idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
|---|---|---|---|---|---|---|
51,201 | How to model the relationship between geocoded and ungeocoded sales data? | As I understand it, the situation is as follows. You have data about store, its whereabouts and the sales-geocoded or ungeocoded. For each block, you have some portion of sales as geocoded and the rest ungeocoded.
Now, if you have data available for many stores, you can use a model to predict FRACTION OF UNGEOCODED SA... | How to model the relationship between geocoded and ungeocoded sales data? | As I understand it, the situation is as follows. You have data about store, its whereabouts and the sales-geocoded or ungeocoded. For each block, you have some portion of sales as geocoded and the res | How to model the relationship between geocoded and ungeocoded sales data?
As I understand it, the situation is as follows. You have data about store, its whereabouts and the sales-geocoded or ungeocoded. For each block, you have some portion of sales as geocoded and the rest ungeocoded.
Now, if you have data available... | How to model the relationship between geocoded and ungeocoded sales data?
As I understand it, the situation is as follows. You have data about store, its whereabouts and the sales-geocoded or ungeocoded. For each block, you have some portion of sales as geocoded and the res |
51,202 | Understanding similarity sensitive hashing algorithm in AdaBoost | It seems like the exponential loss they refer to is:
$\sum_{f,f' \in N}\exp^{−sign(A_{i}f_p+b_i)sign(A_if'_p+b_i)}$
so I would imagine they simply take the argmin over $A \in \mathcal{A}$ and $b \in \mathcal{B}$ where $\mathcal{A}$ is the set of $A$ represented by the top ten eigenvectors, and $\mathcal{B}$ is some ran... | Understanding similarity sensitive hashing algorithm in AdaBoost | It seems like the exponential loss they refer to is:
$\sum_{f,f' \in N}\exp^{−sign(A_{i}f_p+b_i)sign(A_if'_p+b_i)}$
so I would imagine they simply take the argmin over $A \in \mathcal{A}$ and $b \in \ | Understanding similarity sensitive hashing algorithm in AdaBoost
It seems like the exponential loss they refer to is:
$\sum_{f,f' \in N}\exp^{−sign(A_{i}f_p+b_i)sign(A_if'_p+b_i)}$
so I would imagine they simply take the argmin over $A \in \mathcal{A}$ and $b \in \mathcal{B}$ where $\mathcal{A}$ is the set of $A$ repre... | Understanding similarity sensitive hashing algorithm in AdaBoost
It seems like the exponential loss they refer to is:
$\sum_{f,f' \in N}\exp^{−sign(A_{i}f_p+b_i)sign(A_if'_p+b_i)}$
so I would imagine they simply take the argmin over $A \in \mathcal{A}$ and $b \in \ |
51,203 | What kind of statistical method do I need for comparing element concentrations? | Yes, this is an analysis of variance problem. Check out the aov function. You might want something like this ("geno" is the thing you want to test, right?):
> model1 <- aov(conc ~ region*elem*geno+Error(id), data=elemconc)
> model.null <- aov(conc ~ region*elem+Error(id), data=elemconc)
> summary(model1)
Error: id
... | What kind of statistical method do I need for comparing element concentrations? | Yes, this is an analysis of variance problem. Check out the aov function. You might want something like this ("geno" is the thing you want to test, right?):
> model1 <- aov(conc ~ region*elem*geno+E | What kind of statistical method do I need for comparing element concentrations?
Yes, this is an analysis of variance problem. Check out the aov function. You might want something like this ("geno" is the thing you want to test, right?):
> model1 <- aov(conc ~ region*elem*geno+Error(id), data=elemconc)
> model.null <-... | What kind of statistical method do I need for comparing element concentrations?
Yes, this is an analysis of variance problem. Check out the aov function. You might want something like this ("geno" is the thing you want to test, right?):
> model1 <- aov(conc ~ region*elem*geno+E |
51,204 | Understanding MANOVA in case of a single predictor | 1) Is this approach (MANOVA followed by series of ANOVA) justified? Are there strict assumptions before we could take this path?
In the example data you provide, there is no correlation between A, B, and C. Hence, a MANOVA seems beside the point. Unless you are interested in the relationship between A, B, and C, or h... | Understanding MANOVA in case of a single predictor | 1) Is this approach (MANOVA followed by series of ANOVA) justified? Are there strict assumptions before we could take this path?
In the example data you provide, there is no correlation between A, B, | Understanding MANOVA in case of a single predictor
1) Is this approach (MANOVA followed by series of ANOVA) justified? Are there strict assumptions before we could take this path?
In the example data you provide, there is no correlation between A, B, and C. Hence, a MANOVA seems beside the point. Unless you are inter... | Understanding MANOVA in case of a single predictor
1) Is this approach (MANOVA followed by series of ANOVA) justified? Are there strict assumptions before we could take this path?
In the example data you provide, there is no correlation between A, B, |
51,205 | Understanding MANOVA in case of a single predictor | The answer is in how you have simulated your data. It defines the stochastic process that you are assuming, and is enlightening on how you ought to draw inference.
This
set.seed(100)
group <- rep(c(0,1), each=40)
A <- rnorm(80, 5, .5) + .1 * group
B <- rnorm(80, 9, .3) + .2 * group + .5 * A
C <- rnorm(80, 12, .3) + .2 ... | Understanding MANOVA in case of a single predictor | The answer is in how you have simulated your data. It defines the stochastic process that you are assuming, and is enlightening on how you ought to draw inference.
This
set.seed(100)
group <- rep(c(0, | Understanding MANOVA in case of a single predictor
The answer is in how you have simulated your data. It defines the stochastic process that you are assuming, and is enlightening on how you ought to draw inference.
This
set.seed(100)
group <- rep(c(0,1), each=40)
A <- rnorm(80, 5, .5) + .1 * group
B <- rnorm(80, 9, .3)... | Understanding MANOVA in case of a single predictor
The answer is in how you have simulated your data. It defines the stochastic process that you are assuming, and is enlightening on how you ought to draw inference.
This
set.seed(100)
group <- rep(c(0, |
51,206 | Numerical accuracy of multivariate normal distribution | I am guessing you tested the code using a sigma which is not positive semidefinite. The 'accurate' implementation (which I am guessing is from the statistics toolbox) is computing $y^{\top}y$ where $y = C^{-\top} \left(x - \mu\right)$ where $C$ is the output of cholcov on $\Sigma$ (sigma). Note that $y^{\top}y$ must be... | Numerical accuracy of multivariate normal distribution | I am guessing you tested the code using a sigma which is not positive semidefinite. The 'accurate' implementation (which I am guessing is from the statistics toolbox) is computing $y^{\top}y$ where $y | Numerical accuracy of multivariate normal distribution
I am guessing you tested the code using a sigma which is not positive semidefinite. The 'accurate' implementation (which I am guessing is from the statistics toolbox) is computing $y^{\top}y$ where $y = C^{-\top} \left(x - \mu\right)$ where $C$ is the output of cho... | Numerical accuracy of multivariate normal distribution
I am guessing you tested the code using a sigma which is not positive semidefinite. The 'accurate' implementation (which I am guessing is from the statistics toolbox) is computing $y^{\top}y$ where $y |
51,207 | How do I analyse data with a ceiling effect? | Is it the case that each individual's score is composed of the sum of 30 binary questions? If so, then you should analyze the raw data (1 or 0 for each question for each individual) genearlized additive mixed effects models, treating individuals as random effects, and specify a binomial link. For example (in R):
librar... | How do I analyse data with a ceiling effect? | Is it the case that each individual's score is composed of the sum of 30 binary questions? If so, then you should analyze the raw data (1 or 0 for each question for each individual) genearlized additi | How do I analyse data with a ceiling effect?
Is it the case that each individual's score is composed of the sum of 30 binary questions? If so, then you should analyze the raw data (1 or 0 for each question for each individual) genearlized additive mixed effects models, treating individuals as random effects, and specif... | How do I analyse data with a ceiling effect?
Is it the case that each individual's score is composed of the sum of 30 binary questions? If so, then you should analyze the raw data (1 or 0 for each question for each individual) genearlized additi |
51,208 | Interrupted time-series analysis for panel data | I would identify the true date of the intervention i.e. when it was fully realized for each state separately using Intervention Detection schemes. The true date (de facto) can often be different from the "known date" (de jure) because of either a pre or a post effect (delay). With a common ARIMA model and one composite... | Interrupted time-series analysis for panel data | I would identify the true date of the intervention i.e. when it was fully realized for each state separately using Intervention Detection schemes. The true date (de facto) can often be different from | Interrupted time-series analysis for panel data
I would identify the true date of the intervention i.e. when it was fully realized for each state separately using Intervention Detection schemes. The true date (de facto) can often be different from the "known date" (de jure) because of either a pre or a post effect (del... | Interrupted time-series analysis for panel data
I would identify the true date of the intervention i.e. when it was fully realized for each state separately using Intervention Detection schemes. The true date (de facto) can often be different from |
51,209 | Creating an estimator with varying shock levels (SD) in R? | As it turns out, the code above does work. If you remove the hash tags in the middle portion of the code, you have a simulation-based logit estimator (producing intercepts, slopes, the number of iterations until converging on the true value, and an output saying "Done").
The estimator adjusts the standard deviation ... | Creating an estimator with varying shock levels (SD) in R? | As it turns out, the code above does work. If you remove the hash tags in the middle portion of the code, you have a simulation-based logit estimator (producing intercepts, slopes, the number of iter | Creating an estimator with varying shock levels (SD) in R?
As it turns out, the code above does work. If you remove the hash tags in the middle portion of the code, you have a simulation-based logit estimator (producing intercepts, slopes, the number of iterations until converging on the true value, and an output sayi... | Creating an estimator with varying shock levels (SD) in R?
As it turns out, the code above does work. If you remove the hash tags in the middle portion of the code, you have a simulation-based logit estimator (producing intercepts, slopes, the number of iter |
51,210 | Sampling considerations in psychometric applications of item response theory | There are two sets of questions that are relevant here.
Does the model work the same way for different people and different groups in the population? E.g. if males and females have different slopes with respect to their "ability" (in IRT slang; for your case, this would the degree of social anxiety), then that would b... | Sampling considerations in psychometric applications of item response theory | There are two sets of questions that are relevant here.
Does the model work the same way for different people and different groups in the population? E.g. if males and females have different slopes w | Sampling considerations in psychometric applications of item response theory
There are two sets of questions that are relevant here.
Does the model work the same way for different people and different groups in the population? E.g. if males and females have different slopes with respect to their "ability" (in IRT slan... | Sampling considerations in psychometric applications of item response theory
There are two sets of questions that are relevant here.
Does the model work the same way for different people and different groups in the population? E.g. if males and females have different slopes w |
51,211 | Sampling considerations in psychometric applications of item response theory | @Behacad, Building on the comment above, I think the answer is that the article in question was appropriate. Please check out the following link, as Dr. Panayides used the Rasch model and a polytomous set of data. I think you will find his methods of interest and that they will provide the information you need. A... | Sampling considerations in psychometric applications of item response theory | @Behacad, Building on the comment above, I think the answer is that the article in question was appropriate. Please check out the following link, as Dr. Panayides used the Rasch model and a polyto | Sampling considerations in psychometric applications of item response theory
@Behacad, Building on the comment above, I think the answer is that the article in question was appropriate. Please check out the following link, as Dr. Panayides used the Rasch model and a polytomous set of data. I think you will find hi... | Sampling considerations in psychometric applications of item response theory
@Behacad, Building on the comment above, I think the answer is that the article in question was appropriate. Please check out the following link, as Dr. Panayides used the Rasch model and a polyto |
51,212 | Project management for remote collaboration in prediction | I don't know of any off-the-shelf products specifically designed for collaboratively building predictive models, but I do think you can roll your own solution starting from a good version control system like git or hg and scripting tasks to make every step reproducible.
