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 |
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10,701 | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$ | You can rearrange as follows:
$$
\begin{eqnarray}
Var(X) &=& E[X^2] - (E[X])^2\\
E[X^2] &=& (E[X])^2 + Var(X)
\end{eqnarray}
$$
Then, interpret as follows: the expected square of a random variable is equal to the square of its mean plus the expected squared deviation from its mean. | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$ | You can rearrange as follows:
$$
\begin{eqnarray}
Var(X) &=& E[X^2] - (E[X])^2\\
E[X^2] &=& (E[X])^2 + Var(X)
\end{eqnarray}
$$
Then, interpret as follows: the expected square of a random variable | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$
You can rearrange as follows:
$$
\begin{eqnarray}
Var(X) &=& E[X^2] - (E[X])^2\\
E[X^2] &=& (E[X])^2 + Var(X)
\end{eqnarray}
$$
Then, interpret as follows: the expected square of a random variable is equal to the square of its mean plus the expected squa... | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$
You can rearrange as follows:
$$
\begin{eqnarray}
Var(X) &=& E[X^2] - (E[X])^2\\
E[X^2] &=& (E[X])^2 + Var(X)
\end{eqnarray}
$$
Then, interpret as follows: the expected square of a random variable |
10,702 | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$ | Sorry for not having the skill to elaborate and provide a proper answer, but I think the answer lies in the physical classical mechanics concept of moments, especially the conversion between 0 centred "raw" moments and mean centred central moments. Bear in mind that variance is the second order central moment of a rand... | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$ | Sorry for not having the skill to elaborate and provide a proper answer, but I think the answer lies in the physical classical mechanics concept of moments, especially the conversion between 0 centred | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$
Sorry for not having the skill to elaborate and provide a proper answer, but I think the answer lies in the physical classical mechanics concept of moments, especially the conversion between 0 centred "raw" moments and mean centred central moments. Bear in ... | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$
Sorry for not having the skill to elaborate and provide a proper answer, but I think the answer lies in the physical classical mechanics concept of moments, especially the conversion between 0 centred |
10,703 | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$ | The general intuition is that you can relate these moments using the Pythagorean Theorem (PT) in a suitably defined vector space, by showing that two of the moments are perpendicular and the third is the hypotenuse. The only algebra needed is to show that the two legs are indeed orthogonal.
For the sake of the followin... | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$ | The general intuition is that you can relate these moments using the Pythagorean Theorem (PT) in a suitably defined vector space, by showing that two of the moments are perpendicular and the third is | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$
The general intuition is that you can relate these moments using the Pythagorean Theorem (PT) in a suitably defined vector space, by showing that two of the moments are perpendicular and the third is the hypotenuse. The only algebra needed is to show that t... | Intuition (geometric or other) of $Var(X) = E[X^2] - (E[X])^2$
The general intuition is that you can relate these moments using the Pythagorean Theorem (PT) in a suitably defined vector space, by showing that two of the moments are perpendicular and the third is |
10,704 | Detecting changes in time series (R example) | You could use time series outlier detection to detect changes in time series. Tsay's or Chen and Liu's procedures are popular time series outlier detection methods . See my earlier question on this site.
R's tsoutlier package uses Chen and Liu's method for detection outliers. SAS/SPSS/Autobox can also do this. See bel... | Detecting changes in time series (R example) | You could use time series outlier detection to detect changes in time series. Tsay's or Chen and Liu's procedures are popular time series outlier detection methods . See my earlier question on this s | Detecting changes in time series (R example)
You could use time series outlier detection to detect changes in time series. Tsay's or Chen and Liu's procedures are popular time series outlier detection methods . See my earlier question on this site.
R's tsoutlier package uses Chen and Liu's method for detection outlier... | Detecting changes in time series (R example)
You could use time series outlier detection to detect changes in time series. Tsay's or Chen and Liu's procedures are popular time series outlier detection methods . See my earlier question on this s |
10,705 | Detecting changes in time series (R example) | My response using AUTOBOX is quite similar to @forecaster but with a much simpler model. Box and Einstein and others have reflected on keeping solutions simple but not too simple. The model that was automatically developed was . The actual and cleansed plot is very similar . A plot of the residuals (which should alwa... | Detecting changes in time series (R example) | My response using AUTOBOX is quite similar to @forecaster but with a much simpler model. Box and Einstein and others have reflected on keeping solutions simple but not too simple. The model that was a | Detecting changes in time series (R example)
My response using AUTOBOX is quite similar to @forecaster but with a much simpler model. Box and Einstein and others have reflected on keeping solutions simple but not too simple. The model that was automatically developed was . The actual and cleansed plot is very similar ... | Detecting changes in time series (R example)
My response using AUTOBOX is quite similar to @forecaster but with a much simpler model. Box and Einstein and others have reflected on keeping solutions simple but not too simple. The model that was a |
10,706 | Detecting changes in time series (R example) | I would approach this problem from the following perspectives. These are just some ideas off the top of my head - please take them with a grain of salt. Nevertheless, I hope that this will be useful.
Time series clustering. For example, by using popular dynamic time warping (DTW) or alternative approaches. Please see ... | Detecting changes in time series (R example) | I would approach this problem from the following perspectives. These are just some ideas off the top of my head - please take them with a grain of salt. Nevertheless, I hope that this will be useful.
| Detecting changes in time series (R example)
I would approach this problem from the following perspectives. These are just some ideas off the top of my head - please take them with a grain of salt. Nevertheless, I hope that this will be useful.
Time series clustering. For example, by using popular dynamic time warping... | Detecting changes in time series (R example)
I would approach this problem from the following perspectives. These are just some ideas off the top of my head - please take them with a grain of salt. Nevertheless, I hope that this will be useful.
|
10,707 | Detecting changes in time series (R example) | Lots of excellent answers are given here. Apparently, the results will depend largely on the models chosen. With that said, allow me to throw one more possibility to this old question based on a Bayesian time series decomposition model I developed, available in an R package Rbeast (https://github.com/zhaokg/Rbeast).... | Detecting changes in time series (R example) | Lots of excellent answers are given here. Apparently, the results will depend largely on the models chosen. With that said, allow me to throw one more possibility to this old question based on a Ba | Detecting changes in time series (R example)
Lots of excellent answers are given here. Apparently, the results will depend largely on the models chosen. With that said, allow me to throw one more possibility to this old question based on a Bayesian time series decomposition model I developed, available in an R packa... | Detecting changes in time series (R example)
Lots of excellent answers are given here. Apparently, the results will depend largely on the models chosen. With that said, allow me to throw one more possibility to this old question based on a Ba |
10,708 | Detecting changes in time series (R example) | It would seem that your problem would be greatly simplified if you detrended your data. It appears to decline linearly. Once you detrend the data, you could apply a wide variety of tests for non-stationarity. | Detecting changes in time series (R example) | It would seem that your problem would be greatly simplified if you detrended your data. It appears to decline linearly. Once you detrend the data, you could apply a wide variety of tests for non-sta | Detecting changes in time series (R example)
It would seem that your problem would be greatly simplified if you detrended your data. It appears to decline linearly. Once you detrend the data, you could apply a wide variety of tests for non-stationarity. | Detecting changes in time series (R example)
It would seem that your problem would be greatly simplified if you detrended your data. It appears to decline linearly. Once you detrend the data, you could apply a wide variety of tests for non-sta |
10,709 | Detecting changes in time series (R example) | All fine answers, but here is a simple one, as suggested by @MrMeritology, which appears to work well for the time series in question, and likely for many other "similar" data sets.
Here is an R-snippet producing the self-explanatory graphs below.
outl = rep( NA, length(dat.change))
detr = c( 0, diff( dat.change))
ix ... | Detecting changes in time series (R example) | All fine answers, but here is a simple one, as suggested by @MrMeritology, which appears to work well for the time series in question, and likely for many other "similar" data sets.
Here is an R-snipp | Detecting changes in time series (R example)
All fine answers, but here is a simple one, as suggested by @MrMeritology, which appears to work well for the time series in question, and likely for many other "similar" data sets.
Here is an R-snippet producing the self-explanatory graphs below.
outl = rep( NA, length(dat.... | Detecting changes in time series (R example)
All fine answers, but here is a simple one, as suggested by @MrMeritology, which appears to work well for the time series in question, and likely for many other "similar" data sets.
Here is an R-snipp |
10,710 | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | Consider a simple regression without a constant term, and where the single regressor is centered on its sample mean. Then $X'X$ is ($n$ times) its sample variance, and $(X'X)^{-1}$ its recirpocal. So the higher the variance = variability in the regressor, the lower the variance of the coefficient estimator: the more v... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | Consider a simple regression without a constant term, and where the single regressor is centered on its sample mean. Then $X'X$ is ($n$ times) its sample variance, and $(X'X)^{-1}$ its recirpocal. So | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
Consider a simple regression without a constant term, and where the single regressor is centered on its sample mean. Then $X'X$ is ($n$ times) its sample variance, and $(X'X)^{-1}$ its recirpocal. So the higher the variance = var... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
Consider a simple regression without a constant term, and where the single regressor is centered on its sample mean. Then $X'X$ is ($n$ times) its sample variance, and $(X'X)^{-1}$ its recirpocal. So |
10,711 | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | A simple way of viewing $\sigma^2 \left(\mathbf{X}^{T} \mathbf{X} \right)^{-1}$ is as the matrix (multivariate) analogue of $\frac{\sigma^2}{\sum_{i=1}^n \left(X_i-\bar{X}\right)^2}$, which is the variance of the slope coefficient in simple OLS regression. One can even get $\frac{\sigma^2}{\sum_{i=1}^n X_i^2}$ for that... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | A simple way of viewing $\sigma^2 \left(\mathbf{X}^{T} \mathbf{X} \right)^{-1}$ is as the matrix (multivariate) analogue of $\frac{\sigma^2}{\sum_{i=1}^n \left(X_i-\bar{X}\right)^2}$, which is the var | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
A simple way of viewing $\sigma^2 \left(\mathbf{X}^{T} \mathbf{X} \right)^{-1}$ is as the matrix (multivariate) analogue of $\frac{\sigma^2}{\sum_{i=1}^n \left(X_i-\bar{X}\right)^2}$, which is the variance of the slope coefficient... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
A simple way of viewing $\sigma^2 \left(\mathbf{X}^{T} \mathbf{X} \right)^{-1}$ is as the matrix (multivariate) analogue of $\frac{\sigma^2}{\sum_{i=1}^n \left(X_i-\bar{X}\right)^2}$, which is the var |
10,712 | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | I'll take a different approach towards developing the intuition that underlies the formula $\text{Var}\,\hat{\beta}=\sigma^2 (X'X)^{-1}$. When developing intuition for the multiple regression model, it's helpful to consider the bivariate linear regression model, viz., $$y_i=\alpha+\beta x_i + \varepsilon_i, \quad i=1,\... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | I'll take a different approach towards developing the intuition that underlies the formula $\text{Var}\,\hat{\beta}=\sigma^2 (X'X)^{-1}$. When developing intuition for the multiple regression model, i | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
I'll take a different approach towards developing the intuition that underlies the formula $\text{Var}\,\hat{\beta}=\sigma^2 (X'X)^{-1}$. When developing intuition for the multiple regression model, it's helpful to consider the bi... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
I'll take a different approach towards developing the intuition that underlies the formula $\text{Var}\,\hat{\beta}=\sigma^2 (X'X)^{-1}$. When developing intuition for the multiple regression model, i |
10,713 | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | Does linear transformation of Gaussian random variable help? Using the rule that if, $x \sim \mathcal{N}(\mu,\Sigma)$, then $Ax + b ~ \sim \mathcal{N}(A\mu + b,A\Sigma A^T)$.
