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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2,401 | What are disadvantages of using the lasso for variable selection for regression? | If you only care about prediction error and don't care about interpretability, casual-inference, model-simplicity, coefficients' tests, etc, why do you still want to use linear regression model?
You can use something like boosting on decision trees or support vector regression and get better prediction quality and sti... | What are disadvantages of using the lasso for variable selection for regression? | If you only care about prediction error and don't care about interpretability, casual-inference, model-simplicity, coefficients' tests, etc, why do you still want to use linear regression model?
You | What are disadvantages of using the lasso for variable selection for regression?
If you only care about prediction error and don't care about interpretability, casual-inference, model-simplicity, coefficients' tests, etc, why do you still want to use linear regression model?
You can use something like boosting on deci... | What are disadvantages of using the lasso for variable selection for regression?
If you only care about prediction error and don't care about interpretability, casual-inference, model-simplicity, coefficients' tests, etc, why do you still want to use linear regression model?
You |
2,402 | What are disadvantages of using the lasso for variable selection for regression? | LASSO encourages shrinking of coefficients to 0, i.e. dropping those variates from your model. On contrast, other regularization techniques like a ridge tend to keep all variates.
So I'd recommend to think about whether this dropping makes sense for your data. E.g. consider setting up a clinical diagnostic test either... | What are disadvantages of using the lasso for variable selection for regression? | LASSO encourages shrinking of coefficients to 0, i.e. dropping those variates from your model. On contrast, other regularization techniques like a ridge tend to keep all variates.
So I'd recommend to | What are disadvantages of using the lasso for variable selection for regression?
LASSO encourages shrinking of coefficients to 0, i.e. dropping those variates from your model. On contrast, other regularization techniques like a ridge tend to keep all variates.
So I'd recommend to think about whether this dropping make... | What are disadvantages of using the lasso for variable selection for regression?
LASSO encourages shrinking of coefficients to 0, i.e. dropping those variates from your model. On contrast, other regularization techniques like a ridge tend to keep all variates.
So I'd recommend to |
2,403 | What are disadvantages of using the lasso for variable selection for regression? | This is already quite an old question but I feel that in the meantime most of the answers here are quite outdated (and the one that's checked as the correct answer is plain wrong imho).
First, in terms of getting good prediction performance it is not universally true that LASSO is always better than stepwise.
The pap... | What are disadvantages of using the lasso for variable selection for regression? | This is already quite an old question but I feel that in the meantime most of the answers here are quite outdated (and the one that's checked as the correct answer is plain wrong imho).
First, in ter | What are disadvantages of using the lasso for variable selection for regression?
This is already quite an old question but I feel that in the meantime most of the answers here are quite outdated (and the one that's checked as the correct answer is plain wrong imho).
First, in terms of getting good prediction performan... | What are disadvantages of using the lasso for variable selection for regression?
This is already quite an old question but I feel that in the meantime most of the answers here are quite outdated (and the one that's checked as the correct answer is plain wrong imho).
First, in ter |
2,404 | What are disadvantages of using the lasso for variable selection for regression? | If two predictors are highly correlated LASSO can end up dropping one rather arbitrarily. That's not very good when you're wanting to make predictions for a population where those two predictors aren't highly correlated, & perhaps a reason for preferring ridge regression in those circumstances.
You might also think sta... | What are disadvantages of using the lasso for variable selection for regression? | If two predictors are highly correlated LASSO can end up dropping one rather arbitrarily. That's not very good when you're wanting to make predictions for a population where those two predictors aren' | What are disadvantages of using the lasso for variable selection for regression?
If two predictors are highly correlated LASSO can end up dropping one rather arbitrarily. That's not very good when you're wanting to make predictions for a population where those two predictors aren't highly correlated, & perhaps a reason... | What are disadvantages of using the lasso for variable selection for regression?
If two predictors are highly correlated LASSO can end up dropping one rather arbitrarily. That's not very good when you're wanting to make predictions for a population where those two predictors aren' |
2,405 | What are disadvantages of using the lasso for variable selection for regression? | Lasso is only useful if you're restricting yourself to consider models which are linear in the parameters to be estimated. Stated another way, the lasso does not evaluate whether you have chosen the correct form of the relationship between the independent and dependent variable(s).