All datasets should absolutely stay out of versi... | Project management for remote collaboration in prediction | I don't know of any off-the-shelf products specifically designed for collaboratively building predictive models, but I do think you can roll your own solution starting from a good version control syst | Project management for remote collaboration in prediction
I don't know of any off-the-shelf products specifically designed for collaboratively building predictive models, but I do think you can roll your own solution starting from a good version control system like git or hg and scripting tasks to make every step repro... | Project management for remote collaboration in prediction
I don't know of any off-the-shelf products specifically designed for collaboratively building predictive models, but I do think you can roll your own solution starting from a good version control syst |
51,213 | Project management for remote collaboration in prediction | These might be helpful: Kepler, Process Makna, Taverna, and this paper. | Project management for remote collaboration in prediction | These might be helpful: Kepler, Process Makna, Taverna, and this paper. | Project management for remote collaboration in prediction
These might be helpful: Kepler, Process Makna, Taverna, and this paper. | Project management for remote collaboration in prediction
These might be helpful: Kepler, Process Makna, Taverna, and this paper. |
51,214 | Modeling a 1D random walk with nonconstant probabilities | Here is a variant on your suggestion:
If at $0$, go right with probability $k$ and left with probability $1-k$. If right of $0$, go right with probability $p$ and left with probability $1-p$; if left of $0$, go right with probability $1-p$ and left with probability $p$.
Providing $p \lt \frac{1}{2}$, the expected tim... | Modeling a 1D random walk with nonconstant probabilities | Here is a variant on your suggestion:
If at $0$, go right with probability $k$ and left with probability $1-k$. If right of $0$, go right with probability $p$ and left with probability $1-p$; if left | Modeling a 1D random walk with nonconstant probabilities
Here is a variant on your suggestion:
If at $0$, go right with probability $k$ and left with probability $1-k$. If right of $0$, go right with probability $p$ and left with probability $1-p$; if left of $0$, go right with probability $1-p$ and left with probabil... | Modeling a 1D random walk with nonconstant probabilities
Here is a variant on your suggestion:
If at $0$, go right with probability $k$ and left with probability $1-k$. If right of $0$, go right with probability $p$ and left with probability $1-p$; if left |
51,215 | Modeling a 1D random walk with nonconstant probabilities | How about something like $$dx = a*dt + b*d W^1_t - c*\text{sgn}(x)dW^2_t$$ where $W^1_t$ and $W_t^2$ are two distinct Wiener processes? It has a central tendency as long as $c>a$, and $a$ should determine the fraction $k$ it spends over the origin. | Modeling a 1D random walk with nonconstant probabilities | How about something like $$dx = a*dt + b*d W^1_t - c*\text{sgn}(x)dW^2_t$$ where $W^1_t$ and $W_t^2$ are two distinct Wiener processes? It has a central tendency as long as $c>a$, and $a$ should deter | Modeling a 1D random walk with nonconstant probabilities
How about something like $$dx = a*dt + b*d W^1_t - c*\text{sgn}(x)dW^2_t$$ where $W^1_t$ and $W_t^2$ are two distinct Wiener processes? It has a central tendency as long as $c>a$, and $a$ should determine the fraction $k$ it spends over the origin. | Modeling a 1D random walk with nonconstant probabilities
How about something like $$dx = a*dt + b*d W^1_t - c*\text{sgn}(x)dW^2_t$$ where $W^1_t$ and $W_t^2$ are two distinct Wiener processes? It has a central tendency as long as $c>a$, and $a$ should deter |
51,216 | How to predict how much data to collect? | If you can put your question in the form of a t-test, then Lehr's rule can be used to estimate the required sample size. For a 2-sided, one sample t-test at the 0.05 level, one can achieve power of 0.80 by using $n = 8 / \Delta^2$, where $\Delta$ is the 'signal to noise' (mean divided by standard deviation). I cannot f... | How to predict how much data to collect? | If you can put your question in the form of a t-test, then Lehr's rule can be used to estimate the required sample size. For a 2-sided, one sample t-test at the 0.05 level, one can achieve power of 0. | How to predict how much data to collect?
If you can put your question in the form of a t-test, then Lehr's rule can be used to estimate the required sample size. For a 2-sided, one sample t-test at the 0.05 level, one can achieve power of 0.80 by using $n = 8 / \Delta^2$, where $\Delta$ is the 'signal to noise' (mean d... | How to predict how much data to collect?
If you can put your question in the form of a t-test, then Lehr's rule can be used to estimate the required sample size. For a 2-sided, one sample t-test at the 0.05 level, one can achieve power of 0. |
51,217 | How do I calculate error propagation with different measures of error? | In some sense this depends on what you mean by $x$ and $\delta x$. Usually people mean that they are modeling $X$ as a random variable with mean $x$ and variance $(\delta x)^2$. Sometimes they mean the stronger condition that $X$ is actually Gaussian, and sometimes they have a broader meaning that $x$ and $\delta x$ ... | How do I calculate error propagation with different measures of error? | In some sense this depends on what you mean by $x$ and $\delta x$. Usually people mean that they are modeling $X$ as a random variable with mean $x$ and variance $(\delta x)^2$. Sometimes they mean | How do I calculate error propagation with different measures of error?
In some sense this depends on what you mean by $x$ and $\delta x$. Usually people mean that they are modeling $X$ as a random variable with mean $x$ and variance $(\delta x)^2$. Sometimes they mean the stronger condition that $X$ is actually Gauss... | How do I calculate error propagation with different measures of error?
In some sense this depends on what you mean by $x$ and $\delta x$. Usually people mean that they are modeling $X$ as a random variable with mean $x$ and variance $(\delta x)^2$. Sometimes they mean |
51,218 | How do I calculate error propagation with different measures of error? | See my book: "Propagation of Errors" by Mike Peralta at amazon.com
It treats the seldom covered topic of Second Order "Propagation of Errors" | How do I calculate error propagation with different measures of error? | See my book: "Propagation of Errors" by Mike Peralta at amazon.com
It treats the seldom covered topic of Second Order "Propagation of Errors" | How do I calculate error propagation with different measures of error?
See my book: "Propagation of Errors" by Mike Peralta at amazon.com
It treats the seldom covered topic of Second Order "Propagation of Errors" | How do I calculate error propagation with different measures of error?
See my book: "Propagation of Errors" by Mike Peralta at amazon.com
It treats the seldom covered topic of Second Order "Propagation of Errors" |
51,219 | Automatically detecting sudden change of mean | If I understand you you correctly, you might need to learn about multiple comparisons:
http://en.wikipedia.org/wiki/Multiple_comparisons
The choice of a particular procedure is a different question, e.g., Scheffe vs. Tukey vs. Bonferroni.
At least in this framework, there is a clear and straightforward way to have hypo... | Automatically detecting sudden change of mean | If I understand you you correctly, you might need to learn about multiple comparisons:
http://en.wikipedia.org/wiki/Multiple_comparisons
The choice of a particular procedure is a different question, e | Automatically detecting sudden change of mean
If I understand you you correctly, you might need to learn about multiple comparisons:
http://en.wikipedia.org/wiki/Multiple_comparisons
The choice of a particular procedure is a different question, e.g., Scheffe vs. Tukey vs. Bonferroni.
At least in this framework, there i... | Automatically detecting sudden change of mean
If I understand you you correctly, you might need to learn about multiple comparisons:
http://en.wikipedia.org/wiki/Multiple_comparisons
The choice of a particular procedure is a different question, e |
51,220 | Automatically detecting sudden change of mean | The answer to your question can be found deep in http://www.unc.edu/~jbhill/tsay.pdf and easily available from software like AUTOBOX (which I have helped develop) and elsewhere. What you have is a sequence of medians from 1 to 19 and what you want to do is to somehow discriminate between the first k of these medians an... | Automatically detecting sudden change of mean | The answer to your question can be found deep in http://www.unc.edu/~jbhill/tsay.pdf and easily available from software like AUTOBOX (which I have helped develop) and elsewhere. What you have is a seq | Automatically detecting sudden change of mean
The answer to your question can be found deep in http://www.unc.edu/~jbhill/tsay.pdf and easily available from software like AUTOBOX (which I have helped develop) and elsewhere. What you have is a sequence of medians from 1 to 19 and what you want to do is to somehow discri... | Automatically detecting sudden change of mean
The answer to your question can be found deep in http://www.unc.edu/~jbhill/tsay.pdf and easily available from software like AUTOBOX (which I have helped develop) and elsewhere. What you have is a seq |
51,221 | Resume buzz words [closed] | I contacted Sean at RezScore and he clarified some things for me. In a nutshell, inserting buzzwords into a hidden text box seems to be a good idea if you don't want to put them in your actual resume. However, you should be selective about which words you include because many of the algorithms penalize verbosity.
Maybe... | Resume buzz words [closed] | I contacted Sean at RezScore and he clarified some things for me. In a nutshell, inserting buzzwords into a hidden text box seems to be a good idea if you don't want to put them in your actual resume. | Resume buzz words [closed]
I contacted Sean at RezScore and he clarified some things for me. In a nutshell, inserting buzzwords into a hidden text box seems to be a good idea if you don't want to put them in your actual resume. However, you should be selective about which words you include because many of the algorithm... | Resume buzz words [closed]
I contacted Sean at RezScore and he clarified some things for me. In a nutshell, inserting buzzwords into a hidden text box seems to be a good idea if you don't want to put them in your actual resume. |
51,222 | What research tool to use when researching a project? | Steffen's comment and link to the question above is very useful.
I would say that it depends. I am going to assume that you are using LaTeX, at least (for mathematical typesetting), and possibly R (cos its free, and great).
In that case, especially given that you have mentioned org-mode, I would suggest using Emacs to ... | What research tool to use when researching a project? | Steffen's comment and link to the question above is very useful.
I would say that it depends. I am going to assume that you are using LaTeX, at least (for mathematical typesetting), and possibly R (co | What research tool to use when researching a project?
Steffen's comment and link to the question above is very useful.
I would say that it depends. I am going to assume that you are using LaTeX, at least (for mathematical typesetting), and possibly R (cos its free, and great).
In that case, especially given that you ha... | What research tool to use when researching a project?
Steffen's comment and link to the question above is very useful.
I would say that it depends. I am going to assume that you are using LaTeX, at least (for mathematical typesetting), and possibly R (co |
51,223 | Modeling multinomial problems with unknown sample size in BUGS | Better late than never...
The covariance matrix has diagonal entries $np_i(1-p_i)$ and off-diagonal entries $-np_ip_j$. JAGS and BUGS allow you to invert a matrix numerically (sigma[1:K, 1:K] <- inverse(tau[,]) in WinBUGS), so you don't actually need a closed-form expression for the precision matrix.
Your approach d... | Modeling multinomial problems with unknown sample size in BUGS | Better late than never...
The covariance matrix has diagonal entries $np_i(1-p_i)$ and off-diagonal entries $-np_ip_j$. JAGS and BUGS allow you to invert a matrix numerically (sigma[1:K, 1:K] <- inve | Modeling multinomial problems with unknown sample size in BUGS
Better late than never...
The covariance matrix has diagonal entries $np_i(1-p_i)$ and off-diagonal entries $-np_ip_j$. JAGS and BUGS allow you to invert a matrix numerically (sigma[1:K, 1:K] <- inverse(tau[,]) in WinBUGS), so you don't actually need a clo... | Modeling multinomial problems with unknown sample size in BUGS
Better late than never...
The covariance matrix has diagonal entries $np_i(1-p_i)$ and off-diagonal entries $-np_ip_j$. JAGS and BUGS allow you to invert a matrix numerically (sigma[1:K, 1:K] <- inve |
51,224 | Interpretation of a one cluster solution using the EM cluster algorithm | Two assumptions here: 1) Weka's finding the number of clusters (k) without issues, and 2) I believe EM uses mixtures of Gaussians which means the clusters need to be round/elliptical.
So, given that Weka's algorithm is finding the best k, the answer would be that using round/elliptical clusters, the most likely cluster... | Interpretation of a one cluster solution using the EM cluster algorithm | Two assumptions here: 1) Weka's finding the number of clusters (k) without issues, and 2) I believe EM uses mixtures of Gaussians which means the clusters need to be round/elliptical.
So, given that W | Interpretation of a one cluster solution using the EM cluster algorithm
Two assumptions here: 1) Weka's finding the number of clusters (k) without issues, and 2) I believe EM uses mixtures of Gaussians which means the clusters need to be round/elliptical.