Assuming, that $Y = X\beta + \epsilon$ is the underlying model and $\epsilon \sim \mathcal{N}(0, \sigma^2)$.
$$
\therefore Y \sim \mathcal{N}(X\b... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | Does linear transformation of Gaussian random variable help? Using the rule that if, $x \sim \mathcal{N}(\mu,\Sigma)$, then $Ax + b ~ \sim \mathcal{N}(A\mu + b,A\Sigma A^T)$.
Assuming, that $Y = X\bet | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
Does linear transformation of Gaussian random variable help? Using the rule that if, $x \sim \mathcal{N}(\mu,\Sigma)$, then $Ax + b ~ \sim \mathcal{N}(A\mu + b,A\Sigma A^T)$.
Assuming, that $Y = X\beta + \epsilon$ is the underlyin... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
Does linear transformation of Gaussian random variable help? Using the rule that if, $x \sim \mathcal{N}(\mu,\Sigma)$, then $Ax + b ~ \sim \mathcal{N}(A\mu + b,A\Sigma A^T)$.
Assuming, that $Y = X\bet |
10,714 | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | This builds on @Alecos Papadopuolos' answer.
Recall that the result of a least-squares regression doesn't depend on the units of measurement of your variables. Suppose your X-variable is a length measurement, given in inches. Then rescaling X, say by multiplying by 2.54 to change the unit to centimeters, doesn't materi... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | This builds on @Alecos Papadopuolos' answer.
Recall that the result of a least-squares regression doesn't depend on the units of measurement of your variables. Suppose your X-variable is a length meas | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
This builds on @Alecos Papadopuolos' answer.
Recall that the result of a least-squares regression doesn't depend on the units of measurement of your variables. Suppose your X-variable is a length measurement, given in inches. Then... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
This builds on @Alecos Papadopuolos' answer.
Recall that the result of a least-squares regression doesn't depend on the units of measurement of your variables. Suppose your X-variable is a length meas |
10,715 | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | Say we have $n$ observations (or sample size) and $p$ parameters.
The covariance matrix $\operatorname{Var}(\hat{\beta})$ of the estimated parameters $\hat{\beta}_1,\hat{\beta}_2$ etc. is a representation of the accuracy of the estimated parameters.
If in an ideal world the data could be perfectly described by the mode... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator | Say we have $n$ observations (or sample size) and $p$ parameters.
The covariance matrix $\operatorname{Var}(\hat{\beta})$ of the estimated parameters $\hat{\beta}_1,\hat{\beta}_2$ etc. is a representa | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
Say we have $n$ observations (or sample size) and $p$ parameters.
The covariance matrix $\operatorname{Var}(\hat{\beta})$ of the estimated parameters $\hat{\beta}_1,\hat{\beta}_2$ etc. is a representation of the accuracy of the es... | Intuitive explanation of the $(X^TX)^{-1}$ term in the variance of least square estimator
Say we have $n$ observations (or sample size) and $p$ parameters.
The covariance matrix $\operatorname{Var}(\hat{\beta})$ of the estimated parameters $\hat{\beta}_1,\hat{\beta}_2$ etc. is a representa |
10,716 | Real-life examples of Markov Decision Processes | A Markovian Decision Process indeed has to do with going from one state to another and is mainly used for planning and decision making.
The theory
Just repeating the theory quickly, an MDP is:
$$\text{MDP} = \langle S,A,T,R,\gamma \rangle$$
where $S$ are the states, $A$ the actions, $T$ the transition probabilities (i.... | Real-life examples of Markov Decision Processes | A Markovian Decision Process indeed has to do with going from one state to another and is mainly used for planning and decision making.
The theory
Just repeating the theory quickly, an MDP is:
$$\text | Real-life examples of Markov Decision Processes
A Markovian Decision Process indeed has to do with going from one state to another and is mainly used for planning and decision making.
The theory
Just repeating the theory quickly, an MDP is:
$$\text{MDP} = \langle S,A,T,R,\gamma \rangle$$
where $S$ are the states, $A$ t... | Real-life examples of Markov Decision Processes
A Markovian Decision Process indeed has to do with going from one state to another and is mainly used for planning and decision making.
The theory
Just repeating the theory quickly, an MDP is:
$$\text |
10,717 | Real-life examples of Markov Decision Processes | Bonus: It also feels like MDP's is all about getting from one state to
another, is this true?
Since, MDP is about making future decisions by taking action at present, yes! it's about going from the present state to a more returning(that yields more reward) future state.
To answer the comment by @Suhail Gupta:
So an... | Real-life examples of Markov Decision Processes | Bonus: It also feels like MDP's is all about getting from one state to
another, is this true?
Since, MDP is about making future decisions by taking action at present, yes! it's about going from the | Real-life examples of Markov Decision Processes
Bonus: It also feels like MDP's is all about getting from one state to
another, is this true?
Since, MDP is about making future decisions by taking action at present, yes! it's about going from the present state to a more returning(that yields more reward) future state.... | Real-life examples of Markov Decision Processes
Bonus: It also feels like MDP's is all about getting from one state to
another, is this true?
Since, MDP is about making future decisions by taking action at present, yes! it's about going from the |
10,718 | Singular gradient error in nls with correct starting values | I've got bitten by this recently. My intentions were the same, make some artificial model and test it. The main reason is the one given by @whuber and @marco. Such model is not identified. To see that, remember that NLS minimizes the function:
$$\sum_{i=1}^n(y_i-a-br^{x_i-m}-cx_i)^2$$
Say it is minimized by the set of ... | Singular gradient error in nls with correct starting values | I've got bitten by this recently. My intentions were the same, make some artificial model and test it. The main reason is the one given by @whuber and @marco. Such model is not identified. To see that | Singular gradient error in nls with correct starting values
I've got bitten by this recently. My intentions were the same, make some artificial model and test it. The main reason is the one given by @whuber and @marco. Such model is not identified. To see that, remember that NLS minimizes the function:
$$\sum_{i=1}^n(y... | Singular gradient error in nls with correct starting values
I've got bitten by this recently. My intentions were the same, make some artificial model and test it. The main reason is the one given by @whuber and @marco. Such model is not identified. To see that |
10,719 | Singular gradient error in nls with correct starting values | The answers above are, of course, correct. For what its worth, in addition to the explanations given, if you are trying this on an artificial data set, according to the nls help page found at: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/nls.html
R's nls wont be able to handle it. The help page specifica... | Singular gradient error in nls with correct starting values | The answers above are, of course, correct. For what its worth, in addition to the explanations given, if you are trying this on an artificial data set, according to the nls help page found at: http:/ | Singular gradient error in nls with correct starting values
The answers above are, of course, correct. For what its worth, in addition to the explanations given, if you are trying this on an artificial data set, according to the nls help page found at: http://stat.ethz.ch/R-manual/R-patched/library/stats/html/nls.html... | Singular gradient error in nls with correct starting values
The answers above are, of course, correct. For what its worth, in addition to the explanations given, if you are trying this on an artificial data set, according to the nls help page found at: http:/ |
10,720 | What are the implications of scaling the features to xgboost? | XGBoost is not sensitive to monotonic transformations of its features for the same reason that decision trees and random forests are not: the model only needs to pick "cut points" on features to split a node. Splits are not sensitive to monotonic transformations: defining a split on one scale has a corresponding split ... | What are the implications of scaling the features to xgboost? | XGBoost is not sensitive to monotonic transformations of its features for the same reason that decision trees and random forests are not: the model only needs to pick "cut points" on features to split | What are the implications of scaling the features to xgboost?
XGBoost is not sensitive to monotonic transformations of its features for the same reason that decision trees and random forests are not: the model only needs to pick "cut points" on features to split a node. Splits are not sensitive to monotonic transformat... | What are the implications of scaling the features to xgboost?
XGBoost is not sensitive to monotonic transformations of its features for the same reason that decision trees and random forests are not: the model only needs to pick "cut points" on features to split |
10,721 | Why Levene test of equality of variances rather than F ratio? | You could use an F test to assess the variance of two groups, but the using F to test for differences in variance strictly requires that the distributions are normal. Using Levene's test (i.e., absolute values of the deviations from the mean) is more robust, and using the Brown-Forsythe test (i.e., absolute values of ... | Why Levene test of equality of variances rather than F ratio? | You could use an F test to assess the variance of two groups, but the using F to test for differences in variance strictly requires that the distributions are normal. Using Levene's test (i.e., absol | Why Levene test of equality of variances rather than F ratio?
You could use an F test to assess the variance of two groups, but the using F to test for differences in variance strictly requires that the distributions are normal. Using Levene's test (i.e., absolute values of the deviations from the mean) is more robust... | Why Levene test of equality of variances rather than F ratio?
You could use an F test to assess the variance of two groups, but the using F to test for differences in variance strictly requires that the distributions are normal. Using Levene's test (i.e., absol |
10,722 | Bias of moment estimator of lognormal distribution | There is something puzzling in those results since
the first method provides an unbiased estimator of $\mathbb{E}[X^2]$, namely$$\frac{1}{N}\sum_{i=1}^N X_i^2$$has $\mathbb{E}[X^2]$ as its mean. Hence the blue dots should be around the expected value (orange curve);
the second method provides a biased estimator of $\m... | Bias of moment estimator of lognormal distribution | There is something puzzling in those results since
the first method provides an unbiased estimator of $\mathbb{E}[X^2]$, namely$$\frac{1}{N}\sum_{i=1}^N X_i^2$$has $\mathbb{E}[X^2]$ as its mean. Henc | Bias of moment estimator of lognormal distribution
There is something puzzling in those results since
the first method provides an unbiased estimator of $\mathbb{E}[X^2]$, namely$$\frac{1}{N}\sum_{i=1}^N X_i^2$$has $\mathbb{E}[X^2]$ as its mean. Hence the blue dots should be around the expected value (orange curve);
t... | Bias of moment estimator of lognormal distribution
There is something puzzling in those results since
the first method provides an unbiased estimator of $\mathbb{E}[X^2]$, namely$$\frac{1}{N}\sum_{i=1}^N X_i^2$$has $\mathbb{E}[X^2]$ as its mean. Henc |
10,723 | Bias of moment estimator of lognormal distribution | I thought I'd throw up some figs showing that both user29918 and Xi'an's plots are consistent. Fig 1 plots what user29918 did, and Fig 2 (based on same data), does what Xi'an did for his plot. Same result, different presentation.
What's happening is that as T increases, the variances becomes huge and the estimator $\fr... | Bias of moment estimator of lognormal distribution | I thought I'd throw up some figs showing that both user29918 and Xi'an's plots are consistent. Fig 1 plots what user29918 did, and Fig 2 (based on same data), does what Xi'an did for his plot. Same re | Bias of moment estimator of lognormal distribution
I thought I'd throw up some figs showing that both user29918 and Xi'an's plots are consistent. Fig 1 plots what user29918 did, and Fig 2 (based on same data), does what Xi'an did for his plot. Same result, different presentation.
What's happening is that as T increases... | Bias of moment estimator of lognormal distribution
I thought I'd throw up some figs showing that both user29918 and Xi'an's plots are consistent. Fig 1 plots what user29918 did, and Fig 2 (based on same data), does what Xi'an did for his plot. Same re |
10,724 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | It's unusual to not fit an intercept and generally inadvisable - one should only do so if you know it's 0, but I think that (and the fact that you can't compare the $R^2$ for fits with and without intercept) is well and truly covered already (if possibly a little overstated in the case of the 0 intercept); I want to fo... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | It's unusual to not fit an intercept and generally inadvisable - one should only do so if you know it's 0, but I think that (and the fact that you can't compare the $R^2$ for fits with and without int | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
It's unusual to not fit an intercept and generally inadvisable - one should only do so if you know it's 0, but I think that (and the fact that you can't compare the $R^2$ for fits with and without intercept) is well and truly covered a... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
It's unusual to not fit an intercept and generally inadvisable - one should only do so if you know it's 0, but I think that (and the fact that you can't compare the $R^2$ for fits with and without int |
10,725 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | Short answer to question in title: (almost) NEVER. In the linear regression model
$$
y = \alpha + \beta x + \epsilon
$$,
if you set $\alpha=0$, then you say that you KNOW that the expected value of $y$ given $x=0$ is zero. You almost never know that.