It is very plausible that there may b... | What are disadvantages of using the lasso for variable selection for regression? | Lasso is only useful if you're restricting yourself to consider models which are linear in the parameters to be estimated. Stated another way, the lasso does not evaluate whether you have chosen the c | What are disadvantages of using the lasso for variable selection for regression?
Lasso is only useful if you're restricting yourself to consider models which are linear in the parameters to be estimated. Stated another way, the lasso does not evaluate whether you have chosen the correct form of the relationship between... | What are disadvantages of using the lasso for variable selection for regression?
Lasso is only useful if you're restricting yourself to consider models which are linear in the parameters to be estimated. Stated another way, the lasso does not evaluate whether you have chosen the c |
2,406 | What are disadvantages of using the lasso for variable selection for regression? | One practical disadvantage of lasso and other regularization techniques is finding the optimal regularization coefficient, lambda. Using cross validation to find this value can be just as expensive as stepwise selection techniques. | What are disadvantages of using the lasso for variable selection for regression? | One practical disadvantage of lasso and other regularization techniques is finding the optimal regularization coefficient, lambda. Using cross validation to find this value can be just as expensive as | What are disadvantages of using the lasso for variable selection for regression?
One practical disadvantage of lasso and other regularization techniques is finding the optimal regularization coefficient, lambda. Using cross validation to find this value can be just as expensive as stepwise selection techniques. | What are disadvantages of using the lasso for variable selection for regression?
One practical disadvantage of lasso and other regularization techniques is finding the optimal regularization coefficient, lambda. Using cross validation to find this value can be just as expensive as |
2,407 | What are disadvantages of using the lasso for variable selection for regression? | I am not a LASSO expert but I am an expert in time series. If you have time series data or spatial data then I would studiously avoid a solution that was predicated on independent observations. Furthermore if there are unknown deterministic effects that have played havoc with your data (level shifts / time trends etc) ... | What are disadvantages of using the lasso for variable selection for regression? | I am not a LASSO expert but I am an expert in time series. If you have time series data or spatial data then I would studiously avoid a solution that was predicated on independent observations. Furthe | What are disadvantages of using the lasso for variable selection for regression?
I am not a LASSO expert but I am an expert in time series. If you have time series data or spatial data then I would studiously avoid a solution that was predicated on independent observations. Furthermore if there are unknown deterministi... | What are disadvantages of using the lasso for variable selection for regression?
I am not a LASSO expert but I am an expert in time series. If you have time series data or spatial data then I would studiously avoid a solution that was predicated on independent observations. Furthe |
2,408 | What are disadvantages of using the lasso for variable selection for regression? | One big one is the difficulty of doing hypothesis testing. You can't easily figure out which variables are statistically significant with Lasso. With stepwise regression, you can do hypothesis testing to some degree, if you're careful about your treatment of multiple testing. | What are disadvantages of using the lasso for variable selection for regression? | One big one is the difficulty of doing hypothesis testing. You can't easily figure out which variables are statistically significant with Lasso. With stepwise regression, you can do hypothesis testi | What are disadvantages of using the lasso for variable selection for regression?
One big one is the difficulty of doing hypothesis testing. You can't easily figure out which variables are statistically significant with Lasso. With stepwise regression, you can do hypothesis testing to some degree, if you're careful ab... | What are disadvantages of using the lasso for variable selection for regression?
One big one is the difficulty of doing hypothesis testing. You can't easily figure out which variables are statistically significant with Lasso. With stepwise regression, you can do hypothesis testi |
2,409 | What are disadvantages of using the lasso for variable selection for regression? | I have always found variable reduction techniques hurting the predictability, especially for multi classification. Stepwise elimination methods are also not very effective with highly correlated predictors, they are time consuming too. It is a tough area to deal with and it should be done differently on case to case ba... | What are disadvantages of using the lasso for variable selection for regression? | I have always found variable reduction techniques hurting the predictability, especially for multi classification. Stepwise elimination methods are also not very effective with highly correlated predi | What are disadvantages of using the lasso for variable selection for regression?
