Monte carlo for estimating a summation As stated your question does not make complete sense: if you are only interested in$$\mathfrak{A} =\sum_{c=1}^{C} a(c)$$and if $C$ is too large for the computation to be done, then representing $\math
43,404
Fitted value versus probability for logistic regression
It is in fact fine to use logistic regression to summarize observed proportions lying in the range of [0-1] inclusive. In the past, such approaches were discredited when the data were in fact hierarchical and the goal of the analysis was to summarize individual level exposures which were aggregated up to a cluster leve...
Fitted value versus probability for logistic regression
It is in fact fine to use logistic regression to summarize observed proportions lying in the range of [0-1] inclusive. In the past, such approaches were discredited when the data were in fact hierarch
Fitted value versus probability for logistic regression It is in fact fine to use logistic regression to summarize observed proportions lying in the range of [0-1] inclusive. In the past, such approaches were discredited when the data were in fact hierarchical and the goal of the analysis was to summarize individual le...
Fitted value versus probability for logistic regression It is in fact fine to use logistic regression to summarize observed proportions lying in the range of [0-1] inclusive. In the past, such approaches were discredited when the data were in fact hierarch
43,405
How to model multiple inputs to multiple outputs?
tl;dr I recommend this, but only pending extensive visual data exploration. Your problem as univariate classification I was about to write an overview of supervised multivariate techniques, but then I realized I'd rather recast your problem. Given $X$=(charge, hydrophobicity, beta-sheet propensity, ...) and $Y$=(pH, io...
How to model multiple inputs to multiple outputs?
tl;dr I recommend this, but only pending extensive visual data exploration. Your problem as univariate classification I was about to write an overview of supervised multivariate techniques, but then I
How to model multiple inputs to multiple outputs? tl;dr I recommend this, but only pending extensive visual data exploration. Your problem as univariate classification I was about to write an overview of supervised multivariate techniques, but then I realized I'd rather recast your problem. Given $X$=(charge, hydrophob...
How to model multiple inputs to multiple outputs? tl;dr I recommend this, but only pending extensive visual data exploration. Your problem as univariate classification I was about to write an overview of supervised multivariate techniques, but then I
43,406
Calculating test-time perplexity for seq2seq (RNN) language models
How can we get a good but fair decoder hidden state $\hat h_i$ to predict word $\hat w_i$? How can it encode as much as possible about the history? Once the language model has been trained the $\hat h_i$ can be got from the previous words $w_0, w_1, ..., w_{i-1}$ where $w_0$ represents the start of sentence token. The...
Calculating test-time perplexity for seq2seq (RNN) language models
How can we get a good but fair decoder hidden state $\hat h_i$ to predict word $\hat w_i$? How can it encode as much as possible about the history? Once the language model has been trained the $\hat
Calculating test-time perplexity for seq2seq (RNN) language models How can we get a good but fair decoder hidden state $\hat h_i$ to predict word $\hat w_i$? How can it encode as much as possible about the history? Once the language model has been trained the $\hat h_i$ can be got from the previous words $w_0, w_1, .....
Calculating test-time perplexity for seq2seq (RNN) language models How can we get a good but fair decoder hidden state $\hat h_i$ to predict word $\hat w_i$? How can it encode as much as possible about the history? Once the language model has been trained the $\hat
43,407
Calculating test-time perplexity for seq2seq (RNN) language models
At test time, for decoding, choose the word with highest Softmax probability as the input to the next time step. The perplexity is calculated as p(sentence)^(-1/N) where N is number of words in the sentence.
Calculating test-time perplexity for seq2seq (RNN) language models
At test time, for decoding, choose the word with highest Softmax probability as the input to the next time step. The perplexity is calculated as p(sentence)^(-1/N) where N is number of words in the s
Calculating test-time perplexity for seq2seq (RNN) language models At test time, for decoding, choose the word with highest Softmax probability as the input to the next time step. The perplexity is calculated as p(sentence)^(-1/N) where N is number of words in the sentence.
Calculating test-time perplexity for seq2seq (RNN) language models At test time, for decoding, choose the word with highest Softmax probability as the input to the next time step. The perplexity is calculated as p(sentence)^(-1/N) where N is number of words in the s
43,408
Lambda value for BoxCox transformation in time series analysis
You probably want to look at When (and why) should you take the log of a distribution (of numbers)? which discusses power transforms. Unwarranted or incorrect transformations including differences should be studiously avoided as they are often an ill-fashioned /ill-conceived attempt to deal with unidentified anomalies...
Lambda value for BoxCox transformation in time series analysis
You probably want to look at When (and why) should you take the log of a distribution (of numbers)? which discusses power transforms. Unwarranted or incorrect transformations including differences sho
Lambda value for BoxCox transformation in time series analysis You probably want to look at When (and why) should you take the log of a distribution (of numbers)? which discusses power transforms. Unwarranted or incorrect transformations including differences should be studiously avoided as they are often an ill-fashio...
Lambda value for BoxCox transformation in time series analysis You probably want to look at When (and why) should you take the log of a distribution (of numbers)? which discusses power transforms. Unwarranted or incorrect transformations including differences sho
43,409
Is there a measure to describe the degree of linear separability?
As noted in the question and comments, a dataset of $m$ points $(\boldsymbol{x}_i,y_i)$ with $\boldsymbol{x}_i\in\mathbb{R}^n$ and $y_i\in\{-1,+1\}$ is linearly separable if we can find a normal vector $\boldsymbol{a}$ and scalar bias $b$ such that the linear inequality $$y_i(\boldsymbol{a}^T\boldsymbol{x}_i+b)\geq 1$$...
Is there a measure to describe the degree of linear separability?
As noted in the question and comments, a dataset of $m$ points $(\boldsymbol{x}_i,y_i)$ with $\boldsymbol{x}_i\in\mathbb{R}^n$ and $y_i\in\{-1,+1\}$ is linearly separable if we can find a normal vecto
Is there a measure to describe the degree of linear separability? As noted in the question and comments, a dataset of $m$ points $(\boldsymbol{x}_i,y_i)$ with $\boldsymbol{x}_i\in\mathbb{R}^n$ and $y_i\in\{-1,+1\}$ is linearly separable if we can find a normal vector $\boldsymbol{a}$ and scalar bias $b$ such that the l...
Is there a measure to describe the degree of linear separability? As noted in the question and comments, a dataset of $m$ points $(\boldsymbol{x}_i,y_i)$ with $\boldsymbol{x}_i\in\mathbb{R}^n$ and $y_i\in\{-1,+1\}$ is linearly separable if we can find a normal vecto
43,410
equivalence test - why isn't it more common?
I did some more thinking on the consequences of using a "point" null hypothesis. I plotted some power curves below: Basically for a fixed alpha when doing the usual point null hypothesis, as n increases, the power for small true parameters increases. This just doesn't seem like a great property to me in many situation...
equivalence test - why isn't it more common?
I did some more thinking on the consequences of using a "point" null hypothesis. I plotted some power curves below: Basically for a fixed alpha when doing the usual point null hypothesis, as n increa
equivalence test - why isn't it more common? I did some more thinking on the consequences of using a "point" null hypothesis. I plotted some power curves below: Basically for a fixed alpha when doing the usual point null hypothesis, as n increases, the power for small true parameters increases. This just doesn't seem ...
equivalence test - why isn't it more common? I did some more thinking on the consequences of using a "point" null hypothesis. I plotted some power curves below: Basically for a fixed alpha when doing the usual point null hypothesis, as n increa
43,411
Can I use mean absolute scaled error (MASE) from the accuracy function for time series cross validation?
accuracy() uses the training sample on which a particular forecast is based. As you note, this will change in each iteration of your rolling origin evaluation. So indeed, you need to "roll your own". This is less onerous than it looks like. Note that the MASE is the MAE or MAD, divided by some scaling factor. accuracy(...
Can I use mean absolute scaled error (MASE) from the accuracy function for time series cross validat
accuracy() uses the training sample on which a particular forecast is based. As you note, this will change in each iteration of your rolling origin evaluation. So indeed, you need to "roll your own".
Can I use mean absolute scaled error (MASE) from the accuracy function for time series cross validation? accuracy() uses the training sample on which a particular forecast is based. As you note, this will change in each iteration of your rolling origin evaluation. So indeed, you need to "roll your own". This is less on...
Can I use mean absolute scaled error (MASE) from the accuracy function for time series cross validat accuracy() uses the training sample on which a particular forecast is based. As you note, this will change in each iteration of your rolling origin evaluation. So indeed, you need to "roll your own".
43,412
Testing for Benford Law in real time
Sambridge et al. (2010) outline a method for assessing the conformance of time series data to Benford's law. Although your use case is a bit different, it may work for you too. Their method works as you basically describe: group your data into observation windows and test each window for conformance. This method has be...
Testing for Benford Law in real time
Sambridge et al. (2010) outline a method for assessing the conformance of time series data to Benford's law. Although your use case is a bit different, it may work for you too. Their method works as y
Testing for Benford Law in real time Sambridge et al. (2010) outline a method for assessing the conformance of time series data to Benford's law. Although your use case is a bit different, it may work for you too. Their method works as you basically describe: group your data into observation windows and test each windo...
Testing for Benford Law in real time Sambridge et al. (2010) outline a method for assessing the conformance of time series data to Benford's law. Although your use case is a bit different, it may work for you too. Their method works as y
43,413
Instrument Variables and Exclusion Restriction from a Mediation perspective
You correctly state that under the LATE-style IV assumptions with a causal effect of the IV Z on the treatment S, exogenous instrument, and no direct effect on the outcome Y, your treatment effect B of S on Y is identified as $Cov(Y,Z)/Cov(S,Z) = ITT/Compliance Rate$ So clearly, $ITT = Cov(Y, Z)$, and not $Cov(S,...
Instrument Variables and Exclusion Restriction from a Mediation perspective
You correctly state that under the LATE-style IV assumptions with a causal effect of the IV Z on the treatment S, exogenous instrument, and no direct effect on the outcome Y, your treatment effect B o
Instrument Variables and Exclusion Restriction from a Mediation perspective You correctly state that under the LATE-style IV assumptions with a causal effect of the IV Z on the treatment S, exogenous instrument, and no direct effect on the outcome Y, your treatment effect B of S on Y is identified as $Cov(Y,Z)/Cov(S,...
Instrument Variables and Exclusion Restriction from a Mediation perspective You correctly state that under the LATE-style IV assumptions with a causal effect of the IV Z on the treatment S, exogenous instrument, and no direct effect on the outcome Y, your treatment effect B o
43,414
How does a U-Net group pixel classifications into a single spatial region?
It incorporates "prior knowledge" by training the network over a training dataset which will update the weights of the convolution filters. This is how most neural networks are trained with standard backprop. Where the loss to be backproped is based on the segmenation loss in this case. Here's a link to better show a ...
How does a U-Net group pixel classifications into a single spatial region?
It incorporates "prior knowledge" by training the network over a training dataset which will update the weights of the convolution filters. This is how most neural networks are trained with standard
How does a U-Net group pixel classifications into a single spatial region? It incorporates "prior knowledge" by training the network over a training dataset which will update the weights of the convolution filters. This is how most neural networks are trained with standard backprop. Where the loss to be backproped is ...
How does a U-Net group pixel classifications into a single spatial region? It incorporates "prior knowledge" by training the network over a training dataset which will update the weights of the convolution filters. This is how most neural networks are trained with standard
43,415
What is the correct way for correlation and auto correlation plot?
tl;dr: Your time axis is wrong and the correlation values could be rescaled. Time Axis The cross-correlation of two continuous signals $F$ and $G$ is $$(F \star G)(\tau) = \int_{-\infty}^{\infty} F^*(t)G(t+\tau)dt$$ In other words, it is the dot product between $F$ (or its complex conjugate $F^*$ for complex-valued si...
What is the correct way for correlation and auto correlation plot?
tl;dr: Your time axis is wrong and the correlation values could be rescaled. Time Axis The cross-correlation of two continuous signals $F$ and $G$ is $$(F \star G)(\tau) = \int_{-\infty}^{\infty} F^*
What is the correct way for correlation and auto correlation plot? tl;dr: Your time axis is wrong and the correlation values could be rescaled. Time Axis The cross-correlation of two continuous signals $F$ and $G$ is $$(F \star G)(\tau) = \int_{-\infty}^{\infty} F^*(t)G(t+\tau)dt$$ In other words, it is the dot produc...