So, given that Weka's algorithm is finding the best k, the answe... | Interpretation of a one cluster solution using the EM cluster algorithm
Two assumptions here: 1) Weka's finding the number of clusters (k) without issues, and 2) I believe EM uses mixtures of Gaussians which means the clusters need to be round/elliptical.
So, given that W |
51,225 | Simultaneous Equation System for logit/probit? | This is possible. The type of model you need is called multivariate probit. For a textbook treatment you can refer to Greene's Econometric Analysis.
However, from the computational point of view, these models can be laborious. Convergence can be slow or can even fail.
Multivariate probit models are implemented in R an... | Simultaneous Equation System for logit/probit? | This is possible. The type of model you need is called multivariate probit. For a textbook treatment you can refer to Greene's Econometric Analysis.
However, from the computational point of view, the | Simultaneous Equation System for logit/probit?
This is possible. The type of model you need is called multivariate probit. For a textbook treatment you can refer to Greene's Econometric Analysis.
However, from the computational point of view, these models can be laborious. Convergence can be slow or can even fail.
Mul... | Simultaneous Equation System for logit/probit?
This is possible. The type of model you need is called multivariate probit. For a textbook treatment you can refer to Greene's Econometric Analysis.
However, from the computational point of view, the |
51,226 | Simultaneous Equation System for logit/probit? | I am also trying to find a solution to it. But the current available (user-written in stata) command is so slow that I got no solution. A simple solution I am using is the propensity score matching method that solves selective treatment effect. it works only when you have large observations. The estimated variance is t... | Simultaneous Equation System for logit/probit? | I am also trying to find a solution to it. But the current available (user-written in stata) command is so slow that I got no solution. A simple solution I am using is the propensity score matching me | Simultaneous Equation System for logit/probit?
I am also trying to find a solution to it. But the current available (user-written in stata) command is so slow that I got no solution. A simple solution I am using is the propensity score matching method that solves selective treatment effect. it works only when you have ... | Simultaneous Equation System for logit/probit?
I am also trying to find a solution to it. But the current available (user-written in stata) command is so slow that I got no solution. A simple solution I am using is the propensity score matching me |
51,227 | Monte Carlo estimation of convex hull overlap probability | I know it's been a while since @Ganesh posted this question, but hopefully you're still interested in a response.
I've written some R code that does what you want, I think:
library(ggplot2)
library(MASS)
#################################################
#################################################
## Steps: ... | Monte Carlo estimation of convex hull overlap probability | I know it's been a while since @Ganesh posted this question, but hopefully you're still interested in a response.
I've written some R code that does what you want, I think:
library(ggplot2)
library(MA | Monte Carlo estimation of convex hull overlap probability
I know it's been a while since @Ganesh posted this question, but hopefully you're still interested in a response.
I've written some R code that does what you want, I think:
library(ggplot2)
library(MASS)
#################################################
#######... | Monte Carlo estimation of convex hull overlap probability
I know it's been a while since @Ganesh posted this question, but hopefully you're still interested in a response.
I've written some R code that does what you want, I think:
library(ggplot2)
library(MA |
51,228 | Why are cumulative residuals from regression on stock and index returns mean reverting | The significance of modeling the cumulative sum of residuals is to better approximate the Ornstein-Uhlembeck process of equation $(12)$ with discrete real-life data.
This process $X_i(t)$ represents the idiosyncratic above- or below- market fluctuations of the particular stock. More specifically, it is the difference b... | Why are cumulative residuals from regression on stock and index returns mean reverting | The significance of modeling the cumulative sum of residuals is to better approximate the Ornstein-Uhlembeck process of equation $(12)$ with discrete real-life data.
This process $X_i(t)$ represents t | Why are cumulative residuals from regression on stock and index returns mean reverting
The significance of modeling the cumulative sum of residuals is to better approximate the Ornstein-Uhlembeck process of equation $(12)$ with discrete real-life data.
This process $X_i(t)$ represents the idiosyncratic above- or below-... | Why are cumulative residuals from regression on stock and index returns mean reverting
The significance of modeling the cumulative sum of residuals is to better approximate the Ornstein-Uhlembeck process of equation $(12)$ with discrete real-life data.
This process $X_i(t)$ represents t |
51,229 | Adding high-dimensional data to mutivariate Cox model | One approach would simply be to carry on with the forward LR testing, although this would leave me very prone to overfitting.
You could penalise model complexity to avoid overfitting. My favourite is the stepAIC function from the MASS package that uses AIC (can be configured to use BIC) as a goodness of fit. | Adding high-dimensional data to mutivariate Cox model | One approach would simply be to carry on with the forward LR testing, although this would leave me very prone to overfitting.
You could penalise model complexity to avoid overfitting. My favourite i | Adding high-dimensional data to mutivariate Cox model
One approach would simply be to carry on with the forward LR testing, although this would leave me very prone to overfitting.
You could penalise model complexity to avoid overfitting. My favourite is the stepAIC function from the MASS package that uses AIC (can be... | Adding high-dimensional data to mutivariate Cox model
One approach would simply be to carry on with the forward LR testing, although this would leave me very prone to overfitting.
You could penalise model complexity to avoid overfitting. My favourite i |
51,230 | Adding high-dimensional data to mutivariate Cox model | Edit: after the comment below from EdS my original answer was not meaningful any more. @EdS, thanks for the further information! | Adding high-dimensional data to mutivariate Cox model | Edit: after the comment below from EdS my original answer was not meaningful any more. @EdS, thanks for the further information! | Adding high-dimensional data to mutivariate Cox model
Edit: after the comment below from EdS my original answer was not meaningful any more. @EdS, thanks for the further information! | Adding high-dimensional data to mutivariate Cox model
Edit: after the comment below from EdS my original answer was not meaningful any more. @EdS, thanks for the further information! |
51,231 | How to average quantized and truncated data? | http://en.wikipedia.org/wiki/Truncation_%28statistics%29
This is not much help, but at least it gives the correct buzzword (truncated, not quantized; quantization is not your problem) and one pointer to a paper. This should do as a starting point for further search.
Oh, and Winsorized mean is the exact opposite from wh... | How to average quantized and truncated data? | http://en.wikipedia.org/wiki/Truncation_%28statistics%29
This is not much help, but at least it gives the correct buzzword (truncated, not quantized; quantization is not your problem) and one pointer | How to average quantized and truncated data?
http://en.wikipedia.org/wiki/Truncation_%28statistics%29
This is not much help, but at least it gives the correct buzzword (truncated, not quantized; quantization is not your problem) and one pointer to a paper. This should do as a starting point for further search.
Oh, and ... | How to average quantized and truncated data?
http://en.wikipedia.org/wiki/Truncation_%28statistics%29
This is not much help, but at least it gives the correct buzzword (truncated, not quantized; quantization is not your problem) and one pointer |
51,232 | How to average quantized and truncated data? | If your data follow a truncated normal distribution, this link gives you a implementation in R language for the computation of the mean and variance of a truncated normal distribution :
http://www.r-bloggers.com/truncated-normal-distribution/ | How to average quantized and truncated data? | If your data follow a truncated normal distribution, this link gives you a implementation in R language for the computation of the mean and variance of a truncated normal distribution :
http://www.r- | How to average quantized and truncated data?
If your data follow a truncated normal distribution, this link gives you a implementation in R language for the computation of the mean and variance of a truncated normal distribution :
http://www.r-bloggers.com/truncated-normal-distribution/ | How to average quantized and truncated data?
If your data follow a truncated normal distribution, this link gives you a implementation in R language for the computation of the mean and variance of a truncated normal distribution :
http://www.r- |
51,233 | How to estimate time-per-product in a factory? | If you are interested in the amount of time it takes to complete an order, it seems that a duration analysis (aka survival or event history analysis) would be most appropriate. See the Wikipedia entry for an overview:
http://en.wikipedia.org/wiki/Survival_analysis
This introduction, which covers issues such as censorin... | How to estimate time-per-product in a factory? | If you are interested in the amount of time it takes to complete an order, it seems that a duration analysis (aka survival or event history analysis) would be most appropriate. See the Wikipedia entry | How to estimate time-per-product in a factory?
If you are interested in the amount of time it takes to complete an order, it seems that a duration analysis (aka survival or event history analysis) would be most appropriate. See the Wikipedia entry for an overview:
http://en.wikipedia.org/wiki/Survival_analysis
This int... | How to estimate time-per-product in a factory?
If you are interested in the amount of time it takes to complete an order, it seems that a duration analysis (aka survival or event history analysis) would be most appropriate. See the Wikipedia entry |
51,234 | Inverse logistic regression vs. repeated-measures vs. latent class? | My first thought would be to regress education (using a proportional odds model or whatever is appropriate for your education variable) on person-level variables and a few simple transportation choice aggregates. The main variable that comes to mind is the proportion of train vs. bus rides (%train), but if you only hav... | Inverse logistic regression vs. repeated-measures vs. latent class? | My first thought would be to regress education (using a proportional odds model or whatever is appropriate for your education variable) on person-level variables and a few simple transportation choice | Inverse logistic regression vs. repeated-measures vs. latent class?
My first thought would be to regress education (using a proportional odds model or whatever is appropriate for your education variable) on person-level variables and a few simple transportation choice aggregates. The main variable that comes to mind is... | Inverse logistic regression vs. repeated-measures vs. latent class?
My first thought would be to regress education (using a proportional odds model or whatever is appropriate for your education variable) on person-level variables and a few simple transportation choice |
51,235 | Properties of Battacharyya distance vs Kullback-Leibler divergence | First properties are explained competently here and
there.
Which one is better suited to a given purpose will depend on said given purpose so you might think about rephrasing this part of your question. | Properties of Battacharyya distance vs Kullback-Leibler divergence | First properties are explained competently here and
there.
Which one is better suited to a given purpose will depend on said given purpose so you might think about rephrasing this part of your quest | Properties of Battacharyya distance vs Kullback-Leibler divergence
First properties are explained competently here and
there.
Which one is better suited to a given purpose will depend on said given purpose so you might think about rephrasing this part of your question. | Properties of Battacharyya distance vs Kullback-Leibler divergence
First properties are explained competently here and
there.
Which one is better suited to a given purpose will depend on said given purpose so you might think about rephrasing this part of your quest |
51,236 | Quantile extrapolation? | If you are also interested in quantiles with $q>1-1/n$ there is no definitive answer. You need to supply more details, since for distributions with heavy tails the estimation of such quantiles involves quite complicated mathematics. Try google search for tail index estimation and you will get plethora of links. | Quantile extrapolation? | If you are also interested in quantiles with $q>1-1/n$ there is no definitive answer. You need to supply more details, since for distributions with heavy tails the estimation of such quantiles involve | Quantile extrapolation?
If you are also interested in quantiles with $q>1-1/n$ there is no definitive answer. You need to supply more details, since for distributions with heavy tails the estimation of such quantiles involves quite complicated mathematics. Try google search for tail index estimation and you will get pl... | Quantile extrapolation?
If you are also interested in quantiles with $q>1-1/n$ there is no definitive answer. You need to supply more details, since for distributions with heavy tails the estimation of such quantiles involve |
51,237 | Is there a bias correction for effect size in a data mining context? | This answer may be way, way off base as I don't understand the medical context of your question and the nature of the medical test results you allude to, but it might be possible to estimate data mining bias by some sort of Monte Carlo permutation of your results. The type of approach I'm thinking of is taken from a bo... | Is there a bias correction for effect size in a data mining context? | This answer may be way, way off base as I don't understand the medical context of your question and the nature of the medical test results you allude to, but it might be possible to estimate data mini | Is there a bias correction for effect size in a data mining context?
This answer may be way, way off base as I don't understand the medical context of your question and the nature of the medical test results you allude to, but it might be possible to estimate data mining bias by some sort of Monte Carlo permutation of ... | Is there a bias correction for effect size in a data mining context?
This answer may be way, way off base as I don't understand the medical context of your question and the nature of the medical test results you allude to, but it might be possible to estimate data mini |
51,238 | Is there a bias correction for effect size in a data mining context? | Ok, duh, one approach would be to use the James-Stein shrinkage. This will not, I believe, unbias the estimates, but will reduce the mean squared error. | Is there a bias correction for effect size in a data mining context? | Ok, duh, one approach would be to use the James-Stein shrinkage. This will not, I believe, unbias the estimates, but will reduce the mean squared error. | Is there a bias correction for effect size in a data mining context?