I have always found variable reduction techniques hurting the predictability, especially for multi classification. Stepwise elimination methods are also not very effective with highly correlated predictors, they are time consuming too. It ... | What are disadvantages of using the lasso for variable selection for regression?
I have always found variable reduction techniques hurting the predictability, especially for multi classification. Stepwise elimination methods are also not very effective with highly correlated predi |
2,410 | What are disadvantages of using the lasso for variable selection for regression? | There is a simple reason why not using LASSO for variable selection. It just does not work as well as advertised. This is due to its fitting algorithm that includes a penalty factor that penalizes the model against higher regression coefficients. It seems like a good idea, as people think it always reduces model ove... | What are disadvantages of using the lasso for variable selection for regression? | There is a simple reason why not using LASSO for variable selection. It just does not work as well as advertised. This is due to its fitting algorithm that includes a penalty factor that penalizes t | What are disadvantages of using the lasso for variable selection for regression?
There is a simple reason why not using LASSO for variable selection. It just does not work as well as advertised. This is due to its fitting algorithm that includes a penalty factor that penalizes the model against higher regression coef... | What are disadvantages of using the lasso for variable selection for regression?
There is a simple reason why not using LASSO for variable selection. It just does not work as well as advertised. This is due to its fitting algorithm that includes a penalty factor that penalizes t |
2,411 | What is the intuition behind SVD? | Write the SVD of matrix $X$ (real, $n\times p$) as
$$
X = U D V^T
$$
where $U$ is $n\times p$, $D$ is diagonal $p\times p$ and $V^T$ is $p\times p$. In terms of the columns of the matrices $U$ and $V$ we can write
$X=\sum_{i=1}^p d_i u_i v_i^T$. That shows $X$ written as a sum of $p$ rank-1 matrices. What does a ran... | What is the intuition behind SVD? | Write the SVD of matrix $X$ (real, $n\times p$) as
$$
X = U D V^T
$$
where $U$ is $n\times p$, $D$ is diagonal $p\times p$ and $V^T$ is $p\times p$. In terms of the columns of the matrices $U$ and | What is the intuition behind SVD?
Write the SVD of matrix $X$ (real, $n\times p$) as
$$
X = U D V^T
$$
where $U$ is $n\times p$, $D$ is diagonal $p\times p$ and $V^T$ is $p\times p$. In terms of the columns of the matrices $U$ and $V$ we can write
$X=\sum_{i=1}^p d_i u_i v_i^T$. That shows $X$ written as a sum of $p... | What is the intuition behind SVD?
Write the SVD of matrix $X$ (real, $n\times p$) as
$$
X = U D V^T
$$
where $U$ is $n\times p$, $D$ is diagonal $p\times p$ and $V^T$ is $p\times p$. In terms of the columns of the matrices $U$ and |
2,412 | What is the intuition behind SVD? | Let $A$ be a real $m \times n$ matrix. I'll assume that $m \geq n$ for simplicity. It's natural to ask in which direction $v$ does $A$ have the most impact (or the most explosiveness, or the most amplifying power). The answer is
\begin{align}
\tag{1}v_1 = \,\,& \arg \max_{v \in \mathbb R^n} \quad \| A v \|_2 \\
& \text... | What is the intuition behind SVD? | Let $A$ be a real $m \times n$ matrix. I'll assume that $m \geq n$ for simplicity. It's natural to ask in which direction $v$ does $A$ have the most impact (or the most explosiveness, or the most ampl | What is the intuition behind SVD?
Let $A$ be a real $m \times n$ matrix. I'll assume that $m \geq n$ for simplicity. It's natural to ask in which direction $v$ does $A$ have the most impact (or the most explosiveness, or the most amplifying power). The answer is
\begin{align}
\tag{1}v_1 = \,\,& \arg \max_{v \in \mathbb... | What is the intuition behind SVD?
Let $A$ be a real $m \times n$ matrix. I'll assume that $m \geq n$ for simplicity. It's natural to ask in which direction $v$ does $A$ have the most impact (or the most explosiveness, or the most ampl |
2,413 | What is the intuition behind SVD? | Take an hour of your day and watch this lecture.