$R^2$ becomes higher without intercept, not because the model is ... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | Short answer to question in title: (almost) NEVER. In the linear regression model
$$
y = \alpha + \beta x + \epsilon
$$,
if you set $\alpha=0$, then you say that you KNOW that the expected value of | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
Short answer to question in title: (almost) NEVER. In the linear regression model
$$
y = \alpha + \beta x + \epsilon
$$,
if you set $\alpha=0$, then you say that you KNOW that the expected value of $y$ given $x=0$ is zero. You almo... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
Short answer to question in title: (almost) NEVER. In the linear regression model
$$
y = \alpha + \beta x + \epsilon
$$,
if you set $\alpha=0$, then you say that you KNOW that the expected value of |
10,726 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | 1) It is never acceptable to suppress an intercept except in very rare types of DiD models where the outcome and predictors are actually computed differences between groups (this isn't the case for you).
2). Heck no it doesn't. What it means is that you may have a higher degree of internal validity (e.g. the model fit... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | 1) It is never acceptable to suppress an intercept except in very rare types of DiD models where the outcome and predictors are actually computed differences between groups (this isn't the case for yo | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
1) It is never acceptable to suppress an intercept except in very rare types of DiD models where the outcome and predictors are actually computed differences between groups (this isn't the case for you).
2). Heck no it doesn't. What i... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
1) It is never acceptable to suppress an intercept except in very rare types of DiD models where the outcome and predictors are actually computed differences between groups (this isn't the case for yo |
10,727 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | 1) Forcing $0$ intercept is advisable if you know for a fact that it is 0. Anything you know a priori, you should use in your model.
One example is the Hubble model for expansion of the Universe (used in Statistical Sleuth):
$$\mbox{Galaxy Speed} = k (\mbox{Distance from Earth}) $$
This model is rather crude, but uses... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | 1) Forcing $0$ intercept is advisable if you know for a fact that it is 0. Anything you know a priori, you should use in your model.
One example is the Hubble model for expansion of the Universe (used | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
1) Forcing $0$ intercept is advisable if you know for a fact that it is 0. Anything you know a priori, you should use in your model.
One example is the Hubble model for expansion of the Universe (used in Statistical Sleuth):
$$\mbox{Ga... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
1) Forcing $0$ intercept is advisable if you know for a fact that it is 0. Anything you know a priori, you should use in your model.
One example is the Hubble model for expansion of the Universe (used |
10,728 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | It makes sense (actually, is necessary) to leave out the intercept in the second stage of the Engle/Granger cointegration test. The test first estimates a candidate cointegrating relationship via a regression of some dependent variable on a constant (plus sometimes a trend) and the other nonstationary variables.
In th... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | It makes sense (actually, is necessary) to leave out the intercept in the second stage of the Engle/Granger cointegration test. The test first estimates a candidate cointegrating relationship via a re | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
It makes sense (actually, is necessary) to leave out the intercept in the second stage of the Engle/Granger cointegration test. The test first estimates a candidate cointegrating relationship via a regression of some dependent variable... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
It makes sense (actually, is necessary) to leave out the intercept in the second stage of the Engle/Granger cointegration test. The test first estimates a candidate cointegrating relationship via a re |
10,729 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | The only way that I know to constrain all fitted values to be greater than zero is to use a linear programming approach and specify that as a constraint. | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | The only way that I know to constrain all fitted values to be greater than zero is to use a linear programming approach and specify that as a constraint. | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
The only way that I know to constrain all fitted values to be greater than zero is to use a linear programming approach and specify that as a constraint. | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
The only way that I know to constrain all fitted values to be greater than zero is to use a linear programming approach and specify that as a constraint. |
10,730 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | The actual problem is that a linear regression forcing the intercept=0 is a mathematical inconsistency that should never be done:
It is clear that if y=a+bx, then average(y)=a+average(x), and indeed we can easily realize that when we estimate a and b using linear estimation in Excel, we obtain the above relation
Howev... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | The actual problem is that a linear regression forcing the intercept=0 is a mathematical inconsistency that should never be done:
It is clear that if y=a+bx, then average(y)=a+average(x), and indeed | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
The actual problem is that a linear regression forcing the intercept=0 is a mathematical inconsistency that should never be done:
It is clear that if y=a+bx, then average(y)=a+average(x), and indeed we can easily realize that when we ... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
The actual problem is that a linear regression forcing the intercept=0 is a mathematical inconsistency that should never be done:
It is clear that if y=a+bx, then average(y)=a+average(x), and indeed |
10,731 | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | It does make pretty much sense in models with categorical covariate. In this case the removal of the intercept results in an equivalent model with just different parametrization:
> data(mtcars)
> mtcars$cyl_factor <- as.factor(mtcars$cyl)
> summary(lm(mpg ~ cyl_factor, data = mtcars))
Call:
lm(formula = mpg ~ cyl_fact... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate] | It does make pretty much sense in models with categorical covariate. In this case the removal of the intercept results in an equivalent model with just different parametrization:
> data(mtcars)
> mtca | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
It does make pretty much sense in models with categorical covariate. In this case the removal of the intercept results in an equivalent model with just different parametrization:
> data(mtcars)
> mtcars$cyl_factor <- as.factor(mtcars$c... | When forcing intercept of 0 in linear regression is acceptable/advisable [duplicate]
It does make pretty much sense in models with categorical covariate. In this case the removal of the intercept results in an equivalent model with just different parametrization:
> data(mtcars)
> mtca |
10,732 | Why is the formula for standard error the way it is? | This comes from the fact that $\newcommand{\Var}{\operatorname{Var}}\newcommand{\Cov}{\operatorname{Cov}}\Var(X+Y) = \Var(X) + \Var(Y) + 2\cdot\Cov(X,Y)$ and for a constant $a$, $\Var( a X ) = a^2 \Var(X)$.
Since we are assuming that the individual observations are independent the $\Cov(X,Y)$ term is $0$ and since we a... | Why is the formula for standard error the way it is? | This comes from the fact that $\newcommand{\Var}{\operatorname{Var}}\newcommand{\Cov}{\operatorname{Cov}}\Var(X+Y) = \Var(X) + \Var(Y) + 2\cdot\Cov(X,Y)$ and for a constant $a$, $\Var( a X ) = a^2 \Va | Why is the formula for standard error the way it is?
This comes from the fact that $\newcommand{\Var}{\operatorname{Var}}\newcommand{\Cov}{\operatorname{Cov}}\Var(X+Y) = \Var(X) + \Var(Y) + 2\cdot\Cov(X,Y)$ and for a constant $a$, $\Var( a X ) = a^2 \Var(X)$.
Since we are assuming that the individual observations are i... | Why is the formula for standard error the way it is?
This comes from the fact that $\newcommand{\Var}{\operatorname{Var}}\newcommand{\Cov}{\operatorname{Cov}}\Var(X+Y) = \Var(X) + \Var(Y) + 2\cdot\Cov(X,Y)$ and for a constant $a$, $\Var( a X ) = a^2 \Va |
10,733 | Why is the formula for standard error the way it is? | Why √n?
So there is this theory called the central limit theorem that tells us that as sample size increases, sampling distributions of means become normally distributed regardless of the parent distribution. In other words, given a sufficiently large sample size, the mean of all samples from a population will be the ... | Why is the formula for standard error the way it is? | Why √n?
So there is this theory called the central limit theorem that tells us that as sample size increases, sampling distributions of means become normally distributed regardless of the parent distr | Why is the formula for standard error the way it is?
Why √n?
So there is this theory called the central limit theorem that tells us that as sample size increases, sampling distributions of means become normally distributed regardless of the parent distribution. In other words, given a sufficiently large sample size, t... | Why is the formula for standard error the way it is?
Why √n?
So there is this theory called the central limit theorem that tells us that as sample size increases, sampling distributions of means become normally distributed regardless of the parent distr |
10,734 | Visually plotting multi dimensional cluster data | There's no single right visualization. It depends on what aspect of the clusters you want to see or emphasize.
Do want to see how each variable contributes? Consider a parallel coordinates plot.
Do you want to see how clusters are distributed along the principal components? Consider a biplot (in 2D or 3D):
Do you wa... | Visually plotting multi dimensional cluster data | There's no single right visualization. It depends on what aspect of the clusters you want to see or emphasize.
Do want to see how each variable contributes? Consider a parallel coordinates plot.
Do | Visually plotting multi dimensional cluster data
There's no single right visualization. It depends on what aspect of the clusters you want to see or emphasize.
Do want to see how each variable contributes? Consider a parallel coordinates plot.
Do you want to see how clusters are distributed along the principal compon... | Visually plotting multi dimensional cluster data
There's no single right visualization. It depends on what aspect of the clusters you want to see or emphasize.
Do want to see how each variable contributes? Consider a parallel coordinates plot.
Do |
10,735 | Visually plotting multi dimensional cluster data | Multivariate displays are tricky, especially with that number of variables. I have two suggestions.
If there are certain variables that are particularly important to the clustering, or substantively interesting, you can use a scatterplot matrix and display the bivariate relationships between your interesting variables.... | Visually plotting multi dimensional cluster data | Multivariate displays are tricky, especially with that number of variables. I have two suggestions.
If there are certain variables that are particularly important to the clustering, or substantively i | Visually plotting multi dimensional cluster data
Multivariate displays are tricky, especially with that number of variables. I have two suggestions.
If there are certain variables that are particularly important to the clustering, or substantively interesting, you can use a scatterplot matrix and display the bivariate ... | Visually plotting multi dimensional cluster data
Multivariate displays are tricky, especially with that number of variables. I have two suggestions.
If there are certain variables that are particularly important to the clustering, or substantively i |
10,736 | Visually plotting multi dimensional cluster data | You can use fviz_cluster function from factoextra pacakge in R. It will show the scatter plot of your data and different colors of the points will be the cluster.
To the best of my understanding, this function performs the PCA and then chooses the top two pc and plot those on 2D.
Any suggestion/improvement in my answe... | Visually plotting multi dimensional cluster data | You can use fviz_cluster function from factoextra pacakge in R. It will show the scatter plot of your data and different colors of the points will be the cluster.
To the best of my understanding, thi | Visually plotting multi dimensional cluster data
You can use fviz_cluster function from factoextra pacakge in R. It will show the scatter plot of your data and different colors of the points will be the cluster.
To the best of my understanding, this function performs the PCA and then chooses the top two pc and plot th... | Visually plotting multi dimensional cluster data
You can use fviz_cluster function from factoextra pacakge in R. It will show the scatter plot of your data and different colors of the points will be the cluster.