What is the correct way for correlation and auto correlation plot? tl;dr: Your time axis is wrong and the correlation values could be rescaled. Time Axis The cross-correlation of two continuous signals $F$ and $G$ is $$(F \star G)(\tau) = \int_{-\infty}^{\infty} F^*
43,416
Normalization factor in multivariate Gaussian
Indeed the formula $$|2πΣ|=(2π)^d|Σ|$$ is correct. In practice, one would compute $|Σ|$ and then multiply it by $(2π)^d$, rather than multiply $Σ$ by $2π$, which involves $d^2$ operations, and then compute its determinant.
Normalization factor in multivariate Gaussian
Indeed the formula $$|2πΣ|=(2π)^d|Σ|$$ is correct. In practice, one would compute $|Σ|$ and then multiply it by $(2π)^d$, rather than multiply $Σ$ by $2π$, which involves $d^2$ operations, and then c
Normalization factor in multivariate Gaussian Indeed the formula $$|2πΣ|=(2π)^d|Σ|$$ is correct. In practice, one would compute $|Σ|$ and then multiply it by $(2π)^d$, rather than multiply $Σ$ by $2π$, which involves $d^2$ operations, and then compute its determinant.
Normalization factor in multivariate Gaussian Indeed the formula $$|2πΣ|=(2π)^d|Σ|$$ is correct. In practice, one would compute $|Σ|$ and then multiply it by $(2π)^d$, rather than multiply $Σ$ by $2π$, which involves $d^2$ operations, and then c
43,417
Logistic Regression with R
My overall question: Why isn't logistic regression (including "family = "binomial") producing results as expected, but a "NOT-logistic" regression (not including "family = "binomial") does? You get different results as the linear models minimizes $$ \sum_{i = 1}^n (y_i - \eta_i)^2 $$ whereas the logistic regression...
Logistic Regression with R
My overall question: Why isn't logistic regression (including "family = "binomial") producing results as expected, but a "NOT-logistic" regression (not including "family = "binomial") does? You get
Logistic Regression with R My overall question: Why isn't logistic regression (including "family = "binomial") producing results as expected, but a "NOT-logistic" regression (not including "family = "binomial") does? You get different results as the linear models minimizes $$ \sum_{i = 1}^n (y_i - \eta_i)^2 $$ wher...
Logistic Regression with R My overall question: Why isn't logistic regression (including "family = "binomial") producing results as expected, but a "NOT-logistic" regression (not including "family = "binomial") does? You get
43,418
Comparing approaches of MLE estimates of a Weibull distribution
Weibull parameter estimation is typically done with gradient-descent-related algorithms. As far as I know most packages implements this by doing a location-scale transformation and then running the procedure on the resulting Gumbel-log-likelihood. Check related
Comparing approaches of MLE estimates of a Weibull distribution
Weibull parameter estimation is typically done with gradient-descent-related algorithms. As far as I know most packages implements this by doing a location-scale transformation and then running the pr
Comparing approaches of MLE estimates of a Weibull distribution Weibull parameter estimation is typically done with gradient-descent-related algorithms. As far as I know most packages implements this by doing a location-scale transformation and then running the procedure on the resulting Gumbel-log-likelihood. Check r...
Comparing approaches of MLE estimates of a Weibull distribution Weibull parameter estimation is typically done with gradient-descent-related algorithms. As far as I know most packages implements this by doing a location-scale transformation and then running the pr
43,419
Determine if two distributions are the same
Kolmogorov–Smirnov statistic may help you in this case. Following is an implementation which uses Kolmogorov-Smirnov statistic and the function returns the probability of similarity. #include <math.h> #define EPS1 0.001 #define EPS2 1.0e-8 float kstest(float alam) { int j; float a2, fac = 2.0, sum = 0.0, term,...
Determine if two distributions are the same
Kolmogorov–Smirnov statistic may help you in this case. Following is an implementation which uses Kolmogorov-Smirnov statistic and the function returns the probability of similarity. #include <math.h>
Determine if two distributions are the same Kolmogorov–Smirnov statistic may help you in this case. Following is an implementation which uses Kolmogorov-Smirnov statistic and the function returns the probability of similarity. #include <math.h> #define EPS1 0.001 #define EPS2 1.0e-8 float kstest(float alam) { int ...
Determine if two distributions are the same Kolmogorov–Smirnov statistic may help you in this case. Following is an implementation which uses Kolmogorov-Smirnov statistic and the function returns the probability of similarity. #include <math.h>
43,420
Approximate Metropolis algorithm - does it make sense?
No, I don't see why this is a bad idea. It seems to me that it is a natural (and interesting) extension to draw samples from a CDF. However, I believe that the acceptance should be $$ \min\left( \frac{F(Y+\varepsilon) - F(Y)}{F(x^{(t)}+\varepsilon) - F(x^{(t)})} , 1 \right) $$ because by definition $$ \lim_{\varepsil...
Approximate Metropolis algorithm - does it make sense?
No, I don't see why this is a bad idea. It seems to me that it is a natural (and interesting) extension to draw samples from a CDF. However, I believe that the acceptance should be $$ \min\left( \fr
Approximate Metropolis algorithm - does it make sense? No, I don't see why this is a bad idea. It seems to me that it is a natural (and interesting) extension to draw samples from a CDF. However, I believe that the acceptance should be $$ \min\left( \frac{F(Y+\varepsilon) - F(Y)}{F(x^{(t)}+\varepsilon) - F(x^{(t)})} ...
Approximate Metropolis algorithm - does it make sense? No, I don't see why this is a bad idea. It seems to me that it is a natural (and interesting) extension to draw samples from a CDF. However, I believe that the acceptance should be $$ \min\left( \fr
43,421
Aggregation of Correlations Coefficients (Spearman)
I'm curious, since you have these ranks, why are you calculating correlation coefficients? I think a better approach would be to use a procedure that is designed to deal with ranks. The Mann Whitney U test (or Wilcoxon Rank Sum test, they're the same thing) tests. This test concerns itself with whether or not the obser...
Aggregation of Correlations Coefficients (Spearman)
I'm curious, since you have these ranks, why are you calculating correlation coefficients? I think a better approach would be to use a procedure that is designed to deal with ranks. The Mann Whitney U
Aggregation of Correlations Coefficients (Spearman) I'm curious, since you have these ranks, why are you calculating correlation coefficients? I think a better approach would be to use a procedure that is designed to deal with ranks. The Mann Whitney U test (or Wilcoxon Rank Sum test, they're the same thing) tests. Thi...
Aggregation of Correlations Coefficients (Spearman) I'm curious, since you have these ranks, why are you calculating correlation coefficients? I think a better approach would be to use a procedure that is designed to deal with ranks. The Mann Whitney U
43,422
Aggregation of Correlations Coefficients (Spearman)
Mhhhh, so you would like to compare the distributions of correlation coefficients? How about to use a Kolmogorov-Smirnov test? correpl <- t(replicate(1000, { scores <- rnorm(15) a <- rank(scores, ties.method = "r") ### experiment with sd = x to give some weights closer or farther to a b <- rank(scores +...
Aggregation of Correlations Coefficients (Spearman)
Mhhhh, so you would like to compare the distributions of correlation coefficients? How about to use a Kolmogorov-Smirnov test? correpl <- t(replicate(1000, { scores <- rnorm(15) a <- rank(scor
Aggregation of Correlations Coefficients (Spearman) Mhhhh, so you would like to compare the distributions of correlation coefficients? How about to use a Kolmogorov-Smirnov test? correpl <- t(replicate(1000, { scores <- rnorm(15) a <- rank(scores, ties.method = "r") ### experiment with sd = x to give some w...
Aggregation of Correlations Coefficients (Spearman) Mhhhh, so you would like to compare the distributions of correlation coefficients? How about to use a Kolmogorov-Smirnov test? correpl <- t(replicate(1000, { scores <- rnorm(15) a <- rank(scor
43,423
Fractional dependent variable: Why not use Poisson regression?
One reason not to use Poisson regression here is that, since each employee can have at most one account, the number of accounts is bounded by the number of employees. A Poisson distribution would allow nonzero probability for the number of accounts exceeding the number of employees. My understanding is that although ...
Fractional dependent variable: Why not use Poisson regression?
One reason not to use Poisson regression here is that, since each employee can have at most one account, the number of accounts is bounded by the number of employees. A Poisson distribution would all
Fractional dependent variable: Why not use Poisson regression? One reason not to use Poisson regression here is that, since each employee can have at most one account, the number of accounts is bounded by the number of employees. A Poisson distribution would allow nonzero probability for the number of accounts exceedi...
Fractional dependent variable: Why not use Poisson regression? One reason not to use Poisson regression here is that, since each employee can have at most one account, the number of accounts is bounded by the number of employees. A Poisson distribution would all
43,424
Clustering very small datasets
For tiny data sets, hierarchical clustering is the method of choice. The dendrogram visualization allows you to visually verify how well the data clusters, if there are outliers, how clusters nest, and how many clusters exist.
Clustering very small datasets
For tiny data sets, hierarchical clustering is the method of choice. The dendrogram visualization allows you to visually verify how well the data clusters, if there are outliers, how clusters nest, an
Clustering very small datasets For tiny data sets, hierarchical clustering is the method of choice. The dendrogram visualization allows you to visually verify how well the data clusters, if there are outliers, how clusters nest, and how many clusters exist.
Clustering very small datasets For tiny data sets, hierarchical clustering is the method of choice. The dendrogram visualization allows you to visually verify how well the data clusters, if there are outliers, how clusters nest, an
43,425
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features?
As others mentioned, there isn't a "right" model. However, since you used one-hot encoding, you are basically dealing with boolean features now. In other words each term/feature is following a Bernoulli distribution. That being said, I would use a multivariate Bernoulli NB or a multinomial NB with boolean features (whi...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode
As others mentioned, there isn't a "right" model. However, since you used one-hot encoding, you are basically dealing with boolean features now. In other words each term/feature is following a Bernoul
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features? As others mentioned, there isn't a "right" model. However, since you used one-hot encoding, you are basically dealing with boolean features now. In other words each term/feature is following a Bernoulli dist...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode As others mentioned, there isn't a "right" model. However, since you used one-hot encoding, you are basically dealing with boolean features now. In other words each term/feature is following a Bernoul
43,426
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features?
Your choice of statistical model in classification (Gaussian NB, Multinomial NB, etc) depends on the distribution of your input variables. You should plot the histogram of each input parameter in order to determine their distribution. You can use Pandas to do this by creating a dataframe on your input matrix and runn...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode
Your choice of statistical model in classification (Gaussian NB, Multinomial NB, etc) depends on the distribution of your input variables. You should plot the histogram of each input parameter in ord
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features? Your choice of statistical model in classification (Gaussian NB, Multinomial NB, etc) depends on the distribution of your input variables. You should plot the histogram of each input parameter in order to d...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode Your choice of statistical model in classification (Gaussian NB, Multinomial NB, etc) depends on the distribution of your input variables. You should plot the histogram of each input parameter in ord
43,427
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features?
If you're using real-world data, it's very unlikely that any model will be "right," so rather than try to find a model that is "right," you should try to find a model that is accurate. To decide between those two models, you can use cross validation to get an estimate of the accuracy of each model and choose the better...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode
If you're using real-world data, it's very unlikely that any model will be "right," so rather than try to find a model that is "right," you should try to find a model that is accurate. To decide betwe
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features? If you're using real-world data, it's very unlikely that any model will be "right," so rather than try to find a model that is "right," you should try to find a model that is accurate. To decide between thos...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode If you're using real-world data, it's very unlikely that any model will be "right," so rather than try to find a model that is "right," you should try to find a model that is accurate. To decide betwe
43,428
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features?
I would suggest to plot a histogram. For a quick histogram you can do this: Load data into a pandas dataframe: df = pandas.Dataframe( data, optional parameters) df.hist() If most of your features are following a bernoulli distribution , you should be good to use Multinomial (Bernoulli) NB and if they are following...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode
I would suggest to plot a histogram. For a quick histogram you can do this: Load data into a pandas dataframe: df = pandas.Dataframe( data, optional parameters) df.hist() If most of your features ar
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encoded) features? I would suggest to plot a histogram. For a quick histogram you can do this: Load data into a pandas dataframe: df = pandas.Dataframe( data, optional parameters) df.hist() If most of your features are follo...