This guy is super straight-forward; It's important not to skip any of it because it all comes together in the end. Even if it might seem a little slow at the beginning, he is trying to pin down a critical point, which he does!
I'll sum it up for you, rather than just giv... | What is the intuition behind SVD? | Take an hour of your day and watch this lecture.
This guy is super straight-forward; It's important not to skip any of it because it all comes together in the end. Even if it might seem a little slow | What is the intuition behind SVD?
Take an hour of your day and watch this lecture.
This guy is super straight-forward; It's important not to skip any of it because it all comes together in the end. Even if it might seem a little slow at the beginning, he is trying to pin down a critical point, which he does!
I'll sum i... | What is the intuition behind SVD?
Take an hour of your day and watch this lecture.
This guy is super straight-forward; It's important not to skip any of it because it all comes together in the end. Even if it might seem a little slow |
2,414 | Cross-Validation in plain english? | Consider the following situation:
I want to catch the subway to go to my office. My plan is to take my car, park at the subway and then take the train to go to my office. My goal is to catch the train at 8.15 am every day so that I can reach my office on time. I need to decide the following: (a) the time at which I n... | Cross-Validation in plain english? | Consider the following situation:
I want to catch the subway to go to my office. My plan is to take my car, park at the subway and then take the train to go to my office. My goal is to catch the tra | Cross-Validation in plain english?
Consider the following situation:
I want to catch the subway to go to my office. My plan is to take my car, park at the subway and then take the train to go to my office. My goal is to catch the train at 8.15 am every day so that I can reach my office on time. I need to decide the f... | Cross-Validation in plain english?
Consider the following situation:
I want to catch the subway to go to my office. My plan is to take my car, park at the subway and then take the train to go to my office. My goal is to catch the tra |
2,415 | Cross-Validation in plain english? | I think that this is best described with the following picture (in this case showing k-fold cross-validation):
Cross-validation is a technique used to protect against overfitting in a predictive model, particularly in a case where the amount of data may be limited. In cross-validation, you make a fixed number of fold... | Cross-Validation in plain english? | I think that this is best described with the following picture (in this case showing k-fold cross-validation):
Cross-validation is a technique used to protect against overfitting in a predictive mode | Cross-Validation in plain english?
I think that this is best described with the following picture (in this case showing k-fold cross-validation):
Cross-validation is a technique used to protect against overfitting in a predictive model, particularly in a case where the amount of data may be limited. In cross-validati... | Cross-Validation in plain english?
I think that this is best described with the following picture (in this case showing k-fold cross-validation):
Cross-validation is a technique used to protect against overfitting in a predictive mode |
2,416 | Cross-Validation in plain english? | "Avoid learning your training data by heart by making sure the trained model performs well on independent data." | Cross-Validation in plain english? | "Avoid learning your training data by heart by making sure the trained model performs well on independent data." | Cross-Validation in plain english?
"Avoid learning your training data by heart by making sure the trained model performs well on independent data." | Cross-Validation in plain english?
"Avoid learning your training data by heart by making sure the trained model performs well on independent data." |
2,417 | Cross-Validation in plain english? | Let's say you investigate some process; you've gathered some data describing it and you have build a model (either statistical or ML, doesn't matter). But now, how to judge if it is ok? Probably it fits suspiciously good to the data it was build on, so no-one will believe that your model is so splendid that you think.
... | Cross-Validation in plain english? | Let's say you investigate some process; you've gathered some data describing it and you have build a model (either statistical or ML, doesn't matter). But now, how to judge if it is ok? Probably it fi | Cross-Validation in plain english?
Let's say you investigate some process; you've gathered some data describing it and you have build a model (either statistical or ML, doesn't matter). But now, how to judge if it is ok? Probably it fits suspiciously good to the data it was build on, so no-one will believe that your mo... | Cross-Validation in plain english?
Let's say you investigate some process; you've gathered some data describing it and you have build a model (either statistical or ML, doesn't matter). But now, how to judge if it is ok? Probably it fi |
2,418 | Cross-Validation in plain english? | Since you don't have access to the test data at the time of training, and you want your model to do well on the unseen test data, you "pretend" that you have access to some test data by repeatedly subsampling a small part of your training data, hold out this set while training the model, and then treating the held out ... | Cross-Validation in plain english? | Since you don't have access to the test data at the time of training, and you want your model to do well on the unseen test data, you "pretend" that you have access to some test data by repeatedly sub | Cross-Validation in plain english?