To the best of my understanding, thi |
10,737 | Question about standardizing in ridge regression | Ridge regression regularize the linear regression by imposing a penalty on the size of coefficients. Thus the coefficients are shrunk toward zero and toward each other. But when this happens and if the independent variables does not have the same scale, the shrinking is not fair. Two independent variables with differen... | Question about standardizing in ridge regression | Ridge regression regularize the linear regression by imposing a penalty on the size of coefficients. Thus the coefficients are shrunk toward zero and toward each other. But when this happens and if th | Question about standardizing in ridge regression
Ridge regression regularize the linear regression by imposing a penalty on the size of coefficients. Thus the coefficients are shrunk toward zero and toward each other. But when this happens and if the independent variables does not have the same scale, the shrinking is ... | Question about standardizing in ridge regression
Ridge regression regularize the linear regression by imposing a penalty on the size of coefficients. Thus the coefficients are shrunk toward zero and toward each other. But when this happens and if th |
10,738 | Question about standardizing in ridge regression | Though four years late, hope someone will benefit from this.... The way I understood it, coeff is how much target variable changes for a unit change in independent variable (dy / dx). Let us assume we are studying relation between weight and height and weight is measured in Kg. When we use Kilometers for height, you ca... | Question about standardizing in ridge regression | Though four years late, hope someone will benefit from this.... The way I understood it, coeff is how much target variable changes for a unit change in independent variable (dy / dx). Let us assume we | Question about standardizing in ridge regression
Though four years late, hope someone will benefit from this.... The way I understood it, coeff is how much target variable changes for a unit change in independent variable (dy / dx). Let us assume we are studying relation between weight and height and weight is measured... | Question about standardizing in ridge regression
Though four years late, hope someone will benefit from this.... The way I understood it, coeff is how much target variable changes for a unit change in independent variable (dy / dx). Let us assume we |
10,739 | How does the inverse transform method work? | The method is very simple, so I'll describe it in simple words. First, take cumulative distribution function $F_X$ of some distribution that you want to sample from. The function takes as input some value $x$ and tells you what is the probability of obtaining $X \leq x$. So
$$ F_X(x) = \Pr(X \leq x) = p $$
inverse of s... | How does the inverse transform method work? | The method is very simple, so I'll describe it in simple words. First, take cumulative distribution function $F_X$ of some distribution that you want to sample from. The function takes as input some v | How does the inverse transform method work?
The method is very simple, so I'll describe it in simple words. First, take cumulative distribution function $F_X$ of some distribution that you want to sample from. The function takes as input some value $x$ and tells you what is the probability of obtaining $X \leq x$. So
$... | How does the inverse transform method work?
The method is very simple, so I'll describe it in simple words. First, take cumulative distribution function $F_X$ of some distribution that you want to sample from. The function takes as input some v |
10,740 | How does the inverse transform method work? | Yes, $U^θ$ has the distribution of $X$.
Two additional points on the intuition behind inverse transform method might be useful
(1) In order to understand what $F^{-1}$ actually means please refer to a graph in Tim's answer to Help me understand the quantile (inverse CDF) function
(2) [Please, simply ignore the followi... | How does the inverse transform method work? | Yes, $U^θ$ has the distribution of $X$.
Two additional points on the intuition behind inverse transform method might be useful
(1) In order to understand what $F^{-1}$ actually means please refer to | How does the inverse transform method work?
Yes, $U^θ$ has the distribution of $X$.
Two additional points on the intuition behind inverse transform method might be useful
(1) In order to understand what $F^{-1}$ actually means please refer to a graph in Tim's answer to Help me understand the quantile (inverse CDF) fun... | How does the inverse transform method work?
Yes, $U^θ$ has the distribution of $X$.
Two additional points on the intuition behind inverse transform method might be useful
(1) In order to understand what $F^{-1}$ actually means please refer to |
10,741 | Should data be centered+scaled before applying t-SNE? | Centering shouldn't matter since the algorithm only operates on distances between points, however rescaling is necessary if you want the different dimensions to be treated with equal importance, since the 2-norm will be more heavily influenced by dimensions with large variance. | Should data be centered+scaled before applying t-SNE? | Centering shouldn't matter since the algorithm only operates on distances between points, however rescaling is necessary if you want the different dimensions to be treated with equal importance, since | Should data be centered+scaled before applying t-SNE?
Centering shouldn't matter since the algorithm only operates on distances between points, however rescaling is necessary if you want the different dimensions to be treated with equal importance, since the 2-norm will be more heavily influenced by dimensions with lar... | Should data be centered+scaled before applying t-SNE?
Centering shouldn't matter since the algorithm only operates on distances between points, however rescaling is necessary if you want the different dimensions to be treated with equal importance, since |
10,742 | Use of circular predictors in linear regression | Wind direction (here measured in degrees, presumably as a compass direction clockwise from North) is a circular variable. The test is that the conventional beginning of the scale is the same as the end, i.e. $0^\circ = 360^\circ$. When treated as a predictor it is probably best mapped to sine and cosine. Whatever your ... | Use of circular predictors in linear regression | Wind direction (here measured in degrees, presumably as a compass direction clockwise from North) is a circular variable. The test is that the conventional beginning of the scale is the same as the en | Use of circular predictors in linear regression
Wind direction (here measured in degrees, presumably as a compass direction clockwise from North) is a circular variable. The test is that the conventional beginning of the scale is the same as the end, i.e. $0^\circ = 360^\circ$. When treated as a predictor it is probabl... | Use of circular predictors in linear regression
Wind direction (here measured in degrees, presumably as a compass direction clockwise from North) is a circular variable. The test is that the conventional beginning of the scale is the same as the en |
10,743 | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not normal? | In typical EM GMM situations, one does take variance and covariance into account. This is not done in k-means.
But indeed, one of the popular heuristics for k-means (note: k-means is a problem, not an algorithm) - the Lloyd algorithm - is essentially an EM algorithm, using a centroid model (without variance) and hard a... | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not n | In typical EM GMM situations, one does take variance and covariance into account. This is not done in k-means.
But indeed, one of the popular heuristics for k-means (note: k-means is a problem, not an | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not normal?
In typical EM GMM situations, one does take variance and covariance into account. This is not done in k-means.
But indeed, one of the popular heuristics for k-means (note: k-means is a problem, not an algorithm) -... | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not n
In typical EM GMM situations, one does take variance and covariance into account. This is not done in k-means.
But indeed, one of the popular heuristics for k-means (note: k-means is a problem, not an |
10,744 | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not normal? | GMM uses overlapping hills that stretch to infinity (but practically only count for 3 sigma). Each point gets all the hills' probability scores. Also, the hills are "egg-shaped" [okay, they're symmetric ellipses] and, using the full covariance matrix, may be tilted.
K-means hard-assigns a point to a single cluster, s... | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not n | GMM uses overlapping hills that stretch to infinity (but practically only count for 3 sigma). Each point gets all the hills' probability scores. Also, the hills are "egg-shaped" [okay, they're symme | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not normal?
GMM uses overlapping hills that stretch to infinity (but practically only count for 3 sigma). Each point gets all the hills' probability scores. Also, the hills are "egg-shaped" [okay, they're symmetric ellipses... | If k-means clustering is a form of Gaussian mixture modeling, can it be used when the data are not n
GMM uses overlapping hills that stretch to infinity (but practically only count for 3 sigma). Each point gets all the hills' probability scores. Also, the hills are "egg-shaped" [okay, they're symme |
10,745 | What function could be a kernel? | Generally, a function $k(x,y)$ is a valid kernel function (in the sense of the kernel trick) if it satisfies two key properties:
symmetry: $k(x,y) = k(y,x)$
positive semi-definiteness.
Reference: Page 4 of http://www.cs.berkeley.edu/~jordan/courses/281B-spring04/lectures/lec3.pdf
Checking symmetry is usually straigh... | What function could be a kernel? | Generally, a function $k(x,y)$ is a valid kernel function (in the sense of the kernel trick) if it satisfies two key properties:
symmetry: $k(x,y) = k(y,x)$
positive semi-definiteness.
Reference: P | What function could be a kernel?
Generally, a function $k(x,y)$ is a valid kernel function (in the sense of the kernel trick) if it satisfies two key properties:
symmetry: $k(x,y) = k(y,x)$
positive semi-definiteness.
Reference: Page 4 of http://www.cs.berkeley.edu/~jordan/courses/281B-spring04/lectures/lec3.pdf
Che... | What function could be a kernel?
Generally, a function $k(x,y)$ is a valid kernel function (in the sense of the kernel trick) if it satisfies two key properties:
symmetry: $k(x,y) = k(y,x)$
positive semi-definiteness.
Reference: P |
10,746 | What is the curse of dimensionality? | Following up on richiemorrisroe, here is the relevant image from the Elements of Statistical Learning, chapter 2 (pp22-27):
As you can see in the upper right pane, there are more neighbors 1 unit away in 1 dimension than there are neighbors 1 unit away in 2 dimensions. 3 dimensions would be even worse! | What is the curse of dimensionality? | Following up on richiemorrisroe, here is the relevant image from the Elements of Statistical Learning, chapter 2 (pp22-27):
As you can see in the upper right pane, there are more neighbors 1 unit awa | What is the curse of dimensionality?
Following up on richiemorrisroe, here is the relevant image from the Elements of Statistical Learning, chapter 2 (pp22-27):
As you can see in the upper right pane, there are more neighbors 1 unit away in 1 dimension than there are neighbors 1 unit away in 2 dimensions. 3 dimension... | What is the curse of dimensionality?
Following up on richiemorrisroe, here is the relevant image from the Elements of Statistical Learning, chapter 2 (pp22-27):
As you can see in the upper right pane, there are more neighbors 1 unit awa |
10,747 | What is the curse of dimensionality? | This doesn't answer your question directly, but David Donoho has a nice article on High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality (associated slides are here), in which he mentions three curses:
Optimization by Exhaustive Search: "If we must approximately optimize a function of $D$ variable... | What is the curse of dimensionality? | This doesn't answer your question directly, but David Donoho has a nice article on High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality (associated slides are here), in which he | What is the curse of dimensionality?
This doesn't answer your question directly, but David Donoho has a nice article on High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality (associated slides are here), in which he mentions three curses:
Optimization by Exhaustive Search: "If we must approximatel... | What is the curse of dimensionality?
This doesn't answer your question directly, but David Donoho has a nice article on High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality (associated slides are here), in which he |
10,748 | What is the curse of dimensionality? | I know that I keep referring to it, but there's a great explanation of this is the Elements of Statistical Learning, chapter 2 (pp22-27). They basically note that as dimensions increase, the amount of data needs to increase (exponentially) with it or there will not be enough points in the larger sample space for any us... | What is the curse of dimensionality? | I know that I keep referring to it, but there's a great explanation of this is the Elements of Statistical Learning, chapter 2 (pp22-27). They basically note that as dimensions increase, the amount of | What is the curse of dimensionality?
I know that I keep referring to it, but there's a great explanation of this is the Elements of Statistical Learning, chapter 2 (pp22-27). They basically note that as dimensions increase, the amount of data needs to increase (exponentially) with it or there will not be enough points ... | What is the curse of dimensionality?
I know that I keep referring to it, but there's a great explanation of this is the Elements of Statistical Learning, chapter 2 (pp22-27). They basically note that as dimensions increase, the amount of |
10,749 | What is the curse of dimensionality? | Maybe the most notorious impact is captured by the following limit (which is (indirectly) illustrated in above picture):
$$\lim_{dim\rightarrow\infty}\frac{dist_{max}-dist_{min}}{dist_{min}}$$
The distance in the picture is the $L_2$-based euclidian distance. The limit expresses that the notion of distance captures les... | What is the curse of dimensionality? | Maybe the most notorious impact is captured by the following limit (which is (indirectly) illustrated in above picture):
$$\lim_{dim\rightarrow\infty}\frac{dist_{max}-dist_{min}}{dist_{min}}$$
The dis | What is the curse of dimensionality?
Maybe the most notorious impact is captured by the following limit (which is (indirectly) illustrated in above picture):
$$\lim_{dim\rightarrow\infty}\frac{dist_{max}-dist_{min}}{dist_{min}}$$
The distance in the picture is the $L_2$-based euclidian distance. The limit expresses tha... | What is the curse of dimensionality?
Maybe the most notorious impact is captured by the following limit (which is (indirectly) illustrated in above picture):
$$\lim_{dim\rightarrow\infty}\frac{dist_{max}-dist_{min}}{dist_{min}}$$
The dis |
10,750 | Why do lme and aov return different results for repeated measures ANOVA in R? | They are different because the lme model is forcing the variance component of id to be greater than zero. Looking at the raw anova table for all terms, we see that the mean squared error for id is less than that for the residuals.