Ok, duh, one approach would be to use the James-Stein shrinkage. This will not, I believe, unbias the estimates, but will reduce the mean squared error. | Is there a bias correction for effect size in a data mining context?
Ok, duh, one approach would be to use the James-Stein shrinkage. This will not, I believe, unbias the estimates, but will reduce the mean squared error. |
51,239 | How should I objectively test my program results? | You can count the recognition of a chorus track as a 'Success' and the lack of recognition as a 'Failure'. Thus, you have the following data:
Method 1: Proportion of success (say, $p_1$) = $\frac{40}{50}$
Method 2: Proportion of success (say, $p_2$) = $\frac{21}{50}$
It seems that method 2 fails completely for 20 mus... | How should I objectively test my program results? | You can count the recognition of a chorus track as a 'Success' and the lack of recognition as a 'Failure'. Thus, you have the following data:
Method 1: Proportion of success (say, $p_1$) = $\frac{40} | How should I objectively test my program results?
You can count the recognition of a chorus track as a 'Success' and the lack of recognition as a 'Failure'. Thus, you have the following data:
Method 1: Proportion of success (say, $p_1$) = $\frac{40}{50}$
Method 2: Proportion of success (say, $p_2$) = $\frac{21}{50}$
... | How should I objectively test my program results?
You can count the recognition of a chorus track as a 'Success' and the lack of recognition as a 'Failure'. Thus, you have the following data:
Method 1: Proportion of success (say, $p_1$) = $\frac{40} |
51,240 | Lumping in Markov process with absorbing states | If the transition matrix was constant, then your two approaches would yield the same results. So this question is of interest in the non-constant case.
The inf-time redistribution of state 4 into state 2 and 3 is inappropriate. Consider that from time $1$ to time $T$ your matrix was $1 \rightarrow 1$ with probability $... | Lumping in Markov process with absorbing states | If the transition matrix was constant, then your two approaches would yield the same results. So this question is of interest in the non-constant case.
The inf-time redistribution of state 4 into stat | Lumping in Markov process with absorbing states
If the transition matrix was constant, then your two approaches would yield the same results. So this question is of interest in the non-constant case.
The inf-time redistribution of state 4 into state 2 and 3 is inappropriate. Consider that from time $1$ to time $T$ your... | Lumping in Markov process with absorbing states
If the transition matrix was constant, then your two approaches would yield the same results. So this question is of interest in the non-constant case.
The inf-time redistribution of state 4 into stat |
51,241 | Why would an instrumental variable have its strength measured by an F-statistic? | Here I expand somewhat more formally on the comment I made earlier, although the arguments here are not complete or fully rigorous (as you will see). This derivation is a more detailed version of the one given on page 207 of Mostly Harmless Econometrics (Angrist and Pischke) (thanks @dmitriy for the reference). The ref... | Why would an instrumental variable have its strength measured by an F-statistic? | Here I expand somewhat more formally on the comment I made earlier, although the arguments here are not complete or fully rigorous (as you will see). This derivation is a more detailed version of the | Why would an instrumental variable have its strength measured by an F-statistic?
Here I expand somewhat more formally on the comment I made earlier, although the arguments here are not complete or fully rigorous (as you will see). This derivation is a more detailed version of the one given on page 207 of Mostly Harmles... | Why would an instrumental variable have its strength measured by an F-statistic?
Here I expand somewhat more formally on the comment I made earlier, although the arguments here are not complete or fully rigorous (as you will see). This derivation is a more detailed version of the |
51,242 | Definition and Interpretation of Likelihood for non-PhD's | Your interpretations 1 and 2 are both wrong.
Bayesians knew all along you have to multiply the likelihood by a prior to get a posterior probability distribution. The problem is there is no universally agreed upon prior for any given data analysis, the differences are not even proportional to each other.
For frequenti... | Definition and Interpretation of Likelihood for non-PhD's | Your interpretations 1 and 2 are both wrong.
Bayesians knew all along you have to multiply the likelihood by a prior to get a posterior probability distribution. The problem is there is no universall | Definition and Interpretation of Likelihood for non-PhD's
Your interpretations 1 and 2 are both wrong.
Bayesians knew all along you have to multiply the likelihood by a prior to get a posterior probability distribution. The problem is there is no universally agreed upon prior for any given data analysis, the differenc... | Definition and Interpretation of Likelihood for non-PhD's
Your interpretations 1 and 2 are both wrong.
Bayesians knew all along you have to multiply the likelihood by a prior to get a posterior probability distribution. The problem is there is no universall |
51,243 | Definition and Interpretation of Likelihood for non-PhD's | The likelihood does give us what can often be equated with 'plausibility', but it is important to say that it is the relative plausibility according to the statistical model. And it is probably useful to note that you are, in effect, using likelihood as a definition of (statistical?) plausibility. That is, in my opinio... | Definition and Interpretation of Likelihood for non-PhD's | The likelihood does give us what can often be equated with 'plausibility', but it is important to say that it is the relative plausibility according to the statistical model. And it is probably useful | Definition and Interpretation of Likelihood for non-PhD's
The likelihood does give us what can often be equated with 'plausibility', but it is important to say that it is the relative plausibility according to the statistical model. And it is probably useful to note that you are, in effect, using likelihood as a defini... | Definition and Interpretation of Likelihood for non-PhD's
The likelihood does give us what can often be equated with 'plausibility', but it is important to say that it is the relative plausibility according to the statistical model. And it is probably useful |
51,244 | Why typically minimizing a cost instead of maximizing a reward? | Minimising $f(x)$ is entirely equivalent to maximising $-f(x)$, in every aspect: result, numerical precision, computational complexity... everything.
Historically, the convention might have been established because of the "least squares" in linear regression (but don't take my word for it).
If it were the other way rou... | Why typically minimizing a cost instead of maximizing a reward? | Minimising $f(x)$ is entirely equivalent to maximising $-f(x)$, in every aspect: result, numerical precision, computational complexity... everything.
Historically, the convention might have been estab | Why typically minimizing a cost instead of maximizing a reward?
Minimising $f(x)$ is entirely equivalent to maximising $-f(x)$, in every aspect: result, numerical precision, computational complexity... everything.
Historically, the convention might have been established because of the "least squares" in linear regressi... | Why typically minimizing a cost instead of maximizing a reward?
Minimising $f(x)$ is entirely equivalent to maximising $-f(x)$, in every aspect: result, numerical precision, computational complexity... everything.
Historically, the convention might have been estab |
51,245 | Why typically minimizing a cost instead of maximizing a reward? | You tagged this question with the tag "Maximum Likelihood". In maximum likelihood estimation you explicitly maximize an objective function (namely the likelihood).
It just so happens that for an observation that we assume to be drawn from a Gaussian random variable, the likelihood function usually takes a nice form aft... | Why typically minimizing a cost instead of maximizing a reward? | You tagged this question with the tag "Maximum Likelihood". In maximum likelihood estimation you explicitly maximize an objective function (namely the likelihood).
It just so happens that for an obser | Why typically minimizing a cost instead of maximizing a reward?
You tagged this question with the tag "Maximum Likelihood". In maximum likelihood estimation you explicitly maximize an objective function (namely the likelihood).
It just so happens that for an observation that we assume to be drawn from a Gaussian random... | Why typically minimizing a cost instead of maximizing a reward?
You tagged this question with the tag "Maximum Likelihood". In maximum likelihood estimation you explicitly maximize an objective function (namely the likelihood).
It just so happens that for an obser |
51,246 | Why typically minimizing a cost instead of maximizing a reward? | It's my understanding that the only reason for this distinction is that in numerical analysis, it's the standard to talk about convex optimization rather than concave optimization, even though they are really the same procedures. For example, if you do a google scholar search for "concave optimization", you get about 3... | Why typically minimizing a cost instead of maximizing a reward? | It's my understanding that the only reason for this distinction is that in numerical analysis, it's the standard to talk about convex optimization rather than concave optimization, even though they ar | Why typically minimizing a cost instead of maximizing a reward?
It's my understanding that the only reason for this distinction is that in numerical analysis, it's the standard to talk about convex optimization rather than concave optimization, even though they are really the same procedures. For example, if you do a g... | Why typically minimizing a cost instead of maximizing a reward?
It's my understanding that the only reason for this distinction is that in numerical analysis, it's the standard to talk about convex optimization rather than concave optimization, even though they ar |
51,247 | Why typically minimizing a cost instead of maximizing a reward? | History.
A lot of this connects back to estimation in statistics.
For example Gauss. He wanted to estimate the position of an asteroid that was obscured by the sun. He had the idea to minimize the squared error and got much better predictions than his colleagues. When estimating the position of an asteroid, what would ... | Why typically minimizing a cost instead of maximizing a reward? | History.
A lot of this connects back to estimation in statistics.
For example Gauss. He wanted to estimate the position of an asteroid that was obscured by the sun. He had the idea to minimize the squ | Why typically minimizing a cost instead of maximizing a reward?
History.
A lot of this connects back to estimation in statistics.
For example Gauss. He wanted to estimate the position of an asteroid that was obscured by the sun. He had the idea to minimize the squared error and got much better predictions than his coll... | Why typically minimizing a cost instead of maximizing a reward?
History.
A lot of this connects back to estimation in statistics.
For example Gauss. He wanted to estimate the position of an asteroid that was obscured by the sun. He had the idea to minimize the squ |
51,248 | Why typically minimizing a cost instead of maximizing a reward? | I suspect it may also be because quite a lot of optimisation algorithms are developed by people working on Operations Research who I think have historically posed problems in terms of minimisation of losses. We minimise because it what the best software supports. | Why typically minimizing a cost instead of maximizing a reward? | I suspect it may also be because quite a lot of optimisation algorithms are developed by people working on Operations Research who I think have historically posed problems in terms of minimisation of | Why typically minimizing a cost instead of maximizing a reward?
I suspect it may also be because quite a lot of optimisation algorithms are developed by people working on Operations Research who I think have historically posed problems in terms of minimisation of losses. We minimise because it what the best software s... | Why typically minimizing a cost instead of maximizing a reward?
I suspect it may also be because quite a lot of optimisation algorithms are developed by people working on Operations Research who I think have historically posed problems in terms of minimisation of |
51,249 | Why typically minimizing a cost instead of maximizing a reward? | You can just as well maximize a function that is equal to -1 times your cost function. It just happens that it's usually more natural to define a function that increases in value the farther from the optimum we get than the reverse, and for that reason we usually try to minimize a function rather than maximize a functi... | Why typically minimizing a cost instead of maximizing a reward? | You can just as well maximize a function that is equal to -1 times your cost function. It just happens that it's usually more natural to define a function that increases in value the farther from the | Why typically minimizing a cost instead of maximizing a reward?
You can just as well maximize a function that is equal to -1 times your cost function. It just happens that it's usually more natural to define a function that increases in value the farther from the optimum we get than the reverse, and for that reason we ... | Why typically minimizing a cost instead of maximizing a reward?
You can just as well maximize a function that is equal to -1 times your cost function. It just happens that it's usually more natural to define a function that increases in value the farther from the |
51,250 | Distribution that doesn't belong to any maximum domain of attraction? | Does there exist any non-degenerate probability distribution function $F$ such that if $X_1,X_2,\dots \overset{\text{iid}}{\sim} F$, then there do not exist any sequences $(a_n) \subset \mathbb R_{>0}$, $(b_n) \subset \mathbb R$ such that
$$
\frac{\max\{ X_1, \dots, X_n\} - b_n}{a_n}
$$
converges in distribution to a n... | Distribution that doesn't belong to any maximum domain of attraction? | Does there exist any non-degenerate probability distribution function $F$ such that if $X_1,X_2,\dots \overset{\text{iid}}{\sim} F$, then there do not exist any sequences $(a_n) \subset \mathbb R_{>0} | Distribution that doesn't belong to any maximum domain of attraction?