Since you don't have access to the test data at the time of training, and you want your model to do well on the unseen test data, you "pretend" that you have access to some test data by repeatedly subsampling a small part of your training data, hold out this set while training the mod... | Cross-Validation in plain english?
Since you don't have access to the test data at the time of training, and you want your model to do well on the unseen test data, you "pretend" that you have access to some test data by repeatedly sub |
2,419 | Line of best fit does not look like a good fit. Why? | Is there a dependent variable?
The trend line in Excel is from the regression of the dependent variable "lat" on independent variable "lon." What you call a "common sense line" can be obtained when you don't designate dependent variable, and treat both the latitude and longitude equally. The latter can be obtained by a... | Line of best fit does not look like a good fit. Why? | Is there a dependent variable?
The trend line in Excel is from the regression of the dependent variable "lat" on independent variable "lon." What you call a "common sense line" can be obtained when yo | Line of best fit does not look like a good fit. Why?
Is there a dependent variable?
The trend line in Excel is from the regression of the dependent variable "lat" on independent variable "lon." What you call a "common sense line" can be obtained when you don't designate dependent variable, and treat both the latitude a... | Line of best fit does not look like a good fit. Why?
Is there a dependent variable?
The trend line in Excel is from the regression of the dependent variable "lat" on independent variable "lon." What you call a "common sense line" can be obtained when yo |
2,420 | Line of best fit does not look like a good fit. Why? | The answer probably has to do with how you are mentally judging the distance to the regression line. Standard (Type 1) regression minimizes the squared error, where error is calculated based on vertical distance to the line.
Type 2 regression may be more analogous to your judgement of the best line. In it, the squared... | Line of best fit does not look like a good fit. Why? | The answer probably has to do with how you are mentally judging the distance to the regression line. Standard (Type 1) regression minimizes the squared error, where error is calculated based on vertic | Line of best fit does not look like a good fit. Why?
The answer probably has to do with how you are mentally judging the distance to the regression line. Standard (Type 1) regression minimizes the squared error, where error is calculated based on vertical distance to the line.
Type 2 regression may be more analogous t... | Line of best fit does not look like a good fit. Why?
The answer probably has to do with how you are mentally judging the distance to the regression line. Standard (Type 1) regression minimizes the squared error, where error is calculated based on vertic |
2,421 | Line of best fit does not look like a good fit. Why? | The question that Excel tries to answer is: "Assuming that y is dependent on x, which line predicts y best". The answer is that because of the huge variations in y, no line could possibly be particularly good, and what Excel displays is the best you can do.
If you take your proposed red line, and continue you it up to... | Line of best fit does not look like a good fit. Why? | The question that Excel tries to answer is: "Assuming that y is dependent on x, which line predicts y best". The answer is that because of the huge variations in y, no line could possibly be particula | Line of best fit does not look like a good fit. Why?
The question that Excel tries to answer is: "Assuming that y is dependent on x, which line predicts y best". The answer is that because of the huge variations in y, no line could possibly be particularly good, and what Excel displays is the best you can do.
If you t... | Line of best fit does not look like a good fit. Why?
The question that Excel tries to answer is: "Assuming that y is dependent on x, which line predicts y best". The answer is that because of the huge variations in y, no line could possibly be particula |
2,422 | Line of best fit does not look like a good fit. Why? | I don't want to add anything to the other answers, but I do want to say that you have been led astray by bad terminology, in particular the term "line of best fit" which is used in some statistics courses.
Intuitively, a "line of best fit" would look like your red line. But the line produced by Excel is not a "line of ... | Line of best fit does not look like a good fit. Why? | I don't want to add anything to the other answers, but I do want to say that you have been led astray by bad terminology, in particular the term "line of best fit" which is used in some statistics cou | Line of best fit does not look like a good fit. Why?