> anova(lm1 <- lm(value~ factor+id, data=tau.base))
Df Sum Sq Mean Sq F va... | Why do lme and aov return different results for repeated measures ANOVA in R? | They are different because the lme model is forcing the variance component of id to be greater than zero. Looking at the raw anova table for all terms, we see that the mean squared error for id is le | Why do lme and aov return different results for repeated measures ANOVA in R?
They are different because the lme model is forcing the variance component of id to be greater than zero. Looking at the raw anova table for all terms, we see that the mean squared error for id is less than that for the residuals.
> anova(... | Why do lme and aov return different results for repeated measures ANOVA in R?
They are different because the lme model is forcing the variance component of id to be greater than zero. Looking at the raw anova table for all terms, we see that the mean squared error for id is le |
10,751 | Why do lme and aov return different results for repeated measures ANOVA in R? | aov() fits the model via lm() using least squares, lme fits via maximum likelihood. That difference in how the parameters of the linear model are estimated likely accounts for the (very small) difference in your f-values.
In practice, (e.g. for hypothesis testing) these estimates are the same, so I don't see how one c... | Why do lme and aov return different results for repeated measures ANOVA in R? | aov() fits the model via lm() using least squares, lme fits via maximum likelihood. That difference in how the parameters of the linear model are estimated likely accounts for the (very small) differe | Why do lme and aov return different results for repeated measures ANOVA in R?
aov() fits the model via lm() using least squares, lme fits via maximum likelihood. That difference in how the parameters of the linear model are estimated likely accounts for the (very small) difference in your f-values.
In practice, (e.g. ... | Why do lme and aov return different results for repeated measures ANOVA in R?
aov() fits the model via lm() using least squares, lme fits via maximum likelihood. That difference in how the parameters of the linear model are estimated likely accounts for the (very small) differe |
10,752 | Statistics collaboration | My answer is from the point of view of an UK academic statistician. In particular, as an academic that gets judged on advances in statistical methodology.
What would make me (or any other
scientist) a better collaborator?
To be blunt - money. My time isn't free and I (as an academic) don't get employed to carry ou... | Statistics collaboration | My answer is from the point of view of an UK academic statistician. In particular, as an academic that gets judged on advances in statistical methodology.
What would make me (or any other
scientist | Statistics collaboration
My answer is from the point of view of an UK academic statistician. In particular, as an academic that gets judged on advances in statistical methodology.
What would make me (or any other
scientist) a better collaborator?
To be blunt - money. My time isn't free and I (as an academic) don't... | Statistics collaboration
My answer is from the point of view of an UK academic statistician. In particular, as an academic that gets judged on advances in statistical methodology.
What would make me (or any other
scientist |
10,753 | Statistics collaboration | I think the concept that few scientists grasp is this: A statistical result can really only be taken at face value when the statistical methods were chosen in advance while the experiment was being planned (or while preliminary data were collected to polish methods).
You are likely to be mislead if you first analyze ... | Statistics collaboration | I think the concept that few scientists grasp is this: A statistical result can really only be taken at face value when the statistical methods were chosen in advance while the experiment was being p | Statistics collaboration
I think the concept that few scientists grasp is this: A statistical result can really only be taken at face value when the statistical methods were chosen in advance while the experiment was being planned (or while preliminary data were collected to polish methods).
You are likely to be misl... | Statistics collaboration
I think the concept that few scientists grasp is this: A statistical result can really only be taken at face value when the statistical methods were chosen in advance while the experiment was being p |
10,754 | Statistics collaboration | To get a good answer, you must write a good question. Answering a statistics question without context is like boxing blindfolded. You might knock your opponent out, or you might break your hand on the ring post.
What goes into a good question?
Tell us the PROBLEM you are trying to solve. That is, the substantive probl... | Statistics collaboration | To get a good answer, you must write a good question. Answering a statistics question without context is like boxing blindfolded. You might knock your opponent out, or you might break your hand on the | Statistics collaboration
To get a good answer, you must write a good question. Answering a statistics question without context is like boxing blindfolded. You might knock your opponent out, or you might break your hand on the ring post.
What goes into a good question?
Tell us the PROBLEM you are trying to solve. That ... | Statistics collaboration
To get a good answer, you must write a good question. Answering a statistics question without context is like boxing blindfolded. You might knock your opponent out, or you might break your hand on the |
10,755 | Statistics collaboration | Having no preconceived ideas about the method you should use solely based on papers. Their ideas, logic or methods may be faulty. You want to think about your problem and use the most appropriate set of tools. This reminds me of reproducing cited information without checking the source.
On the other hand, paper with me... | Statistics collaboration | Having no preconceived ideas about the method you should use solely based on papers. Their ideas, logic or methods may be faulty. You want to think about your problem and use the most appropriate set | Statistics collaboration
Having no preconceived ideas about the method you should use solely based on papers. Their ideas, logic or methods may be faulty. You want to think about your problem and use the most appropriate set of tools. This reminds me of reproducing cited information without checking the source.
On the ... | Statistics collaboration
Having no preconceived ideas about the method you should use solely based on papers. Their ideas, logic or methods may be faulty. You want to think about your problem and use the most appropriate set |
10,756 | Why does the continuity correction (say, the normal approximation to the binomial distribution) work? | In fact it doesn't always "work" (in the sense of always improving the approximation of the binomial cdf by the normal at any $x$). If the binomial $p$ is 0.5 I think it always helps, except perhaps for the most extreme tail. If $p$ is not too far from 0.5, for reasonably large $n$ it generally works very well except i... | Why does the continuity correction (say, the normal approximation to the binomial distribution) work | In fact it doesn't always "work" (in the sense of always improving the approximation of the binomial cdf by the normal at any $x$). If the binomial $p$ is 0.5 I think it always helps, except perhaps f | Why does the continuity correction (say, the normal approximation to the binomial distribution) work?
In fact it doesn't always "work" (in the sense of always improving the approximation of the binomial cdf by the normal at any $x$). If the binomial $p$ is 0.5 I think it always helps, except perhaps for the most extrem... | Why does the continuity correction (say, the normal approximation to the binomial distribution) work
In fact it doesn't always "work" (in the sense of always improving the approximation of the binomial cdf by the normal at any $x$). If the binomial $p$ is 0.5 I think it always helps, except perhaps f |
10,757 | Why does the continuity correction (say, the normal approximation to the binomial distribution) work? | I believe the factor arises from the fact that we are comparing a continuous distribution to a discrete. We thus need to translate what each discrete value means in the continuous distribution. We could choose another value, however this would be unbalanced about a given integer. (ie you would weight the probability of... | Why does the continuity correction (say, the normal approximation to the binomial distribution) work | I believe the factor arises from the fact that we are comparing a continuous distribution to a discrete. We thus need to translate what each discrete value means in the continuous distribution. We cou | Why does the continuity correction (say, the normal approximation to the binomial distribution) work?
I believe the factor arises from the fact that we are comparing a continuous distribution to a discrete. We thus need to translate what each discrete value means in the continuous distribution. We could choose another ... | Why does the continuity correction (say, the normal approximation to the binomial distribution) work
I believe the factor arises from the fact that we are comparing a continuous distribution to a discrete. We thus need to translate what each discrete value means in the continuous distribution. We cou |
10,758 | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | This sounds like another strident paper by a confused individual. Fisher didn't fall into any such trap, though many students of statistics do.
Hypothesis testing is a decision theoretic problem. Generally, you end up with a test with a given threshold between the two decisions (hypothesis true or hypothesis false). ... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | This sounds like another strident paper by a confused individual. Fisher didn't fall into any such trap, though many students of statistics do.
Hypothesis testing is a decision theoretic problem. Ge | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
This sounds like another strident paper by a confused individual. Fisher didn't fall into any such trap, though many students of statistics do.
Hypothesis testing is a decision theoretic problem. Generally, you end up with a test... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
This sounds like another strident paper by a confused individual. Fisher didn't fall into any such trap, though many students of statistics do.
Hypothesis testing is a decision theoretic problem. Ge |
10,759 | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | I recommend focusing on things like confidence intervals and model-checking. Andrew Gelman has done great work on this. I recommend his textbooks but also check out the stuff he's put online, e.g. http://andrewgelman.com/2011/06/the_holes_in_my/ | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | I recommend focusing on things like confidence intervals and model-checking. Andrew Gelman has done great work on this. I recommend his textbooks but also check out the stuff he's put online, e.g. h | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
I recommend focusing on things like confidence intervals and model-checking. Andrew Gelman has done great work on this. I recommend his textbooks but also check out the stuff he's put online, e.g. http://andrewgelman.com/2011/06/... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
I recommend focusing on things like confidence intervals and model-checking. Andrew Gelman has done great work on this. I recommend his textbooks but also check out the stuff he's put online, e.g. h |
10,760 | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | The ez package provides likelihood ratios when you use the ezMixed() function to do mixed effects modelling. Likelihood ratios aim to quantify evidence for a phenomenon by comparing the likelihood (given the observed data) of two models: a "restricted" model that restricts the influence of the phenomenon to zero and an... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | The ez package provides likelihood ratios when you use the ezMixed() function to do mixed effects modelling. Likelihood ratios aim to quantify evidence for a phenomenon by comparing the likelihood (gi | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
The ez package provides likelihood ratios when you use the ezMixed() function to do mixed effects modelling. Likelihood ratios aim to quantify evidence for a phenomenon by comparing the likelihood (given the observed data) of two m... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
The ez package provides likelihood ratios when you use the ezMixed() function to do mixed effects modelling. Likelihood ratios aim to quantify evidence for a phenomenon by comparing the likelihood (gi |
10,761 | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | All those techniques are available in R in the same sense that all of algebra is available in your pencil. Even p-values are available through many many different functions in R, deciding which function to use to get a p-value or a Bayesian posterior is more complex than a pointer to a single function or package.
On... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they? | All those techniques are available in R in the same sense that all of algebra is available in your pencil. Even p-values are available through many many different functions in R, deciding which funct | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
All those techniques are available in R in the same sense that all of algebra is available in your pencil. Even p-values are available through many many different functions in R, deciding which function to use to get a p-value or ... | Ziliak (2011) opposes the use of p-values and mentions some alternatives; what are they?
All those techniques are available in R in the same sense that all of algebra is available in your pencil. Even p-values are available through many many different functions in R, deciding which funct |
10,762 | Hamiltonian Monte Carlo vs. Sequential Monte Carlo | Hamiltonian Monte Carlo performs well with continuous target distributions with "weird" shapes. It requires the target distribution to be differentiable as it basically uses the slope of the target distribution to know where to go. The perfect example is a banana shaped function.
Here is a standard Metropolis Hastings ... | Hamiltonian Monte Carlo vs. Sequential Monte Carlo | Hamiltonian Monte Carlo performs well with continuous target distributions with "weird" shapes. It requires the target distribution to be differentiable as it basically uses the slope of the target di | Hamiltonian Monte Carlo vs. Sequential Monte Carlo
Hamiltonian Monte Carlo performs well with continuous target distributions with "weird" shapes. It requires the target distribution to be differentiable as it basically uses the slope of the target distribution to know where to go. The perfect example is a banana shape... | Hamiltonian Monte Carlo vs. Sequential Monte Carlo
Hamiltonian Monte Carlo performs well with continuous target distributions with "weird" shapes. It requires the target distribution to be differentiable as it basically uses the slope of the target di |
10,763 | Machine learning algorithms to handle missing data | It depends on the model you use. If you are using some generative model, then there is a principled way to deal with missing values (). For example in models like Naive Bayes or Gaussian Processes you would integrate out missing variables, and choose the best option with the remaining variables.