What is the best form (Gaussian, Multinomial) of Naive Bayes to use with categorical (one-hot encode I would suggest to plot a histogram. For a quick histogram you can do this: Load data into a pandas dataframe: df = pandas.Dataframe( data, optional parameters) df.hist() If most of your features ar
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Why does Bayesian p-value involve the parameters in addition to the data?
The p-value is used to express the outcome in a test of a model and it's parameters (to test a hypothesis). Typically it relates to some statistic that measures a discrepancy (e.g. distance from the expected mean). $P(T> t_{observed}|H_0)$ The probability that an observation of the statistic $T$ given the null hypothes...
Why does Bayesian p-value involve the parameters in addition to the data?
The p-value is used to express the outcome in a test of a model and it's parameters (to test a hypothesis). Typically it relates to some statistic that measures a discrepancy (e.g. distance from the e
Why does Bayesian p-value involve the parameters in addition to the data? The p-value is used to express the outcome in a test of a model and it's parameters (to test a hypothesis). Typically it relates to some statistic that measures a discrepancy (e.g. distance from the expected mean). $P(T> t_{observed}|H_0)$ The pr...
Why does Bayesian p-value involve the parameters in addition to the data? The p-value is used to express the outcome in a test of a model and it's parameters (to test a hypothesis). Typically it relates to some statistic that measures a discrepancy (e.g. distance from the e
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Why does Bayesian p-value involve the parameters in addition to the data?
There is nothing stopping you from using test statistics based solely on the replicate data. The point in the example is that the model assumes $y_i$ is normally distributed around a mean $\theta$ not around $\overline{y}$. Thus the test statistic provided in Gelman et. al. tests something about the normality assumpti...
Why does Bayesian p-value involve the parameters in addition to the data?
There is nothing stopping you from using test statistics based solely on the replicate data. The point in the example is that the model assumes $y_i$ is normally distributed around a mean $\theta$ no
Why does Bayesian p-value involve the parameters in addition to the data? There is nothing stopping you from using test statistics based solely on the replicate data. The point in the example is that the model assumes $y_i$ is normally distributed around a mean $\theta$ not around $\overline{y}$. Thus the test statist...
Why does Bayesian p-value involve the parameters in addition to the data? There is nothing stopping you from using test statistics based solely on the replicate data. The point in the example is that the model assumes $y_i$ is normally distributed around a mean $\theta$ no
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Measure-Theoretic Definition of MLE
That definition of the likelihood function is an approximation. Typically, you have $n$ observations, which are subject to a measurement error. So, in practice, instead of observing $x_j$, you observe $x_j\pm\epsilon$, where $\epsilon\gt 0$ is the measurement error. So, if you have a sample of $n$ i.i.d. observations, ...
Measure-Theoretic Definition of MLE
That definition of the likelihood function is an approximation. Typically, you have $n$ observations, which are subject to a measurement error. So, in practice, instead of observing $x_j$, you observe
Measure-Theoretic Definition of MLE That definition of the likelihood function is an approximation. Typically, you have $n$ observations, which are subject to a measurement error. So, in practice, instead of observing $x_j$, you observe $x_j\pm\epsilon$, where $\epsilon\gt 0$ is the measurement error. So, if you have a...
Measure-Theoretic Definition of MLE That definition of the likelihood function is an approximation. Typically, you have $n$ observations, which are subject to a measurement error. So, in practice, instead of observing $x_j$, you observe
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Measure-Theoretic Definition of MLE
You need the Radon–Nikodym theorem.. In the measure-theoretic problem, you are estimating a distribution $F_0$ that is defined on the sigma-algebra on the sample set, not on the sample set itself. Now suppose you have a parametric model $F(\cdot\mid\theta)$. If this model is dominated by a $\sigma$-finite measure $\mu$...
Measure-Theoretic Definition of MLE
You need the Radon–Nikodym theorem.. In the measure-theoretic problem, you are estimating a distribution $F_0$ that is defined on the sigma-algebra on the sample set, not on the sample set itself. Now
Measure-Theoretic Definition of MLE You need the Radon–Nikodym theorem.. In the measure-theoretic problem, you are estimating a distribution $F_0$ that is defined on the sigma-algebra on the sample set, not on the sample set itself. Now suppose you have a parametric model $F(\cdot\mid\theta)$. If this model is dominate...
Measure-Theoretic Definition of MLE You need the Radon–Nikodym theorem.. In the measure-theoretic problem, you are estimating a distribution $F_0$ that is defined on the sigma-algebra on the sample set, not on the sample set itself. Now
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What is the relationship between LATE and TOT?
Writing out the estimands may help. With $Y$ as the observed outcome, $A$ is the treatment of interest, $Z$ is the instrument, and $Y^a$ is the potential outcome under treatment plan $A=a$. For the TOT (or average treatment effect in the treated, ATT), the estimand is $$E[Y^{a=1} - Y^{a=0} |A=1]$$ For LATE $$E[Y^{a=1}...
What is the relationship between LATE and TOT?
Writing out the estimands may help. With $Y$ as the observed outcome, $A$ is the treatment of interest, $Z$ is the instrument, and $Y^a$ is the potential outcome under treatment plan $A=a$. For the T
What is the relationship between LATE and TOT? Writing out the estimands may help. With $Y$ as the observed outcome, $A$ is the treatment of interest, $Z$ is the instrument, and $Y^a$ is the potential outcome under treatment plan $A=a$. For the TOT (or average treatment effect in the treated, ATT), the estimand is $$E...
What is the relationship between LATE and TOT? Writing out the estimands may help. With $Y$ as the observed outcome, $A$ is the treatment of interest, $Z$ is the instrument, and $Y^a$ is the potential outcome under treatment plan $A=a$. For the T
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What is the relationship between LATE and TOT?
LATE is a subset of TOT....I quote from Mastering 'Metrics by Angrist and Pischke: "Researchers and policy makers are sometimes interested in average causal effects for the entire treated population, as well as in LATE. This average causal effect is called the treatment effect on the treated (TOT for short)" (Chapter 3...
What is the relationship between LATE and TOT?
LATE is a subset of TOT....I quote from Mastering 'Metrics by Angrist and Pischke: "Researchers and policy makers are sometimes interested in average causal effects for the entire treated population,
What is the relationship between LATE and TOT? LATE is a subset of TOT....I quote from Mastering 'Metrics by Angrist and Pischke: "Researchers and policy makers are sometimes interested in average causal effects for the entire treated population, as well as in LATE. This average causal effect is called the treatment ef...
What is the relationship between LATE and TOT? LATE is a subset of TOT....I quote from Mastering 'Metrics by Angrist and Pischke: "Researchers and policy makers are sometimes interested in average causal effects for the entire treated population,
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Deep Learning for Ordinal Classification
There are a few approaches. One is to do a one in hot encoding: https://arxiv.org/pdf/0704.1028.pdf But there should be other approaches. In classical ordinal regression, we fit cut off values st: $ P(X=1) = P(Z \leq \theta_1) = F(\theta_1)$ $ P(X=2) = P(\theta_1 \leq Z \leq \theta_2) = F(\theta_2) - F(\theta_1)$ $ P(...
Deep Learning for Ordinal Classification
There are a few approaches. One is to do a one in hot encoding: https://arxiv.org/pdf/0704.1028.pdf But there should be other approaches. In classical ordinal regression, we fit cut off values st: $
Deep Learning for Ordinal Classification There are a few approaches. One is to do a one in hot encoding: https://arxiv.org/pdf/0704.1028.pdf But there should be other approaches. In classical ordinal regression, we fit cut off values st: $ P(X=1) = P(Z \leq \theta_1) = F(\theta_1)$ $ P(X=2) = P(\theta_1 \leq Z \leq \t...
Deep Learning for Ordinal Classification There are a few approaches. One is to do a one in hot encoding: https://arxiv.org/pdf/0704.1028.pdf But there should be other approaches. In classical ordinal regression, we fit cut off values st: $
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Accuracy of a polygon fitting algorithm
Maybe a different error metric will give you what you want. You can use the F1 score, which is the harmonic mean of precision and recall. Recall is the percentage of the area of the polygon that is contained in the rectangle. Precision is the percentage of area inside the rectangle that is within the polygon. $F1 = \fr...
Accuracy of a polygon fitting algorithm
Maybe a different error metric will give you what you want. You can use the F1 score, which is the harmonic mean of precision and recall. Recall is the percentage of the area of the polygon that is co
Accuracy of a polygon fitting algorithm Maybe a different error metric will give you what you want. You can use the F1 score, which is the harmonic mean of precision and recall. Recall is the percentage of the area of the polygon that is contained in the rectangle. Precision is the percentage of area inside the rectang...
Accuracy of a polygon fitting algorithm Maybe a different error metric will give you what you want. You can use the F1 score, which is the harmonic mean of precision and recall. Recall is the percentage of the area of the polygon that is co
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Why must linear regressions only generate linear functions that resemble "lines or planes" (*Introduction to Statistical Learning* question)?
Unfortunatelly my rating is too low to add a comment, that's why I have to answer. Just imagine that there is some feature $Z$. $X_1 = \sin Z, \ X_2 = \cos Z$, and $f(X) = \beta_0 + \beta_1 X_1 + \beta_2 X_2 = \beta_0 + \beta_1 \sin Z + \beta_2 \cos Z$. Will $f(X)$ be linear if the coordinate system is $(Y, Z)$? And w...
Why must linear regressions only generate linear functions that resemble "lines or planes" (*Introdu
Unfortunatelly my rating is too low to add a comment, that's why I have to answer. Just imagine that there is some feature $Z$. $X_1 = \sin Z, \ X_2 = \cos Z$, and $f(X) = \beta_0 + \beta_1 X_1 + \be
Why must linear regressions only generate linear functions that resemble "lines or planes" (*Introduction to Statistical Learning* question)? Unfortunatelly my rating is too low to add a comment, that's why I have to answer. Just imagine that there is some feature $Z$. $X_1 = \sin Z, \ X_2 = \cos Z$, and $f(X) = \beta...
Why must linear regressions only generate linear functions that resemble "lines or planes" (*Introdu Unfortunatelly my rating is too low to add a comment, that's why I have to answer. Just imagine that there is some feature $Z$. $X_1 = \sin Z, \ X_2 = \cos Z$, and $f(X) = \beta_0 + \beta_1 X_1 + \be
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Does leaving out an important predictor in a mixed linear model violate the independence assumption?
We shouldn't leave out any variables that have a (significant) effect if we are interested in the causal effect and the design is not orthogonal. If a variable is left out and this variable is correlated with an included variable, then the coefficient of the included variable includes part of the effect of the left out...
Does leaving out an important predictor in a mixed linear model violate the independence assumption?
We shouldn't leave out any variables that have a (significant) effect if we are interested in the causal effect and the design is not orthogonal. If a variable is left out and this variable is correla
Does leaving out an important predictor in a mixed linear model violate the independence assumption? We shouldn't leave out any variables that have a (significant) effect if we are interested in the causal effect and the design is not orthogonal. If a variable is left out and this variable is correlated with an include...
Does leaving out an important predictor in a mixed linear model violate the independence assumption? We shouldn't leave out any variables that have a (significant) effect if we are interested in the causal effect and the design is not orthogonal. If a variable is left out and this variable is correla
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Does leaving out an important predictor in a mixed linear model violate the independence assumption?
First of all independence has nothing to do with the fact of dropping or adding a variable; remember that there is not a such test to prove the independence assumption, since it is related with your experimental design. Imagine this silly (but illustrative) example: “A political scientist is interested on people’s op...
Does leaving out an important predictor in a mixed linear model violate the independence assumption?
First of all independence has nothing to do with the fact of dropping or adding a variable; remember that there is not a such test to prove the independence assumption, since it is related with your e
Does leaving out an important predictor in a mixed linear model violate the independence assumption? First of all independence has nothing to do with the fact of dropping or adding a variable; remember that there is not a such test to prove the independence assumption, since it is related with your experimental design....
Does leaving out an important predictor in a mixed linear model violate the independence assumption? First of all independence has nothing to do with the fact of dropping or adding a variable; remember that there is not a such test to prove the independence assumption, since it is related with your e
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Does leaving out an important predictor in a mixed linear model violate the independence assumption?