Does there exist any non-degenerate probability distribution function $F$ such that if $X_1,X_2,\dots \overset{\text{iid}}{\sim} F$, then there do not exist any sequences $(a_n) \subset \mathbb R_{>0}$, $(b_n) \subset \mathbb R$ such that
$$
\frac{\m... | Distribution that doesn't belong to any maximum domain of attraction?
Does there exist any non-degenerate probability distribution function $F$ such that if $X_1,X_2,\dots \overset{\text{iid}}{\sim} F$, then there do not exist any sequences $(a_n) \subset \mathbb R_{>0} |
51,251 | How do we derive the conditional mode as the solution to linear regression, for uniform cost function? | I got the answer from the paper, Is the mode elicitable relative to unimodal
distributions?.
If we consider the cost function, $C(x,y)=\mathrm{1}_{x\ne y}$, the minimization corresponding to mode is $\beta = \min \sum_i \mathrm{1}_{y_i\ne \beta}$. The minimum is obviously attained at the mode, i.e., $\beta = \text{mode... | How do we derive the conditional mode as the solution to linear regression, for uniform cost functio | I got the answer from the paper, Is the mode elicitable relative to unimodal
distributions?.
If we consider the cost function, $C(x,y)=\mathrm{1}_{x\ne y}$, the minimization corresponding to mode is $ | How do we derive the conditional mode as the solution to linear regression, for uniform cost function?
I got the answer from the paper, Is the mode elicitable relative to unimodal
distributions?.
If we consider the cost function, $C(x,y)=\mathrm{1}_{x\ne y}$, the minimization corresponding to mode is $\beta = \min \sum... | How do we derive the conditional mode as the solution to linear regression, for uniform cost functio
I got the answer from the paper, Is the mode elicitable relative to unimodal
distributions?.
If we consider the cost function, $C(x,y)=\mathrm{1}_{x\ne y}$, the minimization corresponding to mode is $ |
51,252 | Expectation of a function of a random variable from CDF | When $F$ is the CDF of a random variable $X$ and $g$ is a (measurable) function, the expectation of $g(X)$ can be found as a Riemann-Stieltjes integral
$$\mathbb{E}(g(X)) = \int_{-\infty}^\infty g(x) dF(x).$$
This expresses the Law of the Unconscious Statistician.
If $g$ is also differentiable, write $dF = -d(1-F)$ and... | Expectation of a function of a random variable from CDF | When $F$ is the CDF of a random variable $X$ and $g$ is a (measurable) function, the expectation of $g(X)$ can be found as a Riemann-Stieltjes integral
$$\mathbb{E}(g(X)) = \int_{-\infty}^\infty g(x) | Expectation of a function of a random variable from CDF
When $F$ is the CDF of a random variable $X$ and $g$ is a (measurable) function, the expectation of $g(X)$ can be found as a Riemann-Stieltjes integral
$$\mathbb{E}(g(X)) = \int_{-\infty}^\infty g(x) dF(x).$$
This expresses the Law of the Unconscious Statistician.... | Expectation of a function of a random variable from CDF
When $F$ is the CDF of a random variable $X$ and $g$ is a (measurable) function, the expectation of $g(X)$ can be found as a Riemann-Stieltjes integral
$$\mathbb{E}(g(X)) = \int_{-\infty}^\infty g(x) |
51,253 | Noise in regression problems and ways to reduce it | As stated by Dr. Kilian Weinberger, that you mentioned in your question, you can never beat this error.
The optimal classifier gives you the mean of the distribution of all the data P, which you can never get. If you want to detect a car, for example, P has to contain all pictures of cars ever exists.
But if you do fin... | Noise in regression problems and ways to reduce it | As stated by Dr. Kilian Weinberger, that you mentioned in your question, you can never beat this error.
The optimal classifier gives you the mean of the distribution of all the data P, which you can n | Noise in regression problems and ways to reduce it
As stated by Dr. Kilian Weinberger, that you mentioned in your question, you can never beat this error.
The optimal classifier gives you the mean of the distribution of all the data P, which you can never get. If you want to detect a car, for example, P has to contain ... | Noise in regression problems and ways to reduce it
As stated by Dr. Kilian Weinberger, that you mentioned in your question, you can never beat this error.
The optimal classifier gives you the mean of the distribution of all the data P, which you can n |
51,254 | Noise in regression problems and ways to reduce it | After some googling I found a great blogpost, whose author (A. Muehlemann, PHD from Oxford) seems to understand noise in the same way as me. I think that his explanation will give your better understanding of my original post.
His conclusion is the following: most of the techniques that reduce bias will also reduce noi... | Noise in regression problems and ways to reduce it | After some googling I found a great blogpost, whose author (A. Muehlemann, PHD from Oxford) seems to understand noise in the same way as me. I think that his explanation will give your better understa | Noise in regression problems and ways to reduce it
After some googling I found a great blogpost, whose author (A. Muehlemann, PHD from Oxford) seems to understand noise in the same way as me. I think that his explanation will give your better understanding of my original post.
His conclusion is the following: most of t... | Noise in regression problems and ways to reduce it
After some googling I found a great blogpost, whose author (A. Muehlemann, PHD from Oxford) seems to understand noise in the same way as me. I think that his explanation will give your better understa |
51,255 | Causal tree v. causal forest - when to use which for HTE? | As it stands at the moment in my mind, a causal forest is built using a combination of causal trees, my bare understanding is that when estimating for a group or cluster average treatment effects given a treatment assignment condition then a causal forest is the best choice, whereas if estimating treatment effect heter... | Causal tree v. causal forest - when to use which for HTE? | As it stands at the moment in my mind, a causal forest is built using a combination of causal trees, my bare understanding is that when estimating for a group or cluster average treatment effects give | Causal tree v. causal forest - when to use which for HTE?
As it stands at the moment in my mind, a causal forest is built using a combination of causal trees, my bare understanding is that when estimating for a group or cluster average treatment effects given a treatment assignment condition then a causal forest is the... | Causal tree v. causal forest - when to use which for HTE?
As it stands at the moment in my mind, a causal forest is built using a combination of causal trees, my bare understanding is that when estimating for a group or cluster average treatment effects give |
51,256 | Causal tree v. causal forest - when to use which for HTE? | As usual, the short answer is: it depends.
From a methodological point of view, a causal tree estimates the CATE function $E \left[ Y (1) - Y(0) | X \right]$ (i.e., the treatment effects conditional on the covariates) by constructing a multi-variate step function. This means that you would be given groups of units and,... | Causal tree v. causal forest - when to use which for HTE? | As usual, the short answer is: it depends.
From a methodological point of view, a causal tree estimates the CATE function $E \left[ Y (1) - Y(0) | X \right]$ (i.e., the treatment effects conditional o | Causal tree v. causal forest - when to use which for HTE?
As usual, the short answer is: it depends.
From a methodological point of view, a causal tree estimates the CATE function $E \left[ Y (1) - Y(0) | X \right]$ (i.e., the treatment effects conditional on the covariates) by constructing a multi-variate step functio... | Causal tree v. causal forest - when to use which for HTE?
As usual, the short answer is: it depends.
From a methodological point of view, a causal tree estimates the CATE function $E \left[ Y (1) - Y(0) | X \right]$ (i.e., the treatment effects conditional o |
51,257 | XGBOOST objective function derivation algebra | The quick answers to your question are:
You are absolutely right: it is not generally valid to swap the order of summation when the interior sum is squared. It's not even true when $n=1$ and $m=2$:
$$
\sum_{i=1}^{1} \left(\sum_{j=1}^{2} x_{ij} \right)^2 = (x_{11} + x_{12})^2 = x_{11}^2 + 2x_{11}x_{12} + x_{12}^2
$$
$... | XGBOOST objective function derivation algebra | The quick answers to your question are:
You are absolutely right: it is not generally valid to swap the order of summation when the interior sum is squared. It's not even true when $n=1$ and $m=2$:
| XGBOOST objective function derivation algebra
The quick answers to your question are:
You are absolutely right: it is not generally valid to swap the order of summation when the interior sum is squared. It's not even true when $n=1$ and $m=2$:
$$
\sum_{i=1}^{1} \left(\sum_{j=1}^{2} x_{ij} \right)^2 = (x_{11} + x_{12}... | XGBOOST objective function derivation algebra
The quick answers to your question are:
You are absolutely right: it is not generally valid to swap the order of summation when the interior sum is squared. It's not even true when $n=1$ and $m=2$:
|
51,258 | Once you have used LASSO to generate regression coefficients, is there another step that gives you information about the model? | You can do repeated cross validation and if it is logistic get the ROC-AUC or perhaps the Brier score. If it is linear regression you can use R^2.
For variable importance you can use the coefficient size. | Once you have used LASSO to generate regression coefficients, is there another step that gives you i | You can do repeated cross validation and if it is logistic get the ROC-AUC or perhaps the Brier score. If it is linear regression you can use R^2.
For variable importance you can use the coefficient s | Once you have used LASSO to generate regression coefficients, is there another step that gives you information about the model?
You can do repeated cross validation and if it is logistic get the ROC-AUC or perhaps the Brier score. If it is linear regression you can use R^2.
For variable importance you can use the coeff... | Once you have used LASSO to generate regression coefficients, is there another step that gives you i
You can do repeated cross validation and if it is logistic get the ROC-AUC or perhaps the Brier score. If it is linear regression you can use R^2.
For variable importance you can use the coefficient s |
51,259 | $R^2$ and adjusted $R^2$ in presence of overlapping observations | I will refer to population, vanilla, adjusted as (1), (2), (3), respectively.
Q1)
As (1) is for population while (2), (3) are its sample analogue, the same will hold for LRVar. For the population you will use $k=\infty$ and some integer for the sample.
Q2)
I haven't done the calculation, but using LRVar will make a dif... | $R^2$ and adjusted $R^2$ in presence of overlapping observations | I will refer to population, vanilla, adjusted as (1), (2), (3), respectively.
Q1)
As (1) is for population while (2), (3) are its sample analogue, the same will hold for LRVar. For the population you | $R^2$ and adjusted $R^2$ in presence of overlapping observations
I will refer to population, vanilla, adjusted as (1), (2), (3), respectively.
Q1)
As (1) is for population while (2), (3) are its sample analogue, the same will hold for LRVar. For the population you will use $k=\infty$ and some integer for the sample.
Q2... | $R^2$ and adjusted $R^2$ in presence of overlapping observations
I will refer to population, vanilla, adjusted as (1), (2), (3), respectively.
Q1)
As (1) is for population while (2), (3) are its sample analogue, the same will hold for LRVar. For the population you |
51,260 | Correlation between logrank (log-rank) test statistics with common control | The correlation of 0.5 is an assumption, it is not derived. I will not accept this as an answer to my question because I do not have a source. This was based on a conversation with an expert, for whatever that's worth.
The assumption is made when there are equal sample sizes in the experimental arm and the control ar... | Correlation between logrank (log-rank) test statistics with common control | The correlation of 0.5 is an assumption, it is not derived. I will not accept this as an answer to my question because I do not have a source. This was based on a conversation with an expert, for what | Correlation between logrank (log-rank) test statistics with common control
The correlation of 0.5 is an assumption, it is not derived. I will not accept this as an answer to my question because I do not have a source. This was based on a conversation with an expert, for whatever that's worth.
The assumption is made w... | Correlation between logrank (log-rank) test statistics with common control
The correlation of 0.5 is an assumption, it is not derived. I will not accept this as an answer to my question because I do not have a source. This was based on a conversation with an expert, for what |
51,261 | How to win this dice probability game? | This is how I look at it, but I'll admit I may have misunderstood the game!
Assuming you have a current banked score of B, the expected return for any given round is:
$$E(return)=\frac{1}{6}(-B)+\frac{1}{6}(1+3+4+5+6)$$
$$E(return)=\frac{1}{6}(19-B)$$
So once you have a bank of 19 points, it is better to get out than t... | How to win this dice probability game? | This is how I look at it, but I'll admit I may have misunderstood the game!
Assuming you have a current banked score of B, the expected return for any given round is:
$$E(return)=\frac{1}{6}(-B)+\frac | How to win this dice probability game?
This is how I look at it, but I'll admit I may have misunderstood the game!
Assuming you have a current banked score of B, the expected return for any given round is:
$$E(return)=\frac{1}{6}(-B)+\frac{1}{6}(1+3+4+5+6)$$
$$E(return)=\frac{1}{6}(19-B)$$
So once you have a bank of 19... | How to win this dice probability game?