For discriminative mode... | Machine learning algorithms to handle missing data | It depends on the model you use. If you are using some generative model, then there is a principled way to deal with missing values (). For example in models like Naive Bayes or Gaussian Processes you | Machine learning algorithms to handle missing data
It depends on the model you use. If you are using some generative model, then there is a principled way to deal with missing values (). For example in models like Naive Bayes or Gaussian Processes you would integrate out missing variables, and choose the best option wi... | Machine learning algorithms to handle missing data
It depends on the model you use. If you are using some generative model, then there is a principled way to deal with missing values (). For example in models like Naive Bayes or Gaussian Processes you |
10,764 | Machine learning algorithms to handle missing data | The R-package randomForestSRC, which implements Breiman's random forests, handles missing data for a wide class of analyses (regression, classification, survival, competing risk, unsupervised, multivariate).
See the following post:
Why doesn't Random Forest handle missing values in predictors? | Machine learning algorithms to handle missing data | The R-package randomForestSRC, which implements Breiman's random forests, handles missing data for a wide class of analyses (regression, classification, survival, competing risk, unsupervised, multiva | Machine learning algorithms to handle missing data
The R-package randomForestSRC, which implements Breiman's random forests, handles missing data for a wide class of analyses (regression, classification, survival, competing risk, unsupervised, multivariate).
See the following post:
Why doesn't Random Forest handle mi... | Machine learning algorithms to handle missing data
The R-package randomForestSRC, which implements Breiman's random forests, handles missing data for a wide class of analyses (regression, classification, survival, competing risk, unsupervised, multiva |
10,765 | Machine learning algorithms to handle missing data | Try imputation using nearest neighbours to get rid of missing data.
Additionally, the Caret package has interfaces to a wide variety of algorithms and they all come with predict methods in R that can be used to predict novel data. Performance metrics can also be estimated using k-fold cross validation using the same p... | Machine learning algorithms to handle missing data | Try imputation using nearest neighbours to get rid of missing data.
Additionally, the Caret package has interfaces to a wide variety of algorithms and they all come with predict methods in R that can | Machine learning algorithms to handle missing data
Try imputation using nearest neighbours to get rid of missing data.
Additionally, the Caret package has interfaces to a wide variety of algorithms and they all come with predict methods in R that can be used to predict novel data. Performance metrics can also be estim... | Machine learning algorithms to handle missing data
Try imputation using nearest neighbours to get rid of missing data.
Additionally, the Caret package has interfaces to a wide variety of algorithms and they all come with predict methods in R that can |
10,766 | Machine learning algorithms to handle missing data | There are also algorithms that can use the missing value as a unique and different value when building the predictive model, such as classification and regression trees. such as xgboost | Machine learning algorithms to handle missing data | There are also algorithms that can use the missing value as a unique and different value when building the predictive model, such as classification and regression trees. such as xgboost | Machine learning algorithms to handle missing data
There are also algorithms that can use the missing value as a unique and different value when building the predictive model, such as classification and regression trees. such as xgboost | Machine learning algorithms to handle missing data
There are also algorithms that can use the missing value as a unique and different value when building the predictive model, such as classification and regression trees. such as xgboost |
10,767 | Machine learning algorithms to handle missing data | lightgbm can handle NaNs from the box(http://lightgbm.readthedocs.io/en/latest/). | Machine learning algorithms to handle missing data | lightgbm can handle NaNs from the box(http://lightgbm.readthedocs.io/en/latest/). | Machine learning algorithms to handle missing data
lightgbm can handle NaNs from the box(http://lightgbm.readthedocs.io/en/latest/). | Machine learning algorithms to handle missing data
lightgbm can handle NaNs from the box(http://lightgbm.readthedocs.io/en/latest/). |
10,768 | Import stock price from Yahoo Finance into R? | This really isn't a statistics question (perhaps this could be moved to SO?), but there's a nice function in quantmod that does what Dirk has done by hand. See getQuote() and yahooQF(). Typing yahooQF() will bring up a menu of all the possible quote formats you can use.
> require(quantmod)
> getQuote("QQQQ;SPY", what... | Import stock price from Yahoo Finance into R? | This really isn't a statistics question (perhaps this could be moved to SO?), but there's a nice function in quantmod that does what Dirk has done by hand. See getQuote() and yahooQF(). Typing yahoo | Import stock price from Yahoo Finance into R?
This really isn't a statistics question (perhaps this could be moved to SO?), but there's a nice function in quantmod that does what Dirk has done by hand. See getQuote() and yahooQF(). Typing yahooQF() will bring up a menu of all the possible quote formats you can use.
>... | Import stock price from Yahoo Finance into R?
This really isn't a statistics question (perhaps this could be moved to SO?), but there's a nice function in quantmod that does what Dirk has done by hand. See getQuote() and yahooQF(). Typing yahoo |
10,769 | Import stock price from Yahoo Finance into R? | That is pretty easy given that R can read directly off a given URL. The key is simply to know how to form the URL. Here is a quick and dirty example based on code Dj Padzensky wrote in the late 1990s and which I have been maintaining in the Perl module Yahoo-FinanceQuote (which is of course also on CPAN here) for almo... | Import stock price from Yahoo Finance into R? | That is pretty easy given that R can read directly off a given URL. The key is simply to know how to form the URL. Here is a quick and dirty example based on code Dj Padzensky wrote in the late 1990s | Import stock price from Yahoo Finance into R?
That is pretty easy given that R can read directly off a given URL. The key is simply to know how to form the URL. Here is a quick and dirty example based on code Dj Padzensky wrote in the late 1990s and which I have been maintaining in the Perl module Yahoo-FinanceQuote (... | Import stock price from Yahoo Finance into R?
That is pretty easy given that R can read directly off a given URL. The key is simply to know how to form the URL. Here is a quick and dirty example based on code Dj Padzensky wrote in the late 1990s |
10,770 | Import stock price from Yahoo Finance into R? | Here's a little function I wrote to gather and chart "pseudo-real time" data from yahoo:
require(quantmod)
Times <- NULL
Prices <- NULL
while(1) {
tryCatch({
#Load current quote
Year <- 1970
currentYear <- as.numeric(format(Sys.time(),'%Y'))
while (Year != currentYear) { #Sometimes yahoo re... | Import stock price from Yahoo Finance into R? | Here's a little function I wrote to gather and chart "pseudo-real time" data from yahoo:
require(quantmod)
Times <- NULL
Prices <- NULL
while(1) {
tryCatch({
#Load current quote
Year | Import stock price from Yahoo Finance into R?
Here's a little function I wrote to gather and chart "pseudo-real time" data from yahoo:
require(quantmod)
Times <- NULL
Prices <- NULL
while(1) {
tryCatch({
#Load current quote
Year <- 1970
currentYear <- as.numeric(format(Sys.time(),'%Y'))
whi... | Import stock price from Yahoo Finance into R?
Here's a little function I wrote to gather and chart "pseudo-real time" data from yahoo:
require(quantmod)
Times <- NULL
Prices <- NULL
while(1) {
tryCatch({
#Load current quote
Year |
10,771 | Import stock price from Yahoo Finance into R? | library(quantmod)
getSymbols("LT.NS",src="yahoo") | Import stock price from Yahoo Finance into R? | library(quantmod)
getSymbols("LT.NS",src="yahoo") | Import stock price from Yahoo Finance into R?
library(quantmod)
getSymbols("LT.NS",src="yahoo") | Import stock price from Yahoo Finance into R?
library(quantmod)
getSymbols("LT.NS",src="yahoo") |
10,772 | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression | The WoE method consists of two steps:
to split (a continuous) variable into few categories or to group (a discrete) variable into few categories (and in both cases you assume that all observations in one category have "same" effect on dependent variable)
to calculate WoE value for each category (then the original x ... | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression | The WoE method consists of two steps:
to split (a continuous) variable into few categories or to group (a discrete) variable into few categories (and in both cases you assume that all observations in | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression
The WoE method consists of two steps:
to split (a continuous) variable into few categories or to group (a discrete) variable into few categories (and in both cases you assume that all observations in one category have "same" effect on dependent var... | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression
The WoE method consists of two steps:
to split (a continuous) variable into few categories or to group (a discrete) variable into few categories (and in both cases you assume that all observations in |
10,773 | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression | The rational for using WOE in logistic regression is to generate what is sometimes called the Semi-Naive Bayesian Classifier (SNBC). The beginning of this blog post explains things pretty well: http://multithreaded.stitchfix.com/blog/2015/08/13/weight-of-evidence/
The beta parameters in the model are the linear bias o... | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression | The rational for using WOE in logistic regression is to generate what is sometimes called the Semi-Naive Bayesian Classifier (SNBC). The beginning of this blog post explains things pretty well: http: | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression
The rational for using WOE in logistic regression is to generate what is sometimes called the Semi-Naive Bayesian Classifier (SNBC). The beginning of this blog post explains things pretty well: http://multithreaded.stitchfix.com/blog/2015/08/13/wei... | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression
The rational for using WOE in logistic regression is to generate what is sometimes called the Semi-Naive Bayesian Classifier (SNBC). The beginning of this blog post explains things pretty well: http: |
10,774 | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression | Weight of Evidence (WoE) is powerful technique to perform variable transformation & selection .
It is widely used In credit scoring to measure the separation of good vs bad customers.(variables).
Advantages :: -
Handles missing values
Handles outliers
the transformation is based on logrithmic value of distribution.
No... | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression | Weight of Evidence (WoE) is powerful technique to perform variable transformation & selection .
It is widely used In credit scoring to measure the separation of good vs bad customers.(variables).
Adv | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression
Weight of Evidence (WoE) is powerful technique to perform variable transformation & selection .
It is widely used In credit scoring to measure the separation of good vs bad customers.(variables).
Advantages :: -
Handles missing values
Handles outli... | Replacing Variables by WoE (Weight of Evidence) in Logistic Regression
Weight of Evidence (WoE) is powerful technique to perform variable transformation & selection .
It is widely used In credit scoring to measure the separation of good vs bad customers.(variables).
Adv |
10,775 | Why is the normality of residuals "barely important at all" for the purpose of estimating the regression line? | For estimation normality isn't exactly an assumption, but a major consideration would be efficiency; in many cases a good linear estimator will do fine and in that case (by Gauss-Markov) the LS estimate would be the best of those things-that-would-be-okay. (If your tails are quite heavy, or very light, it may make sens... | Why is the normality of residuals "barely important at all" for the purpose of estimating the regres | For estimation normality isn't exactly an assumption, but a major consideration would be efficiency; in many cases a good linear estimator will do fine and in that case (by Gauss-Markov) the LS estima | Why is the normality of residuals "barely important at all" for the purpose of estimating the regression line?
For estimation normality isn't exactly an assumption, but a major consideration would be efficiency; in many cases a good linear estimator will do fine and in that case (by Gauss-Markov) the LS estimate would ... | Why is the normality of residuals "barely important at all" for the purpose of estimating the regres
For estimation normality isn't exactly an assumption, but a major consideration would be efficiency; in many cases a good linear estimator will do fine and in that case (by Gauss-Markov) the LS estima |
10,776 | Why is the normality of residuals "barely important at all" for the purpose of estimating the regression line? | 2: When predicting individual data points, the confidence interval around that prediction assumes that the residuals are normally distributed.
This isn't much different than the general assumption about confidence intervals -- to be valid, we need to understand the distribution, and the most common assumption is norm... | Why is the normality of residuals "barely important at all" for the purpose of estimating the regres | 2: When predicting individual data points, the confidence interval around that prediction assumes that the residuals are normally distributed.
This isn't much different than the general assumption a | Why is the normality of residuals "barely important at all" for the purpose of estimating the regression line?
2: When predicting individual data points, the confidence interval around that prediction assumes that the residuals are normally distributed.
This isn't much different than the general assumption about conf... | Why is the normality of residuals "barely important at all" for the purpose of estimating the regres
2: When predicting individual data points, the confidence interval around that prediction assumes that the residuals are normally distributed.