You can still see the effects of group + timepoint + predictability and their interactions even when valence is left in the model. Keep in mind that interpreting interaction terms of continuous variables is quite difficult to interpret. The condition of independence is that we are assuming that our data is a random sam...
Does leaving out an important predictor in a mixed linear model violate the independence assumption?
You can still see the effects of group + timepoint + predictability and their interactions even when valence is left in the model. Keep in mind that interpreting interaction terms of continuous variab
Does leaving out an important predictor in a mixed linear model violate the independence assumption? You can still see the effects of group + timepoint + predictability and their interactions even when valence is left in the model. Keep in mind that interpreting interaction terms of continuous variables is quite diffic...
Does leaving out an important predictor in a mixed linear model violate the independence assumption? You can still see the effects of group + timepoint + predictability and their interactions even when valence is left in the model. Keep in mind that interpreting interaction terms of continuous variab
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Does leaving out an important predictor in a mixed linear model violate the independence assumption?
No, leaving out a dependent variable does not violate any independence assumption. Consider a very simple example where I'm examining the effect of height, weight, baseball batting average on points scored per basketball game. We know that height is a great predictor of basketball skills, but maybe we want to see how b...
Does leaving out an important predictor in a mixed linear model violate the independence assumption?
No, leaving out a dependent variable does not violate any independence assumption. Consider a very simple example where I'm examining the effect of height, weight, baseball batting average on points s
Does leaving out an important predictor in a mixed linear model violate the independence assumption? No, leaving out a dependent variable does not violate any independence assumption. Consider a very simple example where I'm examining the effect of height, weight, baseball batting average on points scored per basketbal...
Does leaving out an important predictor in a mixed linear model violate the independence assumption? No, leaving out a dependent variable does not violate any independence assumption. Consider a very simple example where I'm examining the effect of height, weight, baseball batting average on points s
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In the coupon collector's problem with group drawings, why does the probability decrease with increasing samples?
While late to the game I believe I understand the issue you are having. The case is not, as the comments suggest, because the equation is for exactly the number of stickers, but rather due to the nature of your particular example where $n < l$. If we re-read Wolfgang Stadie's paper where this equation is drawn from, $X...
In the coupon collector's problem with group drawings, why does the probability decrease with increa
While late to the game I believe I understand the issue you are having. The case is not, as the comments suggest, because the equation is for exactly the number of stickers, but rather due to the natu
In the coupon collector's problem with group drawings, why does the probability decrease with increasing samples? While late to the game I believe I understand the issue you are having. The case is not, as the comments suggest, because the equation is for exactly the number of stickers, but rather due to the nature of ...
In the coupon collector's problem with group drawings, why does the probability decrease with increa While late to the game I believe I understand the issue you are having. The case is not, as the comments suggest, because the equation is for exactly the number of stickers, but rather due to the natu
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Statistical methods to validate the performance of a linear Kalman filter algorithm [duplicate]
There are methods to check on the performance of the filter in the absence of truth data. One method is to recompute the measurement residuals after the state update (the a posteriori residual). Once the filter covariance has stabilized, and with constant measurement noise variance (R), the a posteriori residuals sho...
Statistical methods to validate the performance of a linear Kalman filter algorithm [duplicate]
There are methods to check on the performance of the filter in the absence of truth data. One method is to recompute the measurement residuals after the state update (the a posteriori residual). Onc
Statistical methods to validate the performance of a linear Kalman filter algorithm [duplicate] There are methods to check on the performance of the filter in the absence of truth data. One method is to recompute the measurement residuals after the state update (the a posteriori residual). Once the filter covariance ...
Statistical methods to validate the performance of a linear Kalman filter algorithm [duplicate] There are methods to check on the performance of the filter in the absence of truth data. One method is to recompute the measurement residuals after the state update (the a posteriori residual). Onc
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A modeling technique combining $k$ nearest neighbors and multiple linear regression
There was a paper https://projecteuclid.org/euclid.aos/1176325632 Ann. Statist. Volume 22, Number 3 (1994), 1346-1370. "Multivariate Locally Weighted Least Squares Regression" by D. Ruppert and M. P. Wand discussing a multiple regression where the weights on observations are not 0 or 1 as in your method but vary with t...
A modeling technique combining $k$ nearest neighbors and multiple linear regression
There was a paper https://projecteuclid.org/euclid.aos/1176325632 Ann. Statist. Volume 22, Number 3 (1994), 1346-1370. "Multivariate Locally Weighted Least Squares Regression" by D. Ruppert and M. P.
A modeling technique combining $k$ nearest neighbors and multiple linear regression There was a paper https://projecteuclid.org/euclid.aos/1176325632 Ann. Statist. Volume 22, Number 3 (1994), 1346-1370. "Multivariate Locally Weighted Least Squares Regression" by D. Ruppert and M. P. Wand discussing a multiple regressio...
A modeling technique combining $k$ nearest neighbors and multiple linear regression There was a paper https://projecteuclid.org/euclid.aos/1176325632 Ann. Statist. Volume 22, Number 3 (1994), 1346-1370. "Multivariate Locally Weighted Least Squares Regression" by D. Ruppert and M. P.
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A modeling technique combining $k$ nearest neighbors and multiple linear regression
As @Fortranner said, what you describe is locally weighted regression. A particular case, where distances are in a geographical sense, is geographically weighted regression: a reference is Geographically Weighted Regression: The Analysis of Spatially Varying Relationships by A. Stewart Fotheringham, Chris Brunsdon, Mar...
A modeling technique combining $k$ nearest neighbors and multiple linear regression
As @Fortranner said, what you describe is locally weighted regression. A particular case, where distances are in a geographical sense, is geographically weighted regression: a reference is Geographica
A modeling technique combining $k$ nearest neighbors and multiple linear regression As @Fortranner said, what you describe is locally weighted regression. A particular case, where distances are in a geographical sense, is geographically weighted regression: a reference is Geographically Weighted Regression: The Analysi...
A modeling technique combining $k$ nearest neighbors and multiple linear regression As @Fortranner said, what you describe is locally weighted regression. A particular case, where distances are in a geographical sense, is geographically weighted regression: a reference is Geographica
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Can you perform hypothesis testing on mutual information values?
Permutation testing seems like a viable option. You have $n_0$ vectors $Y_{0,1},\dots,Y_{0, n_0}$ in group $0$ and $n_1$ vectors $Y_{1,1},\dots,Y_{1, n_1}$. Calculate the mutual information in each group, and then calculate the difference. Next, permute the group labels, and calculate the difference in mutual informati...
Can you perform hypothesis testing on mutual information values?
Permutation testing seems like a viable option. You have $n_0$ vectors $Y_{0,1},\dots,Y_{0, n_0}$ in group $0$ and $n_1$ vectors $Y_{1,1},\dots,Y_{1, n_1}$. Calculate the mutual information in each gr
Can you perform hypothesis testing on mutual information values? Permutation testing seems like a viable option. You have $n_0$ vectors $Y_{0,1},\dots,Y_{0, n_0}$ in group $0$ and $n_1$ vectors $Y_{1,1},\dots,Y_{1, n_1}$. Calculate the mutual information in each group, and then calculate the difference. Next, permute t...
Can you perform hypothesis testing on mutual information values? Permutation testing seems like a viable option. You have $n_0$ vectors $Y_{0,1},\dots,Y_{0, n_0}$ in group $0$ and $n_1$ vectors $Y_{1,1},\dots,Y_{1, n_1}$. Calculate the mutual information in each gr
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Estimate number of unique items by number of duplicates in a sample
There is a python package estndv for this task. For example, the population has 1e6 items and your sample is [1,1,1,3,5,5,12]: from estndv import ndvEstimator estimator = ndvEstimator() ndv = estimator.sample_predict(S=[1,1,1,3,5,5,12], N=1e6) ndv is the estimated number of unique/distinct values for the population. T...
Estimate number of unique items by number of duplicates in a sample
There is a python package estndv for this task. For example, the population has 1e6 items and your sample is [1,1,1,3,5,5,12]: from estndv import ndvEstimator estimator = ndvEstimator() ndv = estimato
Estimate number of unique items by number of duplicates in a sample There is a python package estndv for this task. For example, the population has 1e6 items and your sample is [1,1,1,3,5,5,12]: from estndv import ndvEstimator estimator = ndvEstimator() ndv = estimator.sample_predict(S=[1,1,1,3,5,5,12], N=1e6) ndv is ...
Estimate number of unique items by number of duplicates in a sample There is a python package estndv for this task. For example, the population has 1e6 items and your sample is [1,1,1,3,5,5,12]: from estndv import ndvEstimator estimator = ndvEstimator() ndv = estimato
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Parametrisation invariance/covariance of the Jeffreys prior
It is simply a matter of normalization. The improper prior distribution is $$p(\sigma) \propto 1/\sigma \\\propto n/\sigma,$$ which bears out the claim of invariance under power transformations. In general, we can we can ignore constants when characterizing closed form probability distributions. For example, to derive ...
Parametrisation invariance/covariance of the Jeffreys prior
It is simply a matter of normalization. The improper prior distribution is $$p(\sigma) \propto 1/\sigma \\\propto n/\sigma,$$ which bears out the claim of invariance under power transformations. In ge
Parametrisation invariance/covariance of the Jeffreys prior It is simply a matter of normalization. The improper prior distribution is $$p(\sigma) \propto 1/\sigma \\\propto n/\sigma,$$ which bears out the claim of invariance under power transformations. In general, we can we can ignore constants when characterizing cl...
Parametrisation invariance/covariance of the Jeffreys prior It is simply a matter of normalization. The improper prior distribution is $$p(\sigma) \propto 1/\sigma \\\propto n/\sigma,$$ which bears out the claim of invariance under power transformations. In ge
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Inferring likely dates based on other related dates in incomplete data set
You have described a missing data problem, and specifically one of censoring. (As a mnemonic device to keep censoring straight in my head from the similar phenomenon of truncation, I like to think of text in a report blacked-out by 'censors'. You know there was a word or sentence there, but you just don't know what it ...
Inferring likely dates based on other related dates in incomplete data set
You have described a missing data problem, and specifically one of censoring. (As a mnemonic device to keep censoring straight in my head from the similar phenomenon of truncation, I like to think of
Inferring likely dates based on other related dates in incomplete data set You have described a missing data problem, and specifically one of censoring. (As a mnemonic device to keep censoring straight in my head from the similar phenomenon of truncation, I like to think of text in a report blacked-out by 'censors'. Yo...
Inferring likely dates based on other related dates in incomplete data set You have described a missing data problem, and specifically one of censoring. (As a mnemonic device to keep censoring straight in my head from the similar phenomenon of truncation, I like to think of
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SVM predicts everything in one class
Interesting.. Hard to answer the question directly. Two things I would try to diagnose would be: 1) How do logistic regression and random forest fare? 2) By "fare", I suggest you look at the calibrations of the classifiers. What do the bins look like? Binarized posterior class probabilities will not be very helpful.
SVM predicts everything in one class
Interesting.. Hard to answer the question directly. Two things I would try to diagnose would be: 1) How do logistic regression and random forest fare? 2) By "fare", I suggest you look at the calibrat
SVM predicts everything in one class Interesting.. Hard to answer the question directly. Two things I would try to diagnose would be: 1) How do logistic regression and random forest fare? 2) By "fare", I suggest you look at the calibrations of the classifiers. What do the bins look like? Binarized posterior class prob...
SVM predicts everything in one class Interesting.. Hard to answer the question directly. Two things I would try to diagnose would be: 1) How do logistic regression and random forest fare? 2) By "fare", I suggest you look at the calibrat
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SVM predicts everything in one class
I'm not sure, but I would suggest trying to add values to c and gamma parameters when tuning them. The reason I say that is because gamma defines a sort of "smoothness" of classification. That's to say a very small value of gamma means any close point will be considered having the same target (thus putting everything i...
SVM predicts everything in one class
I'm not sure, but I would suggest trying to add values to c and gamma parameters when tuning them. The reason I say that is because gamma defines a sort of "smoothness" of classification. That's to sa
SVM predicts everything in one class I'm not sure, but I would suggest trying to add values to c and gamma parameters when tuning them. The reason I say that is because gamma defines a sort of "smoothness" of classification. That's to say a very small value of gamma means any close point will be considered having the s...