This is how I look at it, but I'll admit I may have misunderstood the game!
Assuming you have a current banked score of B, the expected return for any given round is:
$$E(return)=\frac{1}{6}(-B)+\frac |
51,262 | How to win this dice probability game? | The following results are from my simulation in R.
Assuming there are 6 rounds in total, the first two throws are always performed in each round, and after each round (the first 2) everybody resets.
I will simulate the game for only one person, since we assume the players play independently. I will test which strategy ... | How to win this dice probability game? | The following results are from my simulation in R.
Assuming there are 6 rounds in total, the first two throws are always performed in each round, and after each round (the first 2) everybody resets.
I | How to win this dice probability game?
The following results are from my simulation in R.
Assuming there are 6 rounds in total, the first two throws are always performed in each round, and after each round (the first 2) everybody resets.
I will simulate the game for only one person, since we assume the players play ind... | How to win this dice probability game?
The following results are from my simulation in R.
Assuming there are 6 rounds in total, the first two throws are always performed in each round, and after each round (the first 2) everybody resets.
I |
51,263 | Stop-gradient operator in vector-quantized variational autoencoder | I have been looking for the same question. I have finally deduced the following. I think it is a learning factor that balance the importance between terms (codebook loss and commitment loss).
If the Beta factor is smaller than 1, it means that the encoder is updated more faster than the codebook.
That is interesting fo... | Stop-gradient operator in vector-quantized variational autoencoder | I have been looking for the same question. I have finally deduced the following. I think it is a learning factor that balance the importance between terms (codebook loss and commitment loss).
If the B | Stop-gradient operator in vector-quantized variational autoencoder
I have been looking for the same question. I have finally deduced the following. I think it is a learning factor that balance the importance between terms (codebook loss and commitment loss).
If the Beta factor is smaller than 1, it means that the encod... | Stop-gradient operator in vector-quantized variational autoencoder
I have been looking for the same question. I have finally deduced the following. I think it is a learning factor that balance the importance between terms (codebook loss and commitment loss).
If the B |
51,264 | Stop-gradient operator in vector-quantized variational autoencoder | If you take gradients, the two formulas you mentioned are the same.
However, if we write in the form of the first formula, fix $z_e$ (zero gradient), let $e$ approach $z_e$ and inversely.
I think it would be easier for training. | Stop-gradient operator in vector-quantized variational autoencoder | If you take gradients, the two formulas you mentioned are the same.
However, if we write in the form of the first formula, fix $z_e$ (zero gradient), let $e$ approach $z_e$ and inversely.
I think it | Stop-gradient operator in vector-quantized variational autoencoder
If you take gradients, the two formulas you mentioned are the same.
However, if we write in the form of the first formula, fix $z_e$ (zero gradient), let $e$ approach $z_e$ and inversely.
I think it would be easier for training. | Stop-gradient operator in vector-quantized variational autoencoder
If you take gradients, the two formulas you mentioned are the same.
However, if we write in the form of the first formula, fix $z_e$ (zero gradient), let $e$ approach $z_e$ and inversely.
I think it |
51,265 | Calculate percentiles of angles/bearings in Python | If some angular region has very few crimes, you can start from an angle there.
E.g. Consider crime in Chicago, and its angle relative to the center of Chicago’s street grid at Madison & State.
The angles with the fewest crimes are due east of the center, where there is little land.
The bearings in the original data pr... | Calculate percentiles of angles/bearings in Python | If some angular region has very few crimes, you can start from an angle there.
E.g. Consider crime in Chicago, and its angle relative to the center of Chicago’s street grid at Madison & State.
The an | Calculate percentiles of angles/bearings in Python
If some angular region has very few crimes, you can start from an angle there.
E.g. Consider crime in Chicago, and its angle relative to the center of Chicago’s street grid at Madison & State.
The angles with the fewest crimes are due east of the center, where there i... | Calculate percentiles of angles/bearings in Python
If some angular region has very few crimes, you can start from an angle there.
E.g. Consider crime in Chicago, and its angle relative to the center of Chicago’s street grid at Madison & State.
The an |
51,266 | Predictive Accuracy of a Survival Model using Concordance | The best choice would be something similar to the second (bootstrap) option, but taken an additional step to get an estimate closer to how the model will perform when applied to the underlying population.
Bootstrapping doesn't just give you the ability to estimate the standard error of your performance metric. It also ... | Predictive Accuracy of a Survival Model using Concordance | The best choice would be something similar to the second (bootstrap) option, but taken an additional step to get an estimate closer to how the model will perform when applied to the underlying populat | Predictive Accuracy of a Survival Model using Concordance
The best choice would be something similar to the second (bootstrap) option, but taken an additional step to get an estimate closer to how the model will perform when applied to the underlying population.
Bootstrapping doesn't just give you the ability to estima... | Predictive Accuracy of a Survival Model using Concordance
The best choice would be something similar to the second (bootstrap) option, but taken an additional step to get an estimate closer to how the model will perform when applied to the underlying populat |
51,267 | Machine learning models for regression on small data sets | Small datasets and few features are a domain where traditional statistical models tend to do very well, because they offer the ability to actually interpret the importance of your features.
I'm assuming by "simple regression" you mean predicting a real-valued, continuous variable y from your input variables. You menti... | Machine learning models for regression on small data sets | Small datasets and few features are a domain where traditional statistical models tend to do very well, because they offer the ability to actually interpret the importance of your features.
I'm assum | Machine learning models for regression on small data sets
Small datasets and few features are a domain where traditional statistical models tend to do very well, because they offer the ability to actually interpret the importance of your features.
I'm assuming by "simple regression" you mean predicting a real-valued, ... | Machine learning models for regression on small data sets
Small datasets and few features are a domain where traditional statistical models tend to do very well, because they offer the ability to actually interpret the importance of your features.
I'm assum |
51,268 | Machine learning models for regression on small data sets | If you are considering linear models, and are concerned with overfitting, you can consider using linear regression with regularization ie. ridge regression or lasso or a combination("elastic net").
If you want to try out non-linear as well as interaction terms, you can try SVM regression with a polynomial kernel or an... | Machine learning models for regression on small data sets | If you are considering linear models, and are concerned with overfitting, you can consider using linear regression with regularization ie. ridge regression or lasso or a combination("elastic net").
I | Machine learning models for regression on small data sets
If you are considering linear models, and are concerned with overfitting, you can consider using linear regression with regularization ie. ridge regression or lasso or a combination("elastic net").
If you want to try out non-linear as well as interaction terms,... | Machine learning models for regression on small data sets
If you are considering linear models, and are concerned with overfitting, you can consider using linear regression with regularization ie. ridge regression or lasso or a combination("elastic net").
I |
51,269 | Machine learning models for regression on small data sets | The problem with daily data and only 250 days is that you could face seasonality issues that you can't really evaluate statistically, only by business knowledge.
But regardless of seasonality, 250 samples and 10 features are quiet enough in my opinion to build a predictive modeling.
The best way to do it is use boosted... | Machine learning models for regression on small data sets | The problem with daily data and only 250 days is that you could face seasonality issues that you can't really evaluate statistically, only by business knowledge.
But regardless of seasonality, 250 sam | Machine learning models for regression on small data sets
The problem with daily data and only 250 days is that you could face seasonality issues that you can't really evaluate statistically, only by business knowledge.
But regardless of seasonality, 250 samples and 10 features are quiet enough in my opinion to build a... | Machine learning models for regression on small data sets
The problem with daily data and only 250 days is that you could face seasonality issues that you can't really evaluate statistically, only by business knowledge.
But regardless of seasonality, 250 sam |
51,270 | Machine learning models for regression on small data sets | With such a small data set, I would consider a few options:
Neural network with some transfer learning if you can find a larger well-labeled data set to complement what you have
A semi-supervised approach if you can find a large source of unlabeled data to complement your data
Bayes net if you are able to reasonably h... | Machine learning models for regression on small data sets | With such a small data set, I would consider a few options:
Neural network with some transfer learning if you can find a larger well-labeled data set to complement what you have
A semi-supervised app | Machine learning models for regression on small data sets
With such a small data set, I would consider a few options:
Neural network with some transfer learning if you can find a larger well-labeled data set to complement what you have
A semi-supervised approach if you can find a large source of unlabeled data to comp... | Machine learning models for regression on small data sets
With such a small data set, I would consider a few options:
Neural network with some transfer learning if you can find a larger well-labeled data set to complement what you have
A semi-supervised app |
51,271 | Which constant to add when applying 'Box-Cox transformation' to negative values? [duplicate] | Determine the smallest number in your time series , say -10. for example . The constant you would need is then 10.0000000001 or larger in order to make all the adjusted values positive. It doesn't make make any difference as the reverse transformation needed to obtain forecasts will use the same adjustment factor.
Plea... | Which constant to add when applying 'Box-Cox transformation' to negative values? [duplicate] | Determine the smallest number in your time series , say -10. for example . The constant you would need is then 10.0000000001 or larger in order to make all the adjusted values positive. It doesn't mak | Which constant to add when applying 'Box-Cox transformation' to negative values? [duplicate]
Determine the smallest number in your time series , say -10. for example . The constant you would need is then 10.0000000001 or larger in order to make all the adjusted values positive. It doesn't make make any difference as th... | Which constant to add when applying 'Box-Cox transformation' to negative values? [duplicate]
Determine the smallest number in your time series , say -10. for example . The constant you would need is then 10.0000000001 or larger in order to make all the adjusted values positive. It doesn't mak |
51,272 | GAMM with multiple and crossed random effects | Specifying random effect terms in gamm4 is different to mgcv. The syntax I show is provided in this book.
Two random effect terms in gamm4 is:
random = ~(1|xr1 + 1|xr2)
If they are nested, it is:
random = ~(1|xr1/xr2) | GAMM with multiple and crossed random effects | Specifying random effect terms in gamm4 is different to mgcv. The syntax I show is provided in this book.
Two random effect terms in gamm4 is:
random = ~(1|xr1 + 1|xr2)
If they are nested, it is:
ran | GAMM with multiple and crossed random effects
Specifying random effect terms in gamm4 is different to mgcv. The syntax I show is provided in this book.
Two random effect terms in gamm4 is:
random = ~(1|xr1 + 1|xr2)
If they are nested, it is:
random = ~(1|xr1/xr2) | GAMM with multiple and crossed random effects
Specifying random effect terms in gamm4 is different to mgcv. The syntax I show is provided in this book.
Two random effect terms in gamm4 is:
random = ~(1|xr1 + 1|xr2)
If they are nested, it is:
ran |
51,273 | What is the difference between Dice loss vs Jaccard loss in semantic segmentation task? | Jaccard Index is basically the Intersection over Union (IoU). If you subtract Jaccard Index from 1, you will get the Jaccard Loss (or IoU loss). Similarly if you do the same on Dice Coef., you will get the Dice Loss. For a comparison of IoU (or Jaccard) and Dice, I recommend reading this article. | What is the difference between Dice loss vs Jaccard loss in semantic segmentation task? | Jaccard Index is basically the Intersection over Union (IoU). If you subtract Jaccard Index from 1, you will get the Jaccard Loss (or IoU loss). Similarly if you do the same on Dice Coef., you will ge | What is the difference between Dice loss vs Jaccard loss in semantic segmentation task?
Jaccard Index is basically the Intersection over Union (IoU). If you subtract Jaccard Index from 1, you will get the Jaccard Loss (or IoU loss). Similarly if you do the same on Dice Coef., you will get the Dice Loss. For a compariso... | What is the difference between Dice loss vs Jaccard loss in semantic segmentation task?
Jaccard Index is basically the Intersection over Union (IoU). If you subtract Jaccard Index from 1, you will get the Jaccard Loss (or IoU loss). Similarly if you do the same on Dice Coef., you will ge |
51,274 | Importance of regressors in time series data | I would always assess this using a holdout sample. Fit models with and without the predictor and see how much your forecasts improve.
I realize my recommendation makes most sense in the context of forecasting. If you are just looking for in-sample fit, you can do the same thing.