This isn't much different than the general assumption a |
10,777 | How can an improper prior lead to a proper posterior distribution? | We generally accept posteriors from improper priors $\pi(\theta)$ if
$$
\frac{\pi(X \mid \theta) \pi(\theta)}{\pi(X)}
$$
exists and is a valid probability distribution (i.e., it integrates exactly to 1 over the support). Essentially this boils down to $\pi(X) = \int \pi(X \mid \theta) \pi(\theta) \,d\theta$ being finit... | How can an improper prior lead to a proper posterior distribution? | We generally accept posteriors from improper priors $\pi(\theta)$ if
$$
\frac{\pi(X \mid \theta) \pi(\theta)}{\pi(X)}
$$
exists and is a valid probability distribution (i.e., it integrates exactly to | How can an improper prior lead to a proper posterior distribution?
We generally accept posteriors from improper priors $\pi(\theta)$ if
$$
\frac{\pi(X \mid \theta) \pi(\theta)}{\pi(X)}
$$
exists and is a valid probability distribution (i.e., it integrates exactly to 1 over the support). Essentially this boils down to $... | How can an improper prior lead to a proper posterior distribution?
We generally accept posteriors from improper priors $\pi(\theta)$ if
$$
\frac{\pi(X \mid \theta) \pi(\theta)}{\pi(X)}
$$
exists and is a valid probability distribution (i.e., it integrates exactly to |
10,778 | How can an improper prior lead to a proper posterior distribution? | There are a "theoretical" answer and a "pragmatic" one.
From a theroretical point of view, when a prior is improper the posterior does not exist (well, look at Matthew's answer for a sounder statement), but may be approximated by a limiting form.
If the data comprise a conditionally i.i.d. sample from the Bernoulli dis... | How can an improper prior lead to a proper posterior distribution? | There are a "theoretical" answer and a "pragmatic" one.
From a theroretical point of view, when a prior is improper the posterior does not exist (well, look at Matthew's answer for a sounder statement | How can an improper prior lead to a proper posterior distribution?
There are a "theoretical" answer and a "pragmatic" one.
From a theroretical point of view, when a prior is improper the posterior does not exist (well, look at Matthew's answer for a sounder statement), but may be approximated by a limiting form.
If the... | How can an improper prior lead to a proper posterior distribution?
There are a "theoretical" answer and a "pragmatic" one.
From a theroretical point of view, when a prior is improper the posterior does not exist (well, look at Matthew's answer for a sounder statement |
10,779 | How can an improper prior lead to a proper posterior distribution? | However, in the case of an improper prior, how do you know that the
posterior distribution actually exists?
The posterior might not be proper either. If the prior is improper and the likelihood is flat (because there are no meaningful observations), then the posterior equals the prior and is also improper.
Usually ... | How can an improper prior lead to a proper posterior distribution? | However, in the case of an improper prior, how do you know that the
posterior distribution actually exists?
The posterior might not be proper either. If the prior is improper and the likelihood is | How can an improper prior lead to a proper posterior distribution?
However, in the case of an improper prior, how do you know that the
posterior distribution actually exists?
The posterior might not be proper either. If the prior is improper and the likelihood is flat (because there are no meaningful observations),... | How can an improper prior lead to a proper posterior distribution?
However, in the case of an improper prior, how do you know that the
posterior distribution actually exists?
The posterior might not be proper either. If the prior is improper and the likelihood is |
10,780 | How to deal with high correlation among predictors in multiple regression? | The key problem is not correlation but collinearity (see works by Belsley, for instance). This is best tested using condition indexes (available in R, SAS and probably other programs as well. Correlation is neither a necessary nor a sufficient condition for collinearity. Condition indexes over 10 (per Belsley) indicat... | How to deal with high correlation among predictors in multiple regression? | The key problem is not correlation but collinearity (see works by Belsley, for instance). This is best tested using condition indexes (available in R, SAS and probably other programs as well. Correlat | How to deal with high correlation among predictors in multiple regression?
The key problem is not correlation but collinearity (see works by Belsley, for instance). This is best tested using condition indexes (available in R, SAS and probably other programs as well. Correlation is neither a necessary nor a sufficient c... | How to deal with high correlation among predictors in multiple regression?
The key problem is not correlation but collinearity (see works by Belsley, for instance). This is best tested using condition indexes (available in R, SAS and probably other programs as well. Correlat |
10,781 | Best approach for model selection Bayesian or cross-validation? | Are these approaches suitable for solving this problem (deciding how many parameters to include in your model, or selecting among a
number of models)?
Either one could be, yes. If you're interested in obtaining a model that predicts best, out of the list of models you consider, the splitting/cross-validation approa... | Best approach for model selection Bayesian or cross-validation? | Are these approaches suitable for solving this problem (deciding how many parameters to include in your model, or selecting among a
number of models)?
Either one could be, yes. If you're intereste | Best approach for model selection Bayesian or cross-validation?
Are these approaches suitable for solving this problem (deciding how many parameters to include in your model, or selecting among a
number of models)?
Either one could be, yes. If you're interested in obtaining a model that predicts best, out of the li... | Best approach for model selection Bayesian or cross-validation?
Are these approaches suitable for solving this problem (deciding how many parameters to include in your model, or selecting among a
number of models)?
Either one could be, yes. If you're intereste |
10,782 | Best approach for model selection Bayesian or cross-validation? | Optimisation is the root of all evil in statistics! ;o)
Anytime you try to select a model based on a criterion that is evaluated on a finite sample of data, you introduce a risk of over-fitting the model selection criterion and end up with a worse model than you started with. Both cross-validation and marginal likelih... | Best approach for model selection Bayesian or cross-validation? | Optimisation is the root of all evil in statistics! ;o)
Anytime you try to select a model based on a criterion that is evaluated on a finite sample of data, you introduce a risk of over-fitting the mo | Best approach for model selection Bayesian or cross-validation?
Optimisation is the root of all evil in statistics! ;o)
Anytime you try to select a model based on a criterion that is evaluated on a finite sample of data, you introduce a risk of over-fitting the model selection criterion and end up with a worse model th... | Best approach for model selection Bayesian or cross-validation?
Optimisation is the root of all evil in statistics! ;o)
Anytime you try to select a model based on a criterion that is evaluated on a finite sample of data, you introduce a risk of over-fitting the mo |
10,783 | What does "node size" refer to in the Random Forest? | A decision tree works by recursive partition of the training set. Every node $t$ of a decision tree is associated with a set of $n_t$ data points from the training set:
You might find the parameter nodesize in some random forests packages, e.g. R: This is the minimum node size, in the example above the minimum node si... | What does "node size" refer to in the Random Forest? | A decision tree works by recursive partition of the training set. Every node $t$ of a decision tree is associated with a set of $n_t$ data points from the training set:
You might find the parameter n | What does "node size" refer to in the Random Forest?
A decision tree works by recursive partition of the training set. Every node $t$ of a decision tree is associated with a set of $n_t$ data points from the training set:
You might find the parameter nodesize in some random forests packages, e.g. R: This is the minimu... | What does "node size" refer to in the Random Forest?
A decision tree works by recursive partition of the training set. Every node $t$ of a decision tree is associated with a set of $n_t$ data points from the training set:
You might find the parameter n |
10,784 | What does "node size" refer to in the Random Forest? | It is not clear if the nodesize is on the "in-bag" sampling or on the "out-of-bag" error.
If it is on the "out-of-bag" sampling, it is slightly more restrictive. | What does "node size" refer to in the Random Forest? | It is not clear if the nodesize is on the "in-bag" sampling or on the "out-of-bag" error.
If it is on the "out-of-bag" sampling, it is slightly more restrictive. | What does "node size" refer to in the Random Forest?
It is not clear if the nodesize is on the "in-bag" sampling or on the "out-of-bag" error.
If it is on the "out-of-bag" sampling, it is slightly more restrictive. | What does "node size" refer to in the Random Forest?
It is not clear if the nodesize is on the "in-bag" sampling or on the "out-of-bag" error.
If it is on the "out-of-bag" sampling, it is slightly more restrictive. |
10,785 | What are the main differences between Granger's and Pearl's causality frameworks? | Granger causality is essentially usefulness for forecasting: X is said to Granger-cause Y if Y can be better predicted using the histories of both X and Y than it can by using the history of Y alone. GC has very little to do with causality in Pearl's counterfactual sense, which involves comparisons of different states ... | What are the main differences between Granger's and Pearl's causality frameworks? | Granger causality is essentially usefulness for forecasting: X is said to Granger-cause Y if Y can be better predicted using the histories of both X and Y than it can by using the history of Y alone. | What are the main differences between Granger's and Pearl's causality frameworks?
Granger causality is essentially usefulness for forecasting: X is said to Granger-cause Y if Y can be better predicted using the histories of both X and Y than it can by using the history of Y alone. GC has very little to do with causalit... | What are the main differences between Granger's and Pearl's causality frameworks?
Granger causality is essentially usefulness for forecasting: X is said to Granger-cause Y if Y can be better predicted using the histories of both X and Y than it can by using the history of Y alone. |
10,786 | What are the main differences between Granger's and Pearl's causality frameworks? | Pearl provides a calculus for reasoning about causality, Granger provides a method for discovering potential causal relations. I will elaborate:
Pearl's work is based on what he has termed "Structural Causal Models", which is a triple M = (U, V, F). In this model U is the collection of the exogenous (background, or d... | What are the main differences between Granger's and Pearl's causality frameworks? | Pearl provides a calculus for reasoning about causality, Granger provides a method for discovering potential causal relations. I will elaborate:
Pearl's work is based on what he has termed "Structura | What are the main differences between Granger's and Pearl's causality frameworks?
Pearl provides a calculus for reasoning about causality, Granger provides a method for discovering potential causal relations. I will elaborate:
Pearl's work is based on what he has termed "Structural Causal Models", which is a triple M ... | What are the main differences between Granger's and Pearl's causality frameworks?
Pearl provides a calculus for reasoning about causality, Granger provides a method for discovering potential causal relations. I will elaborate:
Pearl's work is based on what he has termed "Structura |
10,787 | P-value in a two-tail test with asymmetric null distribution | If we look at the 2x2 exact test, and take that to be our approach, what's "more extreme" might be directly measured by 'lower likelihood'. (Agresti[1] mentions a number of approaches by various authors to computing two tailed p-values just for this case of the 2x2 Fisher exact test, of which this approach is one of th... | P-value in a two-tail test with asymmetric null distribution | If we look at the 2x2 exact test, and take that to be our approach, what's "more extreme" might be directly measured by 'lower likelihood'. (Agresti[1] mentions a number of approaches by various autho | P-value in a two-tail test with asymmetric null distribution
If we look at the 2x2 exact test, and take that to be our approach, what's "more extreme" might be directly measured by 'lower likelihood'. (Agresti[1] mentions a number of approaches by various authors to computing two tailed p-values just for this case of t... | P-value in a two-tail test with asymmetric null distribution
If we look at the 2x2 exact test, and take that to be our approach, what's "more extreme" might be directly measured by 'lower likelihood'. (Agresti[1] mentions a number of approaches by various autho |
10,788 | P-value in a two-tail test with asymmetric null distribution | A p-value's well-defined once you create a test statistic that partitions the sample space & orders the partitions according to your notions of increasing discrepancy with the null hypothesis. (Or, equivalently, once you create a set of nested rejection regions of decreasing size.) So what R. & S. are getting at is tha... | P-value in a two-tail test with asymmetric null distribution | A p-value's well-defined once you create a test statistic that partitions the sample space & orders the partitions according to your notions of increasing discrepancy with the null hypothesis. (Or, eq | P-value in a two-tail test with asymmetric null distribution
A p-value's well-defined once you create a test statistic that partitions the sample space & orders the partitions according to your notions of increasing discrepancy with the null hypothesis. (Or, equivalently, once you create a set of nested rejection regio... | P-value in a two-tail test with asymmetric null distribution
A p-value's well-defined once you create a test statistic that partitions the sample space & orders the partitions according to your notions of increasing discrepancy with the null hypothesis. (Or, eq |
10,789 | Optimal construction of day feature in neural networks | Your second representation is more traditional for categorical variables like day of week.