SVM predicts everything in one class I'm not sure, but I would suggest trying to add values to c and gamma parameters when tuning them. The reason I say that is because gamma defines a sort of "smoothness" of classification. That's to sa
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Visualizing interrater disagreement
This isn't as sexy as your plot, but it might make it easier to read off actual frequency data. Simulated data -- color indicates the number of raters who initially agreed with the eventual common rating (i.e. 0, 1 or 2). Code: library(ggplot2) theme_set(theme_bw()) theme_update(strip.background=element_rect(colour="...
Visualizing interrater disagreement
This isn't as sexy as your plot, but it might make it easier to read off actual frequency data. Simulated data -- color indicates the number of raters who initially agreed with the eventual common ra
Visualizing interrater disagreement This isn't as sexy as your plot, but it might make it easier to read off actual frequency data. Simulated data -- color indicates the number of raters who initially agreed with the eventual common rating (i.e. 0, 1 or 2). Code: library(ggplot2) theme_set(theme_bw()) theme_update(st...
Visualizing interrater disagreement This isn't as sexy as your plot, but it might make it easier to read off actual frequency data. Simulated data -- color indicates the number of raters who initially agreed with the eventual common ra
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Is the Akaike information criterion inversely proportional to the chi-squared statistic?
Check your formula for AIC against the Wikipedia AIC page, equal-variances case. The negative sign before your first term seems to be in error. (That section of the Wikipedia page omits the correction from AIC to AICc, the third term of your equation, which is discussed higher up on that page.) There might be some conf...
Is the Akaike information criterion inversely proportional to the chi-squared statistic?
Check your formula for AIC against the Wikipedia AIC page, equal-variances case. The negative sign before your first term seems to be in error. (That section of the Wikipedia page omits the correction
Is the Akaike information criterion inversely proportional to the chi-squared statistic? Check your formula for AIC against the Wikipedia AIC page, equal-variances case. The negative sign before your first term seems to be in error. (That section of the Wikipedia page omits the correction from AIC to AICc, the third te...
Is the Akaike information criterion inversely proportional to the chi-squared statistic? Check your formula for AIC against the Wikipedia AIC page, equal-variances case. The negative sign before your first term seems to be in error. (That section of the Wikipedia page omits the correction
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Is there a measure of how well a Markov chain allows movement between states?
Maybe the conductance of the Markov chain is the right notion to look at. Let $P\in[0,1]^{n\times n}$ be a transition matrix with stationary distribution $\pi$ (in your cases, $\pi$ is always the uniform distribution). The conductance of $P$ is $$\Phi(P):=\min_{S\subset [n], \pi(S)\le\frac{1}{2}}\frac{\sum_{i\in S,j\i...
Is there a measure of how well a Markov chain allows movement between states?
Maybe the conductance of the Markov chain is the right notion to look at. Let $P\in[0,1]^{n\times n}$ be a transition matrix with stationary distribution $\pi$ (in your cases, $\pi$ is always the unif
Is there a measure of how well a Markov chain allows movement between states? Maybe the conductance of the Markov chain is the right notion to look at. Let $P\in[0,1]^{n\times n}$ be a transition matrix with stationary distribution $\pi$ (in your cases, $\pi$ is always the uniform distribution). The conductance of $P$ ...
Is there a measure of how well a Markov chain allows movement between states? Maybe the conductance of the Markov chain is the right notion to look at. Let $P\in[0,1]^{n\times n}$ be a transition matrix with stationary distribution $\pi$ (in your cases, $\pi$ is always the unif
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Is there a measure of how well a Markov chain allows movement between states?
If the transition graph is strongly connected (i.e. given an initial state, any other state is reachable with p>0, possibly via intermediate states) , then as time goes to infinity the probability to find the system in a given state does not depend on the initial state. That is to say, there is a chance $$p_i(X)$$ to f...
Is there a measure of how well a Markov chain allows movement between states?
If the transition graph is strongly connected (i.e. given an initial state, any other state is reachable with p>0, possibly via intermediate states) , then as time goes to infinity the probability to
Is there a measure of how well a Markov chain allows movement between states? If the transition graph is strongly connected (i.e. given an initial state, any other state is reachable with p>0, possibly via intermediate states) , then as time goes to infinity the probability to find the system in a given state does not ...
Is there a measure of how well a Markov chain allows movement between states? If the transition graph is strongly connected (i.e. given an initial state, any other state is reachable with p>0, possibly via intermediate states) , then as time goes to infinity the probability to
43,456
Calculating the integral of a PDF inside a closed contour of constant density
A Monte Carlo approach offers an easy solution to this problem. First we need to generate a sample from the PDF - this can be done through interpolation and rejection sampling. Rather than keeping the coordinates of each sample, we need to store the probability density of each sample. Let $z$ be the density of the cont...
Calculating the integral of a PDF inside a closed contour of constant density
A Monte Carlo approach offers an easy solution to this problem. First we need to generate a sample from the PDF - this can be done through interpolation and rejection sampling. Rather than keeping the
Calculating the integral of a PDF inside a closed contour of constant density A Monte Carlo approach offers an easy solution to this problem. First we need to generate a sample from the PDF - this can be done through interpolation and rejection sampling. Rather than keeping the coordinates of each sample, we need to st...
Calculating the integral of a PDF inside a closed contour of constant density A Monte Carlo approach offers an easy solution to this problem. First we need to generate a sample from the PDF - this can be done through interpolation and rejection sampling. Rather than keeping the
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Modeling linear regression with covariate dependent error
You could use iterative feasible generalized least squares. Start by setting weights for each datapoint to 1, i.e. no weighting. Fit a weighted regression model for each dataset using weights. Create a single dataset combining residuals/errors and their respective x values. Fit $e_i^2 = a\cdot x_i + b$. If the noise ...
Modeling linear regression with covariate dependent error
You could use iterative feasible generalized least squares. Start by setting weights for each datapoint to 1, i.e. no weighting. Fit a weighted regression model for each dataset using weights. Create
Modeling linear regression with covariate dependent error You could use iterative feasible generalized least squares. Start by setting weights for each datapoint to 1, i.e. no weighting. Fit a weighted regression model for each dataset using weights. Create a single dataset combining residuals/errors and their respect...
Modeling linear regression with covariate dependent error You could use iterative feasible generalized least squares. Start by setting weights for each datapoint to 1, i.e. no weighting. Fit a weighted regression model for each dataset using weights. Create
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Modeling linear regression with covariate dependent error
If the distribution of your error term can be described by two independent parameters, for example a Gaussian distribution with mean independent of the variance then your problem is familiar. Since $E(error|x)=0$ we can only have the variance/scale of your error depending on $x$. In that case your regression model has...
Modeling linear regression with covariate dependent error
If the distribution of your error term can be described by two independent parameters, for example a Gaussian distribution with mean independent of the variance then your problem is familiar. Since $
Modeling linear regression with covariate dependent error If the distribution of your error term can be described by two independent parameters, for example a Gaussian distribution with mean independent of the variance then your problem is familiar. Since $E(error|x)=0$ we can only have the variance/scale of your erro...
Modeling linear regression with covariate dependent error If the distribution of your error term can be described by two independent parameters, for example a Gaussian distribution with mean independent of the variance then your problem is familiar. Since $
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Predictions for random walk in ARIMA model
Thanks to the help on this forum i was also able to ask this consolidated form of the original question to one of the profs at my university who is teaching a time-series class this semester....which i should have taken :-) I thought his answer was pretty good, and also has some echos of other comments posted for this ...
Predictions for random walk in ARIMA model
Thanks to the help on this forum i was also able to ask this consolidated form of the original question to one of the profs at my university who is teaching a time-series class this semester....which
Predictions for random walk in ARIMA model Thanks to the help on this forum i was also able to ask this consolidated form of the original question to one of the profs at my university who is teaching a time-series class this semester....which i should have taken :-) I thought his answer was pretty good, and also has so...
Predictions for random walk in ARIMA model Thanks to the help on this forum i was also able to ask this consolidated form of the original question to one of the profs at my university who is teaching a time-series class this semester....which
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Predictions for random walk in ARIMA model
" did notice my residuals show a change in variance, so if that violates some kind of ARIMA model assumptions or something let me know." Your residuals suggest non-constant error variance and thusly you should employ a Generalized Least Squares (GLS0) model as suggested by http://www.unc.edu/~jbhill/tsay.pdf . Your sel...
Predictions for random walk in ARIMA model
" did notice my residuals show a change in variance, so if that violates some kind of ARIMA model assumptions or something let me know." Your residuals suggest non-constant error variance and thusly y
Predictions for random walk in ARIMA model " did notice my residuals show a change in variance, so if that violates some kind of ARIMA model assumptions or something let me know." Your residuals suggest non-constant error variance and thusly you should employ a Generalized Least Squares (GLS0) model as suggested by htt...
Predictions for random walk in ARIMA model " did notice my residuals show a change in variance, so if that violates some kind of ARIMA model assumptions or something let me know." Your residuals suggest non-constant error variance and thusly y
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Chi-square/G-test/Fisher exact with replicates
Testing species frequencies I understand the OP's first question to be "Are the proportions of species 1, 2, and 3 identical across all six columns?" I think a chi-square test of independence of rows and columns would be applicable if the cell counts are sufficiently high (that's a whole other topic). When can count da...
Chi-square/G-test/Fisher exact with replicates
Testing species frequencies I understand the OP's first question to be "Are the proportions of species 1, 2, and 3 identical across all six columns?" I think a chi-square test of independence of rows
Chi-square/G-test/Fisher exact with replicates Testing species frequencies I understand the OP's first question to be "Are the proportions of species 1, 2, and 3 identical across all six columns?" I think a chi-square test of independence of rows and columns would be applicable if the cell counts are sufficiently high ...
Chi-square/G-test/Fisher exact with replicates Testing species frequencies I understand the OP's first question to be "Are the proportions of species 1, 2, and 3 identical across all six columns?" I think a chi-square test of independence of rows
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Estimating the prediction variance in kernel ridge regression
For anyone interested, this paper helped me a lot further: Estimating Predictive Variances with Kernel Ridge Regression by G. C. Cawley , N. L. C. Talbot and O. Chapelle Note that this paper explains how to do it for heteroscedastic noise, however you can also use it for homogeous noise as follows. The first method, KR...
Estimating the prediction variance in kernel ridge regression
For anyone interested, this paper helped me a lot further: Estimating Predictive Variances with Kernel Ridge Regression by G. C. Cawley , N. L. C. Talbot and O. Chapelle Note that this paper explains
Estimating the prediction variance in kernel ridge regression For anyone interested, this paper helped me a lot further: Estimating Predictive Variances with Kernel Ridge Regression by G. C. Cawley , N. L. C. Talbot and O. Chapelle Note that this paper explains how to do it for heteroscedastic noise, however you can al...
Estimating the prediction variance in kernel ridge regression For anyone interested, this paper helped me a lot further: Estimating Predictive Variances with Kernel Ridge Regression by G. C. Cawley , N. L. C. Talbot and O. Chapelle Note that this paper explains
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Accounting for overdispersion in binomial glm using proportions, without quasibinomial
Overdispersion occurs for a number of reasons, but often the case of presence/absence data is because of clustering of observations and correlations between observations. Taken from Brostrom & Holmberg (2011) Generalised Linear Models with Clustered Data: Fixed and random effects models with glmmML "Generally speakin...
Accounting for overdispersion in binomial glm using proportions, without quasibinomial
Overdispersion occurs for a number of reasons, but often the case of presence/absence data is because of clustering of observations and correlations between observations. Taken from Brostrom & Holmb
Accounting for overdispersion in binomial glm using proportions, without quasibinomial Overdispersion occurs for a number of reasons, but often the case of presence/absence data is because of clustering of observations and correlations between observations. Taken from Brostrom & Holmberg (2011) Generalised Linear Mod...
Accounting for overdispersion in binomial glm using proportions, without quasibinomial Overdispersion occurs for a number of reasons, but often the case of presence/absence data is because of clustering of observations and correlations between observations. Taken from Brostrom & Holmb
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Intuitive explanation of the F-statistic formula?
Note that if there were no population effect (the population means were identical at every combination of the regressors), there would still be some estimated effect -- the RegressionSS would be nonzero -- it would tend to increase if the error variance increased, or if you added more regressors. Indeed, if there were ...