I don't want to add anything to the other answers, but I do want to say that you have been led astray by bad terminology, in particular the term "line of best fit" which is used in some statistics courses.
Intuitively, a "line of best fit" would look like your red li... | Line of best fit does not look like a good fit. Why?
I don't want to add anything to the other answers, but I do want to say that you have been led astray by bad terminology, in particular the term "line of best fit" which is used in some statistics cou |
2,423 | Line of best fit does not look like a good fit. Why? | Part of the optical issue comes from the different scales - if you use the same scale on both axis, it will look already different.
In other words, you can make most such ‘best fit‘ lines look ‘unintuitive’ by spreading one axis scale out. | Line of best fit does not look like a good fit. Why? | Part of the optical issue comes from the different scales - if you use the same scale on both axis, it will look already different.
In other words, you can make most such ‘best fit‘ lines look ‘unintu | Line of best fit does not look like a good fit. Why?
Part of the optical issue comes from the different scales - if you use the same scale on both axis, it will look already different.
In other words, you can make most such ‘best fit‘ lines look ‘unintuitive’ by spreading one axis scale out. | Line of best fit does not look like a good fit. Why?
Part of the optical issue comes from the different scales - if you use the same scale on both axis, it will look already different.
In other words, you can make most such ‘best fit‘ lines look ‘unintu |
2,424 | Line of best fit does not look like a good fit. Why? | A few individuals have noted that the problem is visual - the graphical scaling employed produces misleading information. More specifically, the scaling of "lon" is such that it it appears to be a tight spiral which suggests the regression line provides a poor fit (an assessment to which I agree, the red line you draw ... | Line of best fit does not look like a good fit. Why? | A few individuals have noted that the problem is visual - the graphical scaling employed produces misleading information. More specifically, the scaling of "lon" is such that it it appears to be a tig | Line of best fit does not look like a good fit. Why?
A few individuals have noted that the problem is visual - the graphical scaling employed produces misleading information. More specifically, the scaling of "lon" is such that it it appears to be a tight spiral which suggests the regression line provides a poor fit (a... | Line of best fit does not look like a good fit. Why?
A few individuals have noted that the problem is visual - the graphical scaling employed produces misleading information. More specifically, the scaling of "lon" is such that it it appears to be a tig |
2,425 | Line of best fit does not look like a good fit. Why? | Your confuse ordinary least squares (OLS) regression (which minimizes the sum of the squared deviation about the predicted values, (observed-predicted)^2) and major axis regression (which minimizes the sums of squares of the perpendicular distance between each point and the regression line, sometimes this is referred t... | Line of best fit does not look like a good fit. Why? | Your confuse ordinary least squares (OLS) regression (which minimizes the sum of the squared deviation about the predicted values, (observed-predicted)^2) and major axis regression (which minimizes th | Line of best fit does not look like a good fit. Why?
Your confuse ordinary least squares (OLS) regression (which minimizes the sum of the squared deviation about the predicted values, (observed-predicted)^2) and major axis regression (which minimizes the sums of squares of the perpendicular distance between each point ... | Line of best fit does not look like a good fit. Why?
Your confuse ordinary least squares (OLS) regression (which minimizes the sum of the squared deviation about the predicted values, (observed-predicted)^2) and major axis regression (which minimizes th |
2,426 | How to normalize data between -1 and 1? | With:
$$
x' = \frac{x - \min{x}}{\max{x} - \min{x}}
$$
you normalize your feature $x$ in $[0,1]$.
To normalize in $[-1,1]$ you can use:
$$
x'' = 2\frac{x - \min{x}}{\max{x} - \min{x}} - 1
$$
In general, you can always get a new variable $x'''$ in $[a,b]$:
$$
x''' = (b-a)\frac{x - \min{x}}{\max{x} - \min{x}} + a
$$
And ... | How to normalize data between -1 and 1? | With:
$$
x' = \frac{x - \min{x}}{\max{x} - \min{x}}
$$
you normalize your feature $x$ in $[0,1]$.
To normalize in $[-1,1]$ you can use:
$$
x'' = 2\frac{x - \min{x}}{\max{x} - \min{x}} - 1
$$
In genera | How to normalize data between -1 and 1?