If you are indeed forecasting, it would ... | Importance of regressors in time series data | I would always assess this using a holdout sample. Fit models with and without the predictor and see how much your forecasts improve.
I realize my recommendation makes most sense in the context of for | Importance of regressors in time series data
I would always assess this using a holdout sample. Fit models with and without the predictor and see how much your forecasts improve.
I realize my recommendation makes most sense in the context of forecasting. If you are just looking for in-sample fit, you can do the same th... | Importance of regressors in time series data
I would always assess this using a holdout sample. Fit models with and without the predictor and see how much your forecasts improve.
I realize my recommendation makes most sense in the context of for |
51,275 | Proof that predictions are unbiased in in endogenous linear model | The answers are actually pretty straightforward. In general the predictions will not be unbiased, to see that just notice:
$$
E[y|X]= X\beta + E[\epsilon|X]
$$
Thus, if $E[\epsilon|X]$ is not linear function of $X$, the population linear regression will not recover the true expectation function $E[y|X]$. Instead, it wi... | Proof that predictions are unbiased in in endogenous linear model | The answers are actually pretty straightforward. In general the predictions will not be unbiased, to see that just notice:
$$
E[y|X]= X\beta + E[\epsilon|X]
$$
Thus, if $E[\epsilon|X]$ is not linear f | Proof that predictions are unbiased in in endogenous linear model
The answers are actually pretty straightforward. In general the predictions will not be unbiased, to see that just notice:
$$
E[y|X]= X\beta + E[\epsilon|X]
$$
Thus, if $E[\epsilon|X]$ is not linear function of $X$, the population linear regression will ... | Proof that predictions are unbiased in in endogenous linear model
The answers are actually pretty straightforward. In general the predictions will not be unbiased, to see that just notice:
$$
E[y|X]= X\beta + E[\epsilon|X]
$$
Thus, if $E[\epsilon|X]$ is not linear f |
51,276 | Proof that predictions are unbiased in in endogenous linear model | Claims 1 and 2 are actually both false. To show that they are false over a broad class of models in which $E[\epsilon|X] \neq 0$, it is enough to pick a single model or a narrow set of models from within that broad class of models, and to disprove the claims for the narrow set. I will follow this strategy in my answer.... | Proof that predictions are unbiased in in endogenous linear model | Claims 1 and 2 are actually both false. To show that they are false over a broad class of models in which $E[\epsilon|X] \neq 0$, it is enough to pick a single model or a narrow set of models from wit | Proof that predictions are unbiased in in endogenous linear model
Claims 1 and 2 are actually both false. To show that they are false over a broad class of models in which $E[\epsilon|X] \neq 0$, it is enough to pick a single model or a narrow set of models from within that broad class of models, and to disprove the cl... | Proof that predictions are unbiased in in endogenous linear model
Claims 1 and 2 are actually both false. To show that they are false over a broad class of models in which $E[\epsilon|X] \neq 0$, it is enough to pick a single model or a narrow set of models from wit |
51,277 | Detrending positive data, avoiding negative data | You need to re-scale your data on the real domain. If the log transform does not work, then try another transform. Then take differences, say. | Detrending positive data, avoiding negative data | You need to re-scale your data on the real domain. If the log transform does not work, then try another transform. Then take differences, say. | Detrending positive data, avoiding negative data
You need to re-scale your data on the real domain. If the log transform does not work, then try another transform. Then take differences, say. | Detrending positive data, avoiding negative data
You need to re-scale your data on the real domain. If the log transform does not work, then try another transform. Then take differences, say. |
51,278 | Covering the unit sphere with sparse vectors | After some thought, I think we can conclude that finding such a cover is impossible. Consider the vector of all $1$'s with appropriate scaling:
$$
v = \frac{1}{\sqrt{d}} \left(1 \; \dots \; 1\right)^\top \in \mathbb{S}^{d-1}
$$
and consider a $k$-sparse vector $\bar{v}$. Then
$$
\#\{i: (v - \bar{v})_i \neq 0\} \geq d -... | Covering the unit sphere with sparse vectors | After some thought, I think we can conclude that finding such a cover is impossible. Consider the vector of all $1$'s with appropriate scaling:
$$
v = \frac{1}{\sqrt{d}} \left(1 \; \dots \; 1\right)^\ | Covering the unit sphere with sparse vectors
After some thought, I think we can conclude that finding such a cover is impossible. Consider the vector of all $1$'s with appropriate scaling:
$$
v = \frac{1}{\sqrt{d}} \left(1 \; \dots \; 1\right)^\top \in \mathbb{S}^{d-1}
$$
and consider a $k$-sparse vector $\bar{v}$. The... | Covering the unit sphere with sparse vectors
After some thought, I think we can conclude that finding such a cover is impossible. Consider the vector of all $1$'s with appropriate scaling:
$$
v = \frac{1}{\sqrt{d}} \left(1 \; \dots \; 1\right)^\ |
51,279 | Test for comparing log likelihoods that include error terms | Taking this from the comment section to the answer part:
If you are doing Bayesian model comparison, then there is no way to include any uncertainties. The comparison will tell you, which model describes the data better.
But, as mentioned in the wikipedia article (https://en.wikipedia.org/wiki/Bayes_factor), this doesn... | Test for comparing log likelihoods that include error terms | Taking this from the comment section to the answer part:
If you are doing Bayesian model comparison, then there is no way to include any uncertainties. The comparison will tell you, which model descri | Test for comparing log likelihoods that include error terms
Taking this from the comment section to the answer part:
If you are doing Bayesian model comparison, then there is no way to include any uncertainties. The comparison will tell you, which model describes the data better.
But, as mentioned in the wikipedia arti... | Test for comparing log likelihoods that include error terms
Taking this from the comment section to the answer part:
If you are doing Bayesian model comparison, then there is no way to include any uncertainties. The comparison will tell you, which model descri |
51,280 | Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \right]$ | I've found approximations for both cases, i.e., independent and dependent cases.
Case (1) where $\textbf{h}$ and $\textbf{y}$ are independent.
$$\mathbb{E} \left[ \frac{\textbf{h}^{H}_{l} \textbf{y}_{k} \textbf{y}^{H} _{k} \textbf{h}_{l} }{ \| \textbf{y}_{k} \|^{4} } \right] = \frac{d_{l}[(M+1)(M-2)+4M+6]}{\zeta_{k... | Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h | I've found approximations for both cases, i.e., independent and dependent cases.
Case (1) where $\textbf{h}$ and $\textbf{y}$ are independent.
$$\mathbb{E} \left[ \frac{\textbf{h}^{H}_{l} \textbf{y}_ | Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h}}{ \| \textbf{y} \|^{4} } \right]$
I've found approximations for both cases, i.e., independent and dependent cases.
Case (1) where $\textbf{h}$ and $\textbf{y}$ are independent.
$$\mathbb{E} \left[ \frac{\textbf{h}^{H}... | Direct way of calculating $\mathbb{E} \left[ \frac{\textbf{h}^{H} \textbf{y}\textbf{y}^{H} \textbf{h
I've found approximations for both cases, i.e., independent and dependent cases.
Case (1) where $\textbf{h}$ and $\textbf{y}$ are independent.
$$\mathbb{E} \left[ \frac{\textbf{h}^{H}_{l} \textbf{y}_ |
51,281 | Combining cross-sectional data with panel data | Visually check the correlation between irrigation and the other variables for that year. If they are correlated, which I imagine they are (different locations probably have different irrigation patterns based on demographics, etc...maybe not though!) then no. If there seems to be little correlation and irrigation just ... | Combining cross-sectional data with panel data | Visually check the correlation between irrigation and the other variables for that year. If they are correlated, which I imagine they are (different locations probably have different irrigation patter | Combining cross-sectional data with panel data
Visually check the correlation between irrigation and the other variables for that year. If they are correlated, which I imagine they are (different locations probably have different irrigation patterns based on demographics, etc...maybe not though!) then no. If there seem... | Combining cross-sectional data with panel data
Visually check the correlation between irrigation and the other variables for that year. If they are correlated, which I imagine they are (different locations probably have different irrigation patter |
51,282 | Multiple imputation: What has to be reported in a paper | In general, it is appropriate to report the results of the planned primary analysis, possibly also all or some of the foreseen sensitivity/supportive analyses (depending on space considerations) and potentially additional analyses requested e.g. by peer reviewers (e.g. in case of a pre-specified complete case analysis ... | Multiple imputation: What has to be reported in a paper | In general, it is appropriate to report the results of the planned primary analysis, possibly also all or some of the foreseen sensitivity/supportive analyses (depending on space considerations) and p | Multiple imputation: What has to be reported in a paper
In general, it is appropriate to report the results of the planned primary analysis, possibly also all or some of the foreseen sensitivity/supportive analyses (depending on space considerations) and potentially additional analyses requested e.g. by peer reviewers ... | Multiple imputation: What has to be reported in a paper
In general, it is appropriate to report the results of the planned primary analysis, possibly also all or some of the foreseen sensitivity/supportive analyses (depending on space considerations) and p |
51,283 | Linear Constraint in SVM optimization | Note that generally, the loss$(w,x_i,y_i)$ term you have written would actually be the $c_i$ value from the constraint, in both versions.
The dual-formulation constraint $\alpha^T y = 0$ arises from the bias term $b$ which offsets the solution plane from the origin. The most common alternative to using the bias term is... | Linear Constraint in SVM optimization | Note that generally, the loss$(w,x_i,y_i)$ term you have written would actually be the $c_i$ value from the constraint, in both versions.
The dual-formulation constraint $\alpha^T y = 0$ arises from t | Linear Constraint in SVM optimization
Note that generally, the loss$(w,x_i,y_i)$ term you have written would actually be the $c_i$ value from the constraint, in both versions.
The dual-formulation constraint $\alpha^T y = 0$ arises from the bias term $b$ which offsets the solution plane from the origin. The most common... | Linear Constraint in SVM optimization
Note that generally, the loss$(w,x_i,y_i)$ term you have written would actually be the $c_i$ value from the constraint, in both versions.
The dual-formulation constraint $\alpha^T y = 0$ arises from t |
51,284 | What type of model can be used to detect changes in periodic behavior? | If you know the original periodicity of the pulses, a simple approach would be to use any seasonal time series forecasting algorithm with this seasonal frequency. Fit the model to your data, holding out the last (say) 10 observations. Forecast, and calculate prediction intervals to a specified level for the holdout dat... | What type of model can be used to detect changes in periodic behavior? | If you know the original periodicity of the pulses, a simple approach would be to use any seasonal time series forecasting algorithm with this seasonal frequency. Fit the model to your data, holding o | What type of model can be used to detect changes in periodic behavior?
If you know the original periodicity of the pulses, a simple approach would be to use any seasonal time series forecasting algorithm with this seasonal frequency. Fit the model to your data, holding out the last (say) 10 observations. Forecast, and ... | What type of model can be used to detect changes in periodic behavior?
If you know the original periodicity of the pulses, a simple approach would be to use any seasonal time series forecasting algorithm with this seasonal frequency. Fit the model to your data, holding o |
51,285 | Why does collecting data until finding a significant result increase Type I error rate? | The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Best two out of three?
To understand this better, consider a simplified--but realistic--model of this sequential procedu... | Why does collecting data until finding a significant result increase Type I error rate? | The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Be | Why does collecting data until finding a significant result increase Type I error rate?
The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Best two out of three?
To unders... | Why does collecting data until finding a significant result increase Type I error rate?
The problem is that you're giving yourself too many chances to pass the test. It's just a fancy version of this dialog:
I'll flip you to see who pays for dinner.
OK, I call heads.
Rats, you won. Be |
51,286 | Why does collecting data until finding a significant result increase Type I error rate? | People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothesis, a p value is uniformly distributed between 0 and 1 and can bounce around quite a bit in that range.
I've simulate... | Why does collecting data until finding a significant result increase Type I error rate? | People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothes | Why does collecting data until finding a significant result increase Type I error rate?
People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothesis, a p value is uniformly distr... | Why does collecting data until finding a significant result increase Type I error rate?