Intuitive explanation of the F-statistic formula?
Note that if there were no population effect (the population means were identical at every combination of the regressors), there would still be some estimated effect -- the RegressionSS would be nonze
Intuitive explanation of the F-statistic formula? Note that if there were no population effect (the population means were identical at every combination of the regressors), there would still be some estimated effect -- the RegressionSS would be nonzero -- it would tend to increase if the error variance increased, or if...
Intuitive explanation of the F-statistic formula? Note that if there were no population effect (the population means were identical at every combination of the regressors), there would still be some estimated effect -- the RegressionSS would be nonze
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Intuitive explanation of the F-statistic formula?
(I typed this thinking you were talking about analysis of variance, but the idea is essentially the same for a more general regression model.) The data you imagine where there is zero between group variation is possible but extremely unlikely. (You may be conflating true values of parameters with their sample estimates...
Intuitive explanation of the F-statistic formula?
(I typed this thinking you were talking about analysis of variance, but the idea is essentially the same for a more general regression model.) The data you imagine where there is zero between group va
Intuitive explanation of the F-statistic formula? (I typed this thinking you were talking about analysis of variance, but the idea is essentially the same for a more general regression model.) The data you imagine where there is zero between group variation is possible but extremely unlikely. (You may be conflating tru...
Intuitive explanation of the F-statistic formula? (I typed this thinking you were talking about analysis of variance, but the idea is essentially the same for a more general regression model.) The data you imagine where there is zero between group va
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How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper
A sufficient condition for sparsity is that $\min_{\theta \neq 0} [ |\theta| + p'_\lambda (|\theta|) ]$ is positive. The reason for this condition is explained on p. 1350 of the paper, but it is only a brief outline, as the authors have chosen to omit most of the demonstration of the asserted results. I will try to f...
How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper
A sufficient condition for sparsity is that $\min_{\theta \neq 0} [ |\theta| + p'_\lambda (|\theta|) ]$ is positive. The reason for this condition is explained on p. 1350 of the paper, but it is only
How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper A sufficient condition for sparsity is that $\min_{\theta \neq 0} [ |\theta| + p'_\lambda (|\theta|) ]$ is positive. The reason for this condition is explained on p. 1350 of the paper, but it is only a brief outline, as the author...
How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper A sufficient condition for sparsity is that $\min_{\theta \neq 0} [ |\theta| + p'_\lambda (|\theta|) ]$ is positive. The reason for this condition is explained on p. 1350 of the paper, but it is only
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How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper
For conclusion A sufficient condition for sparsity is $\text{min}_{\theta \neq 0} \{|\theta| + p_\lambda'(\theta)\} \gt 0$, I think I got some thoughts. Given the condition (2) $\text{min}_{\theta \neq 0} \{|\theta| + p_\lambda'(\theta)\} \gt 0$, then we have two cases regarding $|z|$. If $|z| \lt \text{min}_{\theta...
How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper
For conclusion A sufficient condition for sparsity is $\text{min}_{\theta \neq 0} \{|\theta| + p_\lambda'(\theta)\} \gt 0$, I think I got some thoughts. Given the condition (2) $\text{min}_{\theta \n
How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper For conclusion A sufficient condition for sparsity is $\text{min}_{\theta \neq 0} \{|\theta| + p_\lambda'(\theta)\} \gt 0$, I think I got some thoughts. Given the condition (2) $\text{min}_{\theta \neq 0} \{|\theta| + p_\lambda'(...
How to prove the properties of penalized likelihood estimator in Fan and Li (2001) paper For conclusion A sufficient condition for sparsity is $\text{min}_{\theta \neq 0} \{|\theta| + p_\lambda'(\theta)\} \gt 0$, I think I got some thoughts. Given the condition (2) $\text{min}_{\theta \n
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Maximum likelihood estimation for Gaussian mixture
First regarding the practical issue of vanishing variance most implementations of GMM will have a limit on how small the variance can get, you can set the minimum to some small value based on your specific problem. Secondly EM is guaranteed to improve on the objective function (Likelihood in the case of ML) or remain t...
Maximum likelihood estimation for Gaussian mixture
First regarding the practical issue of vanishing variance most implementations of GMM will have a limit on how small the variance can get, you can set the minimum to some small value based on your spe
Maximum likelihood estimation for Gaussian mixture First regarding the practical issue of vanishing variance most implementations of GMM will have a limit on how small the variance can get, you can set the minimum to some small value based on your specific problem. Secondly EM is guaranteed to improve on the objective ...
Maximum likelihood estimation for Gaussian mixture First regarding the practical issue of vanishing variance most implementations of GMM will have a limit on how small the variance can get, you can set the minimum to some small value based on your spe
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Maximum likelihood estimation for Gaussian mixture
In such a case (like many others : HMM, ME) you should be careful to use a logistic representation of you likelyhoods, ie store log(v) instead of v for a value v. The important point is to avoid floating point underflow/overflow.
Maximum likelihood estimation for Gaussian mixture
In such a case (like many others : HMM, ME) you should be careful to use a logistic representation of you likelyhoods, ie store log(v) instead of v for a value v. The important point is to avoid float
Maximum likelihood estimation for Gaussian mixture In such a case (like many others : HMM, ME) you should be careful to use a logistic representation of you likelyhoods, ie store log(v) instead of v for a value v. The important point is to avoid floating point underflow/overflow.
Maximum likelihood estimation for Gaussian mixture In such a case (like many others : HMM, ME) you should be careful to use a logistic representation of you likelyhoods, ie store log(v) instead of v for a value v. The important point is to avoid float
43,470
chi-squared to test if two variables have the same frequency distribution
It is quite clear that something went wrong with your experiment. Specifically, it is likely that what went wrong was that the support of the two distributions you generated are not the same, and therefore, you are getting a pretty weird result from the chi-square test. Another issue is that the chi-square test is mean...
chi-squared to test if two variables have the same frequency distribution
It is quite clear that something went wrong with your experiment. Specifically, it is likely that what went wrong was that the support of the two distributions you generated are not the same, and ther
chi-squared to test if two variables have the same frequency distribution It is quite clear that something went wrong with your experiment. Specifically, it is likely that what went wrong was that the support of the two distributions you generated are not the same, and therefore, you are getting a pretty weird result f...
chi-squared to test if two variables have the same frequency distribution It is quite clear that something went wrong with your experiment. Specifically, it is likely that what went wrong was that the support of the two distributions you generated are not the same, and ther
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Correlation between principal components
I assume each matrix $A $ and $B $ consist of random variables and observations as columns and rows or viceversa. You can do that analysis of comparing the eigenvectors of the covariance matrices of $A $ and $B $, using the angle between them as a measure of the correlation between them. But I don't know if it is going...
Correlation between principal components
I assume each matrix $A $ and $B $ consist of random variables and observations as columns and rows or viceversa. You can do that analysis of comparing the eigenvectors of the covariance matrices of $
Correlation between principal components I assume each matrix $A $ and $B $ consist of random variables and observations as columns and rows or viceversa. You can do that analysis of comparing the eigenvectors of the covariance matrices of $A $ and $B $, using the angle between them as a measure of the correlation betw...
Correlation between principal components I assume each matrix $A $ and $B $ consist of random variables and observations as columns and rows or viceversa. You can do that analysis of comparing the eigenvectors of the covariance matrices of $
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How to evaluate uncertainty estimates in regression?
In regression, there are two different kinds of "uncertainties", which correspond to the difference (and frequently, confusion) between confidence intervals and prediction intervals: You could have uncertainties in parameter estimates. These are captured in confidence-intervals. These, in turn, are hard to evaluate, b...
How to evaluate uncertainty estimates in regression?
In regression, there are two different kinds of "uncertainties", which correspond to the difference (and frequently, confusion) between confidence intervals and prediction intervals: You could have u
How to evaluate uncertainty estimates in regression? In regression, there are two different kinds of "uncertainties", which correspond to the difference (and frequently, confusion) between confidence intervals and prediction intervals: You could have uncertainties in parameter estimates. These are captured in confiden...
How to evaluate uncertainty estimates in regression? In regression, there are two different kinds of "uncertainties", which correspond to the difference (and frequently, confusion) between confidence intervals and prediction intervals: You could have u
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Why use a mixture model with RNN instead of just directly predictive real values?
I am very new in the area so please take my comments with care ! I saw a lecture from Alex in this youtube channel https://www.youtube.com/channel/UC0z_jCi0XWqI8awUuQRFnyw In this video, the first objective of Alex was to build a simulation model. Therefore, I think that the output of the model which is searched for i...
Why use a mixture model with RNN instead of just directly predictive real values?
I am very new in the area so please take my comments with care ! I saw a lecture from Alex in this youtube channel https://www.youtube.com/channel/UC0z_jCi0XWqI8awUuQRFnyw In this video, the first ob
Why use a mixture model with RNN instead of just directly predictive real values? I am very new in the area so please take my comments with care ! I saw a lecture from Alex in this youtube channel https://www.youtube.com/channel/UC0z_jCi0XWqI8awUuQRFnyw In this video, the first objective of Alex was to build a simulat...
Why use a mixture model with RNN instead of just directly predictive real values? I am very new in the area so please take my comments with care ! I saw a lecture from Alex in this youtube channel https://www.youtube.com/channel/UC0z_jCi0XWqI8awUuQRFnyw In this video, the first ob
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Is F test used for feature selection only for features with numerical and continuous domain?
Assuming you are in the context of stepwise regression, the scale of the feature does not matter. The F-test is done on the difference of RSS values between the smaller and larger model as calculated on the outcome variable (also taking into to account the difference in the number of parameters). For more information ...
Is F test used for feature selection only for features with numerical and continuous domain?
Assuming you are in the context of stepwise regression, the scale of the feature does not matter. The F-test is done on the difference of RSS values between the smaller and larger model as calculated
Is F test used for feature selection only for features with numerical and continuous domain? Assuming you are in the context of stepwise regression, the scale of the feature does not matter. The F-test is done on the difference of RSS values between the smaller and larger model as calculated on the outcome variable (al...
Is F test used for feature selection only for features with numerical and continuous domain? Assuming you are in the context of stepwise regression, the scale of the feature does not matter. The F-test is done on the difference of RSS values between the smaller and larger model as calculated
43,475
Hamiltonian Monte-Carlo with piecewise differentiable log likelihood
This paper is likely relevant. Abstract: Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics with non-smooth functions, leading to poor performance. This paper is motivated by the behavior of Hamiltonian dynami...
Hamiltonian Monte-Carlo with piecewise differentiable log likelihood
This paper is likely relevant. Abstract: Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics
Hamiltonian Monte-Carlo with piecewise differentiable log likelihood This paper is likely relevant. Abstract: Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics with non-smooth functions, leading to poor perform...
Hamiltonian Monte-Carlo with piecewise differentiable log likelihood This paper is likely relevant. Abstract: Hamiltonian Monte Carlo (HMC) is a successful approach for sampling from continuous densities. However, it has difficulty simulating Hamiltonian dynamics
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What determines the precision of uncertainties?
Your pencil example is peculiar. You'll see why when I describe how this precision thing works in a typical case. Say, you're measuring a room with a measuring tape that has 1 mm ticks. You get 10033 mm measurement. The way to report this is 10033$\pm$0.5 mm. You usually take the half the tick as an a priori uncertaint...
What determines the precision of uncertainties?
Your pencil example is peculiar. You'll see why when I describe how this precision thing works in a typical case. Say, you're measuring a room with a measuring tape that has 1 mm ticks. You get 10033
What determines the precision of uncertainties? Your pencil example is peculiar. You'll see why when I describe how this precision thing works in a typical case. Say, you're measuring a room with a measuring tape that has 1 mm ticks. You get 10033 mm measurement. The way to report this is 10033$\pm$0.5 mm. You usually ...
What determines the precision of uncertainties? Your pencil example is peculiar. You'll see why when I describe how this precision thing works in a typical case. Say, you're measuring a room with a measuring tape that has 1 mm ticks. You get 10033
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What determines the precision of uncertainties?
In A, a standard deviation in the measured values which is smaller than the error on a single measurement would come about from measuring, say, 7.30 $\pm$ 0.05 cm over and over again, in which case the uncertainty in each measurement cannot be ignored in the error propagation -- in fact it dominates. In B and C, roundi...