This is also known as creating dummy variables and is a widely used method for encoding categorical variables. If you used 1-7 encoding you're telling the model that days 4 and 5 are very similar, while days 1 and 7 are very dis... | Optimal construction of day feature in neural networks | Your second representation is more traditional for categorical variables like day of week.
This is also known as creating dummy variables and is a widely used method for encoding categorical variables | Optimal construction of day feature in neural networks
Your second representation is more traditional for categorical variables like day of week.
This is also known as creating dummy variables and is a widely used method for encoding categorical variables. If you used 1-7 encoding you're telling the model that days 4 ... | Optimal construction of day feature in neural networks
Your second representation is more traditional for categorical variables like day of week.
This is also known as creating dummy variables and is a widely used method for encoding categorical variables |
10,790 | How robust is Pearson's correlation coefficient to violations of normality? | Short answer: Very non-robust. The correlation is a measure of linear dependence, and when one variable can’t be written as a linear function of the other (and still have the given marginal distribution), you can’t have perfect (positive or negative) correlation. In fact, the possible correlations values can be severel... | How robust is Pearson's correlation coefficient to violations of normality? | Short answer: Very non-robust. The correlation is a measure of linear dependence, and when one variable can’t be written as a linear function of the other (and still have the given marginal distributi | How robust is Pearson's correlation coefficient to violations of normality?
Short answer: Very non-robust. The correlation is a measure of linear dependence, and when one variable can’t be written as a linear function of the other (and still have the given marginal distribution), you can’t have perfect (positive or neg... | How robust is Pearson's correlation coefficient to violations of normality?
Short answer: Very non-robust. The correlation is a measure of linear dependence, and when one variable can’t be written as a linear function of the other (and still have the given marginal distributi |
10,791 | How robust is Pearson's correlation coefficient to violations of normality? | What do the distributions of these variables look like (beyond being skewed)? If the only non-normality is skewness, then a transformation of some sort must help. But if these variables have a lot of lumping, then no transformation will bring them to normality. If the variable isn't continuous, the same is true.
How r... | How robust is Pearson's correlation coefficient to violations of normality? | What do the distributions of these variables look like (beyond being skewed)? If the only non-normality is skewness, then a transformation of some sort must help. But if these variables have a lot of | How robust is Pearson's correlation coefficient to violations of normality?
What do the distributions of these variables look like (beyond being skewed)? If the only non-normality is skewness, then a transformation of some sort must help. But if these variables have a lot of lumping, then no transformation will bring t... | How robust is Pearson's correlation coefficient to violations of normality?
What do the distributions of these variables look like (beyond being skewed)? If the only non-normality is skewness, then a transformation of some sort must help. But if these variables have a lot of |
10,792 | General Linear Model vs. Generalized Linear Model (with an identity link function?) | A generalized linear model specifying an identity link function and a normal family distribution is exactly equivalent to a (general) linear model. If you're getting noticeably different results from each, you're doing something wrong.
Note that specifying an identity link is not the same thing as specifying a normal d... | General Linear Model vs. Generalized Linear Model (with an identity link function?) | A generalized linear model specifying an identity link function and a normal family distribution is exactly equivalent to a (general) linear model. If you're getting noticeably different results from | General Linear Model vs. Generalized Linear Model (with an identity link function?)
A generalized linear model specifying an identity link function and a normal family distribution is exactly equivalent to a (general) linear model. If you're getting noticeably different results from each, you're doing something wrong.
... | General Linear Model vs. Generalized Linear Model (with an identity link function?)
A generalized linear model specifying an identity link function and a normal family distribution is exactly equivalent to a (general) linear model. If you're getting noticeably different results from |
10,793 | General Linear Model vs. Generalized Linear Model (with an identity link function?) | I would like to include my experience in this discussion. I have seen that a generalized linear model (specifying an identity link function and a normal family distribution) is identical to a general linear model only when you use the maximum likelihood estimate as scale parameter method. Otherwise if "fixed value = 1"... | General Linear Model vs. Generalized Linear Model (with an identity link function?) | I would like to include my experience in this discussion. I have seen that a generalized linear model (specifying an identity link function and a normal family distribution) is identical to a general | General Linear Model vs. Generalized Linear Model (with an identity link function?)
I would like to include my experience in this discussion. I have seen that a generalized linear model (specifying an identity link function and a normal family distribution) is identical to a general linear model only when you use the m... | General Linear Model vs. Generalized Linear Model (with an identity link function?)
I would like to include my experience in this discussion. I have seen that a generalized linear model (specifying an identity link function and a normal family distribution) is identical to a general |
10,794 | Can (should?) regularization techniques be used in a random effects model? | There are a few papers that deal with this question. I would look up in no special order:
Pen.LME: Howard D Bondell, Arun Krishna, and Sujit K Ghosh. Joint variable selection
for fixed and random eects in linear mixed-eects models. Biometrics,
66(4):1069-1077, 2010.
GLMMLASSO: Jurg Schelldorfer, Peter Buhlmann, Sara v... | Can (should?) regularization techniques be used in a random effects model? | There are a few papers that deal with this question. I would look up in no special order:
Pen.LME: Howard D Bondell, Arun Krishna, and Sujit K Ghosh. Joint variable selection
for fixed and random eec | Can (should?) regularization techniques be used in a random effects model?
There are a few papers that deal with this question. I would look up in no special order:
Pen.LME: Howard D Bondell, Arun Krishna, and Sujit K Ghosh. Joint variable selection
for fixed and random eects in linear mixed-eects models. Biometrics,
... | Can (should?) regularization techniques be used in a random effects model?
There are a few papers that deal with this question. I would look up in no special order:
Pen.LME: Howard D Bondell, Arun Krishna, and Sujit K Ghosh. Joint variable selection
for fixed and random eec |
10,795 | Can (should?) regularization techniques be used in a random effects model? | I always viewed ridge regression as just empirical random effects models not limited to a single categorical variable (and no fancy correlation matrices). You can almost always get the same predictions from cross validating a ridge penalty and fitting/estimating a simple random effect. In your example, you could get ... | Can (should?) regularization techniques be used in a random effects model? | I always viewed ridge regression as just empirical random effects models not limited to a single categorical variable (and no fancy correlation matrices). You can almost always get the same predictio | Can (should?) regularization techniques be used in a random effects model?
I always viewed ridge regression as just empirical random effects models not limited to a single categorical variable (and no fancy correlation matrices). You can almost always get the same predictions from cross validating a ridge penalty and ... | Can (should?) regularization techniques be used in a random effects model?
I always viewed ridge regression as just empirical random effects models not limited to a single categorical variable (and no fancy correlation matrices). You can almost always get the same predictio |
10,796 | Can (should?) regularization techniques be used in a random effects model? | I am currently thinking about a similar question. I think in application, you can do it if it works and you believe using this is reasonable. If it is a usual setting in random effects (that means, you have repeated measurements for each group), then it is just about estimation technique, which is less controversial. I... | Can (should?) regularization techniques be used in a random effects model? | I am currently thinking about a similar question. I think in application, you can do it if it works and you believe using this is reasonable. If it is a usual setting in random effects (that means, yo | Can (should?) regularization techniques be used in a random effects model?
I am currently thinking about a similar question. I think in application, you can do it if it works and you believe using this is reasonable. If it is a usual setting in random effects (that means, you have repeated measurements for each group),... | Can (should?) regularization techniques be used in a random effects model?
I am currently thinking about a similar question. I think in application, you can do it if it works and you believe using this is reasonable. If it is a usual setting in random effects (that means, yo |
10,797 | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | Likelihood is a function of $\theta$, given $x$, while $P$ is a function of $x$, given $\theta$.
Roughly like so (excuse the quick effort in MS paint):
In this sketch we have a single $x$ as our observation. Densities (functions of $x$ at some $\theta$) are in black running left to right and the likelihood functions (... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | Likelihood is a function of $\theta$, given $x$, while $P$ is a function of $x$, given $\theta$.
Roughly like so (excuse the quick effort in MS paint):
In this sketch we have a single $x$ as our obse | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
Likelihood is a function of $\theta$, given $x$, while $P$ is a function of $x$, given $\theta$.
Roughly like so (excuse the quick effort in MS paint):
In this sketch we have a single $x$ as our observation. Densities (functions of $x$ ... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
Likelihood is a function of $\theta$, given $x$, while $P$ is a function of $x$, given $\theta$.
Roughly like so (excuse the quick effort in MS paint):
In this sketch we have a single $x$ as our obse |
10,798 | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | According to the Bayesian theory, $f(\theta|x_1,...,x_n) = \frac{f(x_1,...,x_n|\theta) * f(\theta)}{f(x_1,...,x_n)}$ holds, that is $\text{posterior} = \frac{\text{likelihood} * \text{prior}}{evidence}$.
Notice that the maximum likelihood estimate omits the prior beliefs(or defaults it to zero-mean Gaussian and count ... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | According to the Bayesian theory, $f(\theta|x_1,...,x_n) = \frac{f(x_1,...,x_n|\theta) * f(\theta)}{f(x_1,...,x_n)}$ holds, that is $\text{posterior} = \frac{\text{likelihood} * \text{prior}}{evidence | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
According to the Bayesian theory, $f(\theta|x_1,...,x_n) = \frac{f(x_1,...,x_n|\theta) * f(\theta)}{f(x_1,...,x_n)}$ holds, that is $\text{posterior} = \frac{\text{likelihood} * \text{prior}}{evidence}$.
Notice that the maximum likeliho... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
According to the Bayesian theory, $f(\theta|x_1,...,x_n) = \frac{f(x_1,...,x_n|\theta) * f(\theta)}{f(x_1,...,x_n)}$ holds, that is $\text{posterior} = \frac{\text{likelihood} * \text{prior}}{evidence |
10,799 | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | I agree with @Big Agnes. Here is what my professor taught in class: One way is to think of likelihood function $L(\theta | \mathbf{x})$ as a random function which depends on the data. Different data gives us different likelihood functions. So you may say conditioning on data. Given a realization of data, we want to fin... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | I agree with @Big Agnes. Here is what my professor taught in class: One way is to think of likelihood function $L(\theta | \mathbf{x})$ as a random function which depends on the data. Different data g | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
I agree with @Big Agnes. Here is what my professor taught in class: One way is to think of likelihood function $L(\theta | \mathbf{x})$ as a random function which depends on the data. Different data gives us different likelihood function... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
I agree with @Big Agnes. Here is what my professor taught in class: One way is to think of likelihood function $L(\theta | \mathbf{x})$ as a random function which depends on the data. Different data g |
10,800 | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | I think the other answers given by jwyao and Glen_b are quite good. I just wanted to add a very simple example which is too long for a comment.
Consider one observation $X$ from a Bernoulli distribution with probability of success $\theta$. With $\theta$ fixed (known or unknown), the distribution of $X$ is given by $p(... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$? | I think the other answers given by jwyao and Glen_b are quite good. I just wanted to add a very simple example which is too long for a comment.
Consider one observation $X$ from a Bernoulli distributi | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
I think the other answers given by jwyao and Glen_b are quite good. I just wanted to add a very simple example which is too long for a comment.
Consider one observation $X$ from a Bernoulli distribution with probability of success $\thet... | Why do people use $\mathcal{L}(\theta|x)$ for likelihood instead of $P(x|\theta)$?
I think the other answers given by jwyao and Glen_b are quite good. I just wanted to add a very simple example which is too long for a comment.
Consider one observation $X$ from a Bernoulli distributi |
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