People who are new to hypothesis testing tend to think that once a p value goes below .05, adding more participants will only decrease the p value further. But this isn't true. Under the null hypothes |
51,287 | Why does collecting data until finding a significant result increase Type I error rate? | This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + X_2 + \dots + X_t$ denote the value of the test statistic after $t$ observations have been collected and assume that th... | Why does collecting data until finding a significant result increase Type I error rate? | This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + | Why does collecting data until finding a significant result increase Type I error rate?
This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + X_2 + \dots + X_t$ denote the v... | Why does collecting data until finding a significant result increase Type I error rate?
This answer only concerns the probability of ultimately getting a "significant" result and the distribution of the time to this event under @whuber's model.
As in the model of @whuber, let $S(t)=X_1 + |
51,288 | Why does collecting data until finding a significant result increase Type I error rate? | It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to exist. The root cause of the problem is that p-values and type I errors use backwards-time backwards-information flow ... | Why does collecting data until finding a significant result increase Type I error rate? | It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to | Why does collecting data until finding a significant result increase Type I error rate?
It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to exist. The root cause of the p... | Why does collecting data until finding a significant result increase Type I error rate?
It needs to be said that the above discussion is for a frequentist world view for which multiplicity comes from the chances you give data to be more extreme, not from the chances you give an effect to |
51,289 | Why does collecting data until finding a significant result increase Type I error rate? | We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. If it does not, he collects another sample of size $n$, $x_2$, and rejects if the test rejects for the combined sample $(... | Why does collecting data until finding a significant result increase Type I error rate? | We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. I | Why does collecting data until finding a significant result increase Type I error rate?
We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. If it does not, he collects anoth... | Why does collecting data until finding a significant result increase Type I error rate?
We consider a researcher collecting a sample of size $n$, $x_1$, to test some hypothesis $\theta=\theta_0$. He rejects if a suitable test statistic $t$ exceeds its level-$\alpha$ critical value $c$. I |
51,290 | Trying to emulate linear regression using Keras [closed] | You seem to read data with Pandas and, probably, there is a mess with your input. You should definitely try generating it using numpy:
import numpy as np
X_train = np.linspace(0, 80, 100).reshape(-1, 1)
Y_train = 5 * X_train
For linear approximation single neuron is ok:
# define base mode
def baseline_model():
# ... | Trying to emulate linear regression using Keras [closed] | You seem to read data with Pandas and, probably, there is a mess with your input. You should definitely try generating it using numpy:
import numpy as np
X_train = np.linspace(0, 80, 100).reshape(-1, | Trying to emulate linear regression using Keras [closed]
You seem to read data with Pandas and, probably, there is a mess with your input. You should definitely try generating it using numpy:
import numpy as np
X_train = np.linspace(0, 80, 100).reshape(-1, 1)
Y_train = 5 * X_train
For linear approximation single neur... | Trying to emulate linear regression using Keras [closed]
You seem to read data with Pandas and, probably, there is a mess with your input. You should definitely try generating it using numpy:
import numpy as np
X_train = np.linspace(0, 80, 100).reshape(-1, |
51,291 | Probability theory books for self-study | I recommend Head First Statistics. The 'Head First' Series is of superior didactic quality and fun to read. It has a lot of exercises, and was one of the few books were I liked doing the exercises.
http://www.amazon.com/Head-First-Statistics-Dawn-Griffiths/dp/0596527586 | Probability theory books for self-study | I recommend Head First Statistics. The 'Head First' Series is of superior didactic quality and fun to read. It has a lot of exercises, and was one of the few books were I liked doing the exercises.
ht | Probability theory books for self-study
I recommend Head First Statistics. The 'Head First' Series is of superior didactic quality and fun to read. It has a lot of exercises, and was one of the few books were I liked doing the exercises.
http://www.amazon.com/Head-First-Statistics-Dawn-Griffiths/dp/0596527586 | Probability theory books for self-study
I recommend Head First Statistics. The 'Head First' Series is of superior didactic quality and fun to read. It has a lot of exercises, and was one of the few books were I liked doing the exercises.
ht |
51,292 | Probability theory books for self-study | I was looking for the same a week ago. I found from another post on stackexchange about this book Intuitive biostatistics: A Nonmathematical Guide to Statistical Thinking by Harvey Motulsky. I think the second part of the title is pretty lame. But generally I have/had no problems in understanding the math, but found no... | Probability theory books for self-study | I was looking for the same a week ago. I found from another post on stackexchange about this book Intuitive biostatistics: A Nonmathematical Guide to Statistical Thinking by Harvey Motulsky. I think t | Probability theory books for self-study
I was looking for the same a week ago. I found from another post on stackexchange about this book Intuitive biostatistics: A Nonmathematical Guide to Statistical Thinking by Harvey Motulsky. I think the second part of the title is pretty lame. But generally I have/had no problems... | Probability theory books for self-study
I was looking for the same a week ago. I found from another post on stackexchange about this book Intuitive biostatistics: A Nonmathematical Guide to Statistical Thinking by Harvey Motulsky. I think t |
51,293 | Probability theory books for self-study | Schaeffer's book from Duxbury press seems ok. Sheldon Ross' books are always awesome. Note, these are both books on Probability, not stats, which is what you asked. | Probability theory books for self-study | Schaeffer's book from Duxbury press seems ok. Sheldon Ross' books are always awesome. Note, these are both books on Probability, not stats, which is what you asked. | Probability theory books for self-study
Schaeffer's book from Duxbury press seems ok. Sheldon Ross' books are always awesome. Note, these are both books on Probability, not stats, which is what you asked. | Probability theory books for self-study
Schaeffer's book from Duxbury press seems ok. Sheldon Ross' books are always awesome. Note, these are both books on Probability, not stats, which is what you asked. |
51,294 | Probability theory books for self-study | I'd strongly recommend Bulmer's Principles of Statistics as a leaping-off point. It's a touch dated, but it's short, clear and available in a cheap Dover edition - around $10 from Amazon. For a more modern and to the point statistical book I'd suggest Wasserman's "All of Statistics". I got it a few months back and i... | Probability theory books for self-study | I'd strongly recommend Bulmer's Principles of Statistics as a leaping-off point. It's a touch dated, but it's short, clear and available in a cheap Dover edition - around $10 from Amazon. For a more | Probability theory books for self-study
I'd strongly recommend Bulmer's Principles of Statistics as a leaping-off point. It's a touch dated, but it's short, clear and available in a cheap Dover edition - around $10 from Amazon. For a more modern and to the point statistical book I'd suggest Wasserman's "All of Statis... | Probability theory books for self-study
I'd strongly recommend Bulmer's Principles of Statistics as a leaping-off point. It's a touch dated, but it's short, clear and available in a cheap Dover edition - around $10 from Amazon. For a more |
51,295 | Probability theory books for self-study | https://www.crcpress.com/Introduction-to-Probability/Blitzstein-Hwang/p/book/9781466575578 - Introduction to Probability
I had no experience in probability before; this is a good book that explains the basic probability distributions with motivating context. Begins with discrete random variables and moves to continuous... | Probability theory books for self-study | https://www.crcpress.com/Introduction-to-Probability/Blitzstein-Hwang/p/book/9781466575578 - Introduction to Probability
I had no experience in probability before; this is a good book that explains th | Probability theory books for self-study
https://www.crcpress.com/Introduction-to-Probability/Blitzstein-Hwang/p/book/9781466575578 - Introduction to Probability
I had no experience in probability before; this is a good book that explains the basic probability distributions with motivating context. Begins with discrete ... | Probability theory books for self-study
https://www.crcpress.com/Introduction-to-Probability/Blitzstein-Hwang/p/book/9781466575578 - Introduction to Probability
I had no experience in probability before; this is a good book that explains th |
51,296 | Probability theory books for self-study | Yes, I agree that the John Rice book is not good for self-study. It jumps around topics of varying difficulty, although it is obvious the author is a very experienced practitioner. For my level, it does more confusion than enlightenment.
I would highly recommend:
Dimitri Bertsekas
Sheldon Ross
Ron C. Mittelhammer
Rich... | Probability theory books for self-study | Yes, I agree that the John Rice book is not good for self-study. It jumps around topics of varying difficulty, although it is obvious the author is a very experienced practitioner. For my level, it do | Probability theory books for self-study
Yes, I agree that the John Rice book is not good for self-study. It jumps around topics of varying difficulty, although it is obvious the author is a very experienced practitioner. For my level, it does more confusion than enlightenment.
I would highly recommend:
Dimitri Bertsek... | Probability theory books for self-study
Yes, I agree that the John Rice book is not good for self-study. It jumps around topics of varying difficulty, although it is obvious the author is a very experienced practitioner. For my level, it do |
51,297 | Difference between time series prediction vs point process prediction | Let's start with AR. AR by default is a time-discrete model, HP or general point process can be defined on continuous space, such as a timeline. In practice, point process data can be discretized using time bins. The data counts in each interval can be either binary or integers.
In AR, $X_t$ is a linear combination of ... | Difference between time series prediction vs point process prediction | Let's start with AR. AR by default is a time-discrete model, HP or general point process can be defined on continuous space, such as a timeline. In practice, point process data can be discretized usin | Difference between time series prediction vs point process prediction
Let's start with AR. AR by default is a time-discrete model, HP or general point process can be defined on continuous space, such as a timeline. In practice, point process data can be discretized using time bins. The data counts in each interval can ... | Difference between time series prediction vs point process prediction
Let's start with AR. AR by default is a time-discrete model, HP or general point process can be defined on continuous space, such as a timeline. In practice, point process data can be discretized usin |
51,298 | Difference between time series prediction vs point process prediction | A time series has time measurements made at regular time intervals, whereas in a Poisson process, including the Hawkes process, the time measurements are distributed in a Poissonian way. | Difference between time series prediction vs point process prediction | A time series has time measurements made at regular time intervals, whereas in a Poisson process, including the Hawkes process, the time measurements are distributed in a Poissonian way. | Difference between time series prediction vs point process prediction
A time series has time measurements made at regular time intervals, whereas in a Poisson process, including the Hawkes process, the time measurements are distributed in a Poissonian way. | Difference between time series prediction vs point process prediction
A time series has time measurements made at regular time intervals, whereas in a Poisson process, including the Hawkes process, the time measurements are distributed in a Poissonian way. |
51,299 | How to maximize min.entropy from a bounded log normal distribution? | This answer is valid for $H$ as defined by the OP. It is also valid for $H=p\ln{p}$, because the solution will still occur where $P(V_{mode})=P(V_{max})$, the factor of $p$ will drop out.
This answer assumes that the discrete (integer-valued) distribution in the question is "similar enough" to a log-normal that the fol... | How to maximize min.entropy from a bounded log normal distribution? | This answer is valid for $H$ as defined by the OP. It is also valid for $H=p\ln{p}$, because the solution will still occur where $P(V_{mode})=P(V_{max})$, the factor of $p$ will drop out.
This answer | How to maximize min.entropy from a bounded log normal distribution?
This answer is valid for $H$ as defined by the OP. It is also valid for $H=p\ln{p}$, because the solution will still occur where $P(V_{mode})=P(V_{max})$, the factor of $p$ will drop out.
This answer assumes that the discrete (integer-valued) distribut... | How to maximize min.entropy from a bounded log normal distribution?
This answer is valid for $H$ as defined by the OP. It is also valid for $H=p\ln{p}$, because the solution will still occur where $P(V_{mode})=P(V_{max})$, the factor of $p$ will drop out.
This answer |
51,300 | Visualising activity | You can try using a horizontal stacked bar in Excel to show people's activity days in colour blocks with gaps painted white, like so:
It will mean doing some transformations to your data, though, as you'd need two rows for each day with 1 and 0 depending on whether a customer engaged in an activity that day. If you're... | Visualising activity | You can try using a horizontal stacked bar in Excel to show people's activity days in colour blocks with gaps painted white, like so:
It will mean doing some transformations to your data, though, as | Visualising activity
You can try using a horizontal stacked bar in Excel to show people's activity days in colour blocks with gaps painted white, like so:
It will mean doing some transformations to your data, though, as you'd need two rows for each day with 1 and 0 depending on whether a customer engaged in an activit... | Visualising activity
You can try using a horizontal stacked bar in Excel to show people's activity days in colour blocks with gaps painted white, like so:
It will mean doing some transformations to your data, though, as |
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