With:
$$
x' = \frac{x - \min{x}}{\max{x} - \min{x}}
$$
you normalize your feature $x$ in $[0,1]$.
To normalize in $[-1,1]$ you can use:
$$
x'' = 2\frac{x - \min{x}}{\max{x} - \min{x}} - 1
$$
In general, you can always get a new variable $x'''$ in $[a,b]$:
$$
x''' = (b-a)\frac{x -... | How to normalize data between -1 and 1?
With:
$$
x' = \frac{x - \min{x}}{\max{x} - \min{x}}
$$
you normalize your feature $x$ in $[0,1]$.
To normalize in $[-1,1]$ you can use:
$$
x'' = 2\frac{x - \min{x}}{\max{x} - \min{x}} - 1
$$
In genera |
2,427 | How to normalize data between -1 and 1? | I tested on randomly generated data, and
\begin{equation}
X_{out} = (b-a)\frac{X_{in} - \min{X_{in}}}{\max{X_{in}} - \min{X_{in}}} + a
\end{equation}
does not preserve the shape of the distribution. Would really like to see the proper derivation of this using functions of random variables.
The approach that did pr... | How to normalize data between -1 and 1? | I tested on randomly generated data, and
\begin{equation}
X_{out} = (b-a)\frac{X_{in} - \min{X_{in}}}{\max{X_{in}} - \min{X_{in}}} + a
\end{equation}
does not preserve the shape of the distributi | How to normalize data between -1 and 1?
I tested on randomly generated data, and
\begin{equation}
X_{out} = (b-a)\frac{X_{in} - \min{X_{in}}}{\max{X_{in}} - \min{X_{in}}} + a
\end{equation}
does not preserve the shape of the distribution. Would really like to see the proper derivation of this using functions of ra... | How to normalize data between -1 and 1?
I tested on randomly generated data, and
\begin{equation}
X_{out} = (b-a)\frac{X_{in} - \min{X_{in}}}{\max{X_{in}} - \min{X_{in}}} + a
\end{equation}
does not preserve the shape of the distributi |
2,428 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | If you check the references below you'll find quite a bit of variation in the background, though there are some common elements.
Those numbers are at least partly based on some comments from Fisher, where he said
(while discussing a level of 1/20)
It is convenient to take this point as a limit in judging
whether... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | If you check the references below you'll find quite a bit of variation in the background, though there are some common elements.
Those numbers are at least partly based on some comments from Fisher, w | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
If you check the references below you'll find quite a bit of variation in the background, though there are some common elements.
Those numbers are at least partly based on some comments from Fisher, where he said
(while discussing a level of 1/20)
It is conveni... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
If you check the references below you'll find quite a bit of variation in the background, though there are some common elements.
Those numbers are at least partly based on some comments from Fisher, w |
2,429 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | I have to give a non-answer (same as here):
"... surely, God loves the .06 nearly as much as the .05. Can there be
any doubt that God views the strength of evidence for or against the
null as a fairly continuous function of the magnitude of p?" (p.1277)
Rosnow, R. L., & Rosenthal, R. (1989). Statistical procedure... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | I have to give a non-answer (same as here):
"... surely, God loves the .06 nearly as much as the .05. Can there be
any doubt that God views the strength of evidence for or against the
null as a f | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
I have to give a non-answer (same as here):
"... surely, God loves the .06 nearly as much as the .05. Can there be
any doubt that God views the strength of evidence for or against the
null as a fairly continuous function of the magnitude of p?" (p.1277)
Rosnow... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
I have to give a non-answer (same as here):
"... surely, God loves the .06 nearly as much as the .05. Can there be
any doubt that God views the strength of evidence for or against the
null as a f |
2,430 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | I believe there is some underlying psychology for the 5%. I have to say I don't remember where I picked this up, but here's the exercise I used to do with every undergrad intro stats class.
Imagine a stranger approaches you in a pub and tells you: "I have a biased coin that produces heads more often than tails. Would ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | I believe there is some underlying psychology for the 5%. I have to say I don't remember where I picked this up, but here's the exercise I used to do with every undergrad intro stats class.