What determines the precision of uncertainties?
In A, a standard deviation in the measured values which is smaller than the error on a single measurement would come about from measuring, say, 7.30 $\pm$ 0.05 cm over and over again, in which case th
What determines the precision of uncertainties? In A, a standard deviation in the measured values which is smaller than the error on a single measurement would come about from measuring, say, 7.30 $\pm$ 0.05 cm over and over again, in which case the uncertainty in each measurement cannot be ignored in the error propaga...
What determines the precision of uncertainties? In A, a standard deviation in the measured values which is smaller than the error on a single measurement would come about from measuring, say, 7.30 $\pm$ 0.05 cm over and over again, in which case th
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What determines the precision of uncertainties?
You asked "Would there ever be a reason where one is justified in reporting an uncertainty with more than one significant figure? For example, 7.3 ± 1.3 cm?" On one hand, 7.3 ± 1.3 has a relative uncertainty of 1.3/7.3 = 0.178 whereas 7.3 ± 1 has a relative uncertainty of 1/7.3 = 0.137. You are saying you "know more...
What determines the precision of uncertainties?
You asked "Would there ever be a reason where one is justified in reporting an uncertainty with more than one significant figure? For example, 7.3 ± 1.3 cm?" On one hand, 7.3 ± 1.3 has a relative u
What determines the precision of uncertainties? You asked "Would there ever be a reason where one is justified in reporting an uncertainty with more than one significant figure? For example, 7.3 ± 1.3 cm?" On one hand, 7.3 ± 1.3 has a relative uncertainty of 1.3/7.3 = 0.178 whereas 7.3 ± 1 has a relative uncertainty...
What determines the precision of uncertainties? You asked "Would there ever be a reason where one is justified in reporting an uncertainty with more than one significant figure? For example, 7.3 ± 1.3 cm?" On one hand, 7.3 ± 1.3 has a relative u
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How do you find the population size N based on the highest n values?
This is a nice question. I’ll give it a try... Denote by $\Phi$ the cdf of the normal distribution and by $\phi$ its density. The joint distribution of the $n$ highest scores $y_{(N-n+1)}, \dots, y_{(N)} $ is $$ {N ! \over (N-n) !} \Phi(y_{(N-n+1)})^{N-n} \phi(y_{(N-n+1)}) \cdots \phi( y_{(N)} ), $$ (that is, $N-n$ va...
How do you find the population size N based on the highest n values?
This is a nice question. I’ll give it a try... Denote by $\Phi$ the cdf of the normal distribution and by $\phi$ its density. The joint distribution of the $n$ highest scores $y_{(N-n+1)}, \dots, y_{(
How do you find the population size N based on the highest n values? This is a nice question. I’ll give it a try... Denote by $\Phi$ the cdf of the normal distribution and by $\phi$ its density. The joint distribution of the $n$ highest scores $y_{(N-n+1)}, \dots, y_{(N)} $ is $$ {N ! \over (N-n) !} \Phi(y_{(N-n+1)})^...
How do you find the population size N based on the highest n values? This is a nice question. I’ll give it a try... Denote by $\Phi$ the cdf of the normal distribution and by $\phi$ its density. The joint distribution of the $n$ highest scores $y_{(N-n+1)}, \dots, y_{(
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two margin comparison and one conclusion?
Since the value of $\phi_2$ is twice that of $\phi_1$, all the distances in $\phi_2$-space are twice as big as the distances in $\phi_1$-space. This means that the margin (which is roughly the "thickness" of the separating hyperplane that the SVM learns) is twice as big also. We can show this with an even simpler pair ...
two margin comparison and one conclusion?
Since the value of $\phi_2$ is twice that of $\phi_1$, all the distances in $\phi_2$-space are twice as big as the distances in $\phi_1$-space. This means that the margin (which is roughly the "thickn
two margin comparison and one conclusion? Since the value of $\phi_2$ is twice that of $\phi_1$, all the distances in $\phi_2$-space are twice as big as the distances in $\phi_1$-space. This means that the margin (which is roughly the "thickness" of the separating hyperplane that the SVM learns) is twice as big also. W...
two margin comparison and one conclusion? Since the value of $\phi_2$ is twice that of $\phi_1$, all the distances in $\phi_2$-space are twice as big as the distances in $\phi_1$-space. This means that the margin (which is roughly the "thickn
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How to make a trained neural network "forget" an instance?
It depends on the type of Neural Network you are using. A single layer Perceptron could do this by subtracting the eta value from each node the number of iterations you trained on based on the activated or not activated features and outputs. If you are using any optimization techniques like early stopping however it wo...
How to make a trained neural network "forget" an instance?
It depends on the type of Neural Network you are using. A single layer Perceptron could do this by subtracting the eta value from each node the number of iterations you trained on based on the activat
How to make a trained neural network "forget" an instance? It depends on the type of Neural Network you are using. A single layer Perceptron could do this by subtracting the eta value from each node the number of iterations you trained on based on the activated or not activated features and outputs. If you are using an...
How to make a trained neural network "forget" an instance? It depends on the type of Neural Network you are using. A single layer Perceptron could do this by subtracting the eta value from each node the number of iterations you trained on based on the activat
43,482
Ridge regression in multivariate Gaussian distribution
It is beyond my current knowledge to present a detailed answer. However, I hope that the following resources will help you figure out the solution. Check this set of presentation slides. Take a look at page 9 of this document: see references to Thisted (1976) and to Brown and Zidek (1980) before equation 18. Finally, t...
Ridge regression in multivariate Gaussian distribution
It is beyond my current knowledge to present a detailed answer. However, I hope that the following resources will help you figure out the solution. Check this set of presentation slides. Take a look a
Ridge regression in multivariate Gaussian distribution It is beyond my current knowledge to present a detailed answer. However, I hope that the following resources will help you figure out the solution. Check this set of presentation slides. Take a look at page 9 of this document: see references to Thisted (1976) and t...
Ridge regression in multivariate Gaussian distribution It is beyond my current knowledge to present a detailed answer. However, I hope that the following resources will help you figure out the solution. Check this set of presentation slides. Take a look a
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Can I penalize an arbitrary regression model and get Elastic-Net-esque results?
I'll try to address this question in a general way. For generalized linear models (GLM), it makes complete sense to use elastic-net priors on the parameters as you describe. This is merely to say that the standard elastic-net regularization framework works out-of-the-box for a broader class of models than simply Bern...
Can I penalize an arbitrary regression model and get Elastic-Net-esque results?
I'll try to address this question in a general way. For generalized linear models (GLM), it makes complete sense to use elastic-net priors on the parameters as you describe. This is merely to say th
Can I penalize an arbitrary regression model and get Elastic-Net-esque results? I'll try to address this question in a general way. For generalized linear models (GLM), it makes complete sense to use elastic-net priors on the parameters as you describe. This is merely to say that the standard elastic-net regularizati...
Can I penalize an arbitrary regression model and get Elastic-Net-esque results? I'll try to address this question in a general way. For generalized linear models (GLM), it makes complete sense to use elastic-net priors on the parameters as you describe. This is merely to say th
43,484
An 'easy' exercise on conditional expectations and filtrations
Following the hint given by Windridge, let $\mathbb{E} \left[ \mathbb{E} \left[X \middle \vert F\right] \middle\vert G\right] = \mathbb{E} \left[ Y \middle\vert G\right]$, where $Y = \mathbb{E} \left[X \middle\vert F\right]$. $\mathbb{E} \left[Y \middle\vert G\right] = \sum y \, \Pr\left(Y = y \middle\vert G\right)$. I...
An 'easy' exercise on conditional expectations and filtrations
Following the hint given by Windridge, let $\mathbb{E} \left[ \mathbb{E} \left[X \middle \vert F\right] \middle\vert G\right] = \mathbb{E} \left[ Y \middle\vert G\right]$, where $Y = \mathbb{E} \left[
An 'easy' exercise on conditional expectations and filtrations Following the hint given by Windridge, let $\mathbb{E} \left[ \mathbb{E} \left[X \middle \vert F\right] \middle\vert G\right] = \mathbb{E} \left[ Y \middle\vert G\right]$, where $Y = \mathbb{E} \left[X \middle\vert F\right]$. $\mathbb{E} \left[Y \middle\ver...
An 'easy' exercise on conditional expectations and filtrations Following the hint given by Windridge, let $\mathbb{E} \left[ \mathbb{E} \left[X \middle \vert F\right] \middle\vert G\right] = \mathbb{E} \left[ Y \middle\vert G\right]$, where $Y = \mathbb{E} \left[
43,485
An 'easy' exercise on conditional expectations and filtrations
Let $ \Omega = ${a,b,c} with $\mathbb{P}$({a}) = 1/2, $\mathbb{P}$({b}) = 1/4 and $\mathbb{P}$({c}) = 1/4. Define a random variable X $$ X = \begin{cases} 1 , \quad & w = \{ a \}, P(X = 1) = 1/2\\ 2 , \quad & w = \{ b,c \}, P(X = 2) = 1/2\\ \end{cases} \\ $$ Define 2 sigma-algebra: $ \mathcal{F}:=\left\{ \emptyset ...
An 'easy' exercise on conditional expectations and filtrations
Let $ \Omega = ${a,b,c} with $\mathbb{P}$({a}) = 1/2, $\mathbb{P}$({b}) = 1/4 and $\mathbb{P}$({c}) = 1/4. Define a random variable X $$ X = \begin{cases} 1 , \quad & w = \{ a \}, P(X = 1) = 1/2\\
An 'easy' exercise on conditional expectations and filtrations Let $ \Omega = ${a,b,c} with $\mathbb{P}$({a}) = 1/2, $\mathbb{P}$({b}) = 1/4 and $\mathbb{P}$({c}) = 1/4. Define a random variable X $$ X = \begin{cases} 1 , \quad & w = \{ a \}, P(X = 1) = 1/2\\ 2 , \quad & w = \{ b,c \}, P(X = 2) = 1/2\\ \end{cases} \...
An 'easy' exercise on conditional expectations and filtrations Let $ \Omega = ${a,b,c} with $\mathbb{P}$({a}) = 1/2, $\mathbb{P}$({b}) = 1/4 and $\mathbb{P}$({c}) = 1/4. Define a random variable X $$ X = \begin{cases} 1 , \quad & w = \{ a \}, P(X = 1) = 1/2\\
43,486
Statistics for model selection and model evaluation
I'll attempt to answer each question in turn. Contrary to fg nu's comment, I think there are real questions here - and real, although perhaps difficult, answers, too. Throughout, when I refer to the mis-use of statistics, I mean failing to recognise that one has made the mistake of mis-using the statistics for both mod...
Statistics for model selection and model evaluation
I'll attempt to answer each question in turn. Contrary to fg nu's comment, I think there are real questions here - and real, although perhaps difficult, answers, too. Throughout, when I refer to the m
Statistics for model selection and model evaluation I'll attempt to answer each question in turn. Contrary to fg nu's comment, I think there are real questions here - and real, although perhaps difficult, answers, too. Throughout, when I refer to the mis-use of statistics, I mean failing to recognise that one has made ...
Statistics for model selection and model evaluation I'll attempt to answer each question in turn. Contrary to fg nu's comment, I think there are real questions here - and real, although perhaps difficult, answers, too. Throughout, when I refer to the m
43,487
Deviance of a regression model
I'm also trying to understand how the dispersion parameter should be included in the formula to compute the deviance of a linear model from its log-likelihood, and I cannot find any reference in books about GLMs. This is really a mystery to me. Even if this is quite a basic point, the fact that nobody answered seems to...
Deviance of a regression model
I'm also trying to understand how the dispersion parameter should be included in the formula to compute the deviance of a linear model from its log-likelihood, and I cannot find any reference in books
Deviance of a regression model I'm also trying to understand how the dispersion parameter should be included in the formula to compute the deviance of a linear model from its log-likelihood, and I cannot find any reference in books about GLMs. This is really a mystery to me. Even if this is quite a basic point, the fac...
Deviance of a regression model I'm also trying to understand how the dispersion parameter should be included in the formula to compute the deviance of a linear model from its log-likelihood, and I cannot find any reference in books
43,488
How to implement Gaussian process using GPML toolbox with known output noise?
The output noise in the GPML toolbox is defined in a very different way. As clearly described here: Likelihood vs. noise kernel hyper-parameter in GPML Toolbox If you are using the @likGauss function then the output noise will be represented by the "hyp.lik" and not by adding the @covNoise covariance function to your c...
How to implement Gaussian process using GPML toolbox with known output noise?
The output noise in the GPML toolbox is defined in a very different way. As clearly described here: Likelihood vs. noise kernel hyper-parameter in GPML Toolbox If you are using the @likGauss function
How to implement Gaussian process using GPML toolbox with known output noise? The output noise in the GPML toolbox is defined in a very different way. As clearly described here: Likelihood vs. noise kernel hyper-parameter in GPML Toolbox If you are using the @likGauss function then the output noise will be represented ...
How to implement Gaussian process using GPML toolbox with known output noise? The output noise in the GPML toolbox is defined in a very different way. As clearly described here: Likelihood vs. noise kernel hyper-parameter in GPML Toolbox If you are using the @likGauss function
43,489
How to implement Gaussian process using GPML toolbox with known output noise?
The first thing that came to mind is to create your own kernel. GPML allows for that fairly easily, so just copy the kernel you want to use and change one of he hyper parameters to a constant. Remove the code where it calculates the derivative too for that hyper parameter. This might not be the only way to do it but i...
How to implement Gaussian process using GPML toolbox with known output noise?
The first thing that came to mind is to create your own kernel. GPML allows for that fairly easily, so just copy the kernel you want to use and change one of he hyper parameters to a constant. Remove
How to implement Gaussian process using GPML toolbox with known output noise? The first thing that came to mind is to create your own kernel. GPML allows for that fairly easily, so just copy the kernel you want to use and change one of he hyper parameters to a constant. Remove the code where it calculates the derivativ...
How to implement Gaussian process using GPML toolbox with known output noise? The first thing that came to mind is to create your own kernel. GPML allows for that fairly easily, so just copy the kernel you want to use and change one of he hyper parameters to a constant. Remove
43,490
Difference between calculated inclusion probability and what is returned by sampling function?
Sampling with replacement is boring. Sampling without replacement is very interesting. That's why the authors of library(sampling) restricted their attention to sampling WOR. So inclusionprobabilities() takes the baseline rates in your y, and figure out what would the inclusion probabilities be should a proper unequal ...
Difference between calculated inclusion probability and what is returned by sampling function?
Sampling with replacement is boring. Sampling without replacement is very interesting. That's why the authors of library(sampling) restricted their attention to sampling WOR. So inclusionprobabilities
Difference between calculated inclusion probability and what is returned by sampling function? Sampling with replacement is boring. Sampling without replacement is very interesting. That's why the authors of library(sampling) restricted their attention to sampling WOR. So inclusionprobabilities() takes the baseline rat...
Difference between calculated inclusion probability and what is returned by sampling function? Sampling with replacement is boring. Sampling without replacement is very interesting. That's why the authors of library(sampling) restricted their attention to sampling WOR. So inclusionprobabilities
43,491
Simulating a data generating process
I would start with fraction of variance unexplained, and think of what would be a reasonable value for your domain. Maybe in your field you expect the models have VFU 20%. In this case you can use $\sigma^2\sim0.2Var[y_t]$ for errors.
Simulating a data generating process
I would start with fraction of variance unexplained, and think of what would be a reasonable value for your domain. Maybe in your field you expect the models have VFU 20%. In this case you can use $\s
Simulating a data generating process I would start with fraction of variance unexplained, and think of what would be a reasonable value for your domain. Maybe in your field you expect the models have VFU 20%. In this case you can use $\sigma^2\sim0.2Var[y_t]$ for errors.
Simulating a data generating process I would start with fraction of variance unexplained, and think of what would be a reasonable value for your domain. Maybe in your field you expect the models have VFU 20%. In this case you can use $\s
43,492
Simulating a data generating process
Just saw your question ... Please look at how to generate random time series for a given one, including all trends? for my suggestion as to how to simulate a series given its DGF ( read model form ! ) . I determine the error variance from a useful model and then use it in conjunction with estimated model parameters to ...
Simulating a data generating process
Just saw your question ... Please look at how to generate random time series for a given one, including all trends? for my suggestion as to how to simulate a series given its DGF ( read model form ! )
Simulating a data generating process Just saw your question ... Please look at how to generate random time series for a given one, including all trends? for my suggestion as to how to simulate a series given its DGF ( read model form ! ) . I determine the error variance from a useful model and then use it in conjunctio...
Simulating a data generating process Just saw your question ... Please look at how to generate random time series for a given one, including all trends? for my suggestion as to how to simulate a series given its DGF ( read model form ! )
43,493
variable reduction before doing random forest in R
There might be two reasons for which you would want to reduce the number of features: Predictive Power: Random forest model accuracy does not really get impacted by the multicollinearity much. You can have a look at this. It actually selects random samples of the training data and also subsets of features while runni...
variable reduction before doing random forest in R
There might be two reasons for which you would want to reduce the number of features: Predictive Power: Random forest model accuracy does not really get impacted by the multicollinearity much. You ca
variable reduction before doing random forest in R There might be two reasons for which you would want to reduce the number of features: Predictive Power: Random forest model accuracy does not really get impacted by the multicollinearity much. You can have a look at this. It actually selects random samples of the tra...
variable reduction before doing random forest in R There might be two reasons for which you would want to reduce the number of features: Predictive Power: Random forest model accuracy does not really get impacted by the multicollinearity much. You ca
43,494
Explain log likelihood behaviour
Several things could be wrong; I can only suggest some things to look at. What's the smallest $N$ to debug with — 5, 10 ? Plot that with $N_r = N/2, N, 2N$ . Follow the steps, with rug plots or quantiles of $|p_i - q_j|, exp_{ij}$, row sums. (It's not clear to me if $1 / M_r$ scaling is correct, maybe row sums 1 in the...
Explain log likelihood behaviour
Several things could be wrong; I can only suggest some things to look at. What's the smallest $N$ to debug with — 5, 10 ? Plot that with $N_r = N/2, N, 2N$ . Follow the steps, with rug plots or quanti
Explain log likelihood behaviour Several things could be wrong; I can only suggest some things to look at. What's the smallest $N$ to debug with — 5, 10 ? Plot that with $N_r = N/2, N, 2N$ . Follow the steps, with rug plots or quantiles of $|p_i - q_j|, exp_{ij}$, row sums. (It's not clear to me if $1 / M_r$ scaling is...
Explain log likelihood behaviour Several things could be wrong; I can only suggest some things to look at. What's the smallest $N$ to debug with — 5, 10 ? Plot that with $N_r = N/2, N, 2N$ . Follow the steps, with rug plots or quanti
43,495
Should additional crime reports about someone change our level of doubt about an initial crime report?
An approach to the matter may be as follows: There exists a Bernouli random variable $Y_i$, which models whether the politician drunk ($Y_i=1$) or not ($Y_i=0$) during a specific party, indexed by $i$. Since nothing is really unprobable under the moon (parties being held usually during night hours), there exists some s...
Should additional crime reports about someone change our level of doubt about an initial crime repor
An approach to the matter may be as follows: There exists a Bernouli random variable $Y_i$, which models whether the politician drunk ($Y_i=1$) or not ($Y_i=0$) during a specific party, indexed by $i$
Should additional crime reports about someone change our level of doubt about an initial crime report? An approach to the matter may be as follows: There exists a Bernouli random variable $Y_i$, which models whether the politician drunk ($Y_i=1$) or not ($Y_i=0$) during a specific party, indexed by $i$. Since nothing i...
Should additional crime reports about someone change our level of doubt about an initial crime repor An approach to the matter may be as follows: There exists a Bernouli random variable $Y_i$, which models whether the politician drunk ($Y_i=1$) or not ($Y_i=0$) during a specific party, indexed by $i$
43,496
Building a predictive model, regression with a long right tail
The two modelling methods you propose seem to me to be legitimate in principle, but obviously the best model will emerge from analysis. Modelling the data under a logarithmic transformation (assuming you have no zero values that would stuff it up) implicitly gives you a non-linear model anyway, so that is fine ...
Building a predictive model, regression with a long right tail
The two modelling methods you propose seem to me to be legitimate in principle, but obviously the best model will emerge from analysis. Modelling the data under a logarithmic transformation (assum
Building a predictive model, regression with a long right tail The two modelling methods you propose seem to me to be legitimate in principle, but obviously the best model will emerge from analysis. Modelling the data under a logarithmic transformation (assuming you have no zero values that would stuff it up) imp...
Building a predictive model, regression with a long right tail The two modelling methods you propose seem to me to be legitimate in principle, but obviously the best model will emerge from analysis. Modelling the data under a logarithmic transformation (assum
43,497
Predict Failure time/ Weibull analysis
The precision of survival analysis is typically limited by the number of events. A rule of thumb is that you need about 15 events per parameter that you want to fit; you only have 13 events while a Weibull (and many parametric survival models) has 2 parameters. I'm not sure that there are enough events to rule out a We...
Predict Failure time/ Weibull analysis
The precision of survival analysis is typically limited by the number of events. A rule of thumb is that you need about 15 events per parameter that you want to fit; you only have 13 events while a We
Predict Failure time/ Weibull analysis The precision of survival analysis is typically limited by the number of events. A rule of thumb is that you need about 15 events per parameter that you want to fit; you only have 13 events while a Weibull (and many parametric survival models) has 2 parameters. I'm not sure that t...
Predict Failure time/ Weibull analysis The precision of survival analysis is typically limited by the number of events. A rule of thumb is that you need about 15 events per parameter that you want to fit; you only have 13 events while a We
43,498
Identifiability in generalized linear random effect model?
The identifiability problem in the probit model occurs because each latent vector $\boldsymbol{\lambda}_i$ affects the observable outcome only through its sign, and so if the underlying parameters do not affect the distributions of the sign, they are not identifiable. To see this, we note that it is possible to rewrit...
Identifiability in generalized linear random effect model?
The identifiability problem in the probit model occurs because each latent vector $\boldsymbol{\lambda}_i$ affects the observable outcome only through its sign, and so if the underlying parameters do
Identifiability in generalized linear random effect model? The identifiability problem in the probit model occurs because each latent vector $\boldsymbol{\lambda}_i$ affects the observable outcome only through its sign, and so if the underlying parameters do not affect the distributions of the sign, they are not identi...
Identifiability in generalized linear random effect model? The identifiability problem in the probit model occurs because each latent vector $\boldsymbol{\lambda}_i$ affects the observable outcome only through its sign, and so if the underlying parameters do
43,499
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators?
"Clustering by firms" doesn't exclude OLS as a possibility. One could simply adjust for a dummy variable indicating the firm and objectively call that a "cluster". More commonly, "clustering by firm" means adding a random intercept term for firms. This is the preferred approach when the number of firms is large relativ...
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators?
"Clustering by firms" doesn't exclude OLS as a possibility. One could simply adjust for a dummy variable indicating the firm and objectively call that a "cluster". More commonly, "clustering by firm"
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators? "Clustering by firms" doesn't exclude OLS as a possibility. One could simply adjust for a dummy variable indicating the firm and objectively call that a "cluster". More commonly, "clustering by firm" means adding a random int...
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators? "Clustering by firms" doesn't exclude OLS as a possibility. One could simply adjust for a dummy variable indicating the firm and objectively call that a "cluster". More commonly, "clustering by firm"
43,500
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators?
You can check FE vs POLS through this method, Source: Park, Hun Myoung. 2011. Practical Guides To Panel Data Modeling: A Step-by-step Analysis Using Stata. Tutorial Working Paper. Graduate School of International Relations, International University of Japan
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators?
You can check FE vs POLS through this method, Source: Park, Hun Myoung. 2011. Practical Guides To Panel Data Modeling: A Step-by-step Analysis Using Stata. Tutorial Working Paper. Graduate School of
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators? You can check FE vs POLS through this method, Source: Park, Hun Myoung. 2011. Practical Guides To Panel Data Modeling: A Step-by-step Analysis Using Stata. Tutorial Working Paper. Graduate School of International Relations, ...
Unbalanced Panel: pooled OLS vs FE vs RE - which method yields unbiased and robust estimators? You can check FE vs POLS through this method, Source: Park, Hun Myoung. 2011. Practical Guides To Panel Data Modeling: A Step-by-step Analysis Using Stata. Tutorial Working Paper. Graduate School of