Imagine a | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
I believe there is some underlying psychology for the 5%. I have to say I don't remember where I picked this up, but here's the exercise I used to do with every undergrad intro stats class.
Imagine a stranger approaches you in a pub and tells you: "I have a biased ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
I believe there is some underlying psychology for the 5%. I have to say I don't remember where I picked this up, but here's the exercise I used to do with every undergrad intro stats class.
Imagine a |
2,431 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | 5% seems to have been rounded from 4.56% by Fisher, corresponding to "the tail areas of the curve beyond the mean plus three or minus three probable errors" (Hurlbert & Lombardi, 2009).
Another element of the story seems to be the reproduction of tables with critical vlaues (Pearson et al., 1990; Lehmann, 1993). Fisher... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | 5% seems to have been rounded from 4.56% by Fisher, corresponding to "the tail areas of the curve beyond the mean plus three or minus three probable errors" (Hurlbert & Lombardi, 2009).
Another elemen | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
5% seems to have been rounded from 4.56% by Fisher, corresponding to "the tail areas of the curve beyond the mean plus three or minus three probable errors" (Hurlbert & Lombardi, 2009).
Another element of the story seems to be the reproduction of tables with critica... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
5% seems to have been rounded from 4.56% by Fisher, corresponding to "the tail areas of the curve beyond the mean plus three or minus three probable errors" (Hurlbert & Lombardi, 2009).
Another elemen |
2,432 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | Seems to me the answer is more in the game theory of research than in the statistics. Having 1% and 5% burned into the general consciousness means that researchers aren't effectively free to choose significance levels that suit their predispositions. Say we saw a paper with a p-value of .055 and where the significance ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | Seems to me the answer is more in the game theory of research than in the statistics. Having 1% and 5% burned into the general consciousness means that researchers aren't effectively free to choose si | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
Seems to me the answer is more in the game theory of research than in the statistics. Having 1% and 5% burned into the general consciousness means that researchers aren't effectively free to choose significance levels that suit their predispositions. Say we saw a pa... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
Seems to me the answer is more in the game theory of research than in the statistics. Having 1% and 5% burned into the general consciousness means that researchers aren't effectively free to choose si |
2,433 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | The only correct number is .04284731
...which is a flippant response intended to mean that the choice of .05 is essentially arbitrary. I usually just report the p value, rather than what the p value is greater or less than.
"Significance" is a continuous variable, and, in my opinion, discretizing it often does more ha... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | The only correct number is .04284731
...which is a flippant response intended to mean that the choice of .05 is essentially arbitrary. I usually just report the p value, rather than what the p value | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
The only correct number is .04284731
...which is a flippant response intended to mean that the choice of .05 is essentially arbitrary. I usually just report the p value, rather than what the p value is greater or less than.
"Significance" is a continuous variable, ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
The only correct number is .04284731
...which is a flippant response intended to mean that the choice of .05 is essentially arbitrary. I usually just report the p value, rather than what the p value |
2,434 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | My personal hypothesis is that 0.05 (or 1 in 20) is associated with a t/z value of (very close to) 2. Using 2 is nice, because it's very easy to spot if your result is statistically significant. There aren't other confluences of round numbers. | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | My personal hypothesis is that 0.05 (or 1 in 20) is associated with a t/z value of (very close to) 2. Using 2 is nice, because it's very easy to spot if your result is statistically significant. There | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
My personal hypothesis is that 0.05 (or 1 in 20) is associated with a t/z value of (very close to) 2. Using 2 is nice, because it's very easy to spot if your result is statistically significant. There aren't other confluences of round numbers. | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
My personal hypothesis is that 0.05 (or 1 in 20) is associated with a t/z value of (very close to) 2. Using 2 is nice, because it's very easy to spot if your result is statistically significant. There |
2,435 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | A recent article sheds some light on the arbitrariness of $p$-values; the selection of two thresholds was motivated, at least in part, as a work-around to a dispute over publishing rights. Briefly, Fisher sought to use continuous-valued $p$-values as a characterization of strength of evidence. But he would not be able ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | A recent article sheds some light on the arbitrariness of $p$-values; the selection of two thresholds was motivated, at least in part, as a work-around to a dispute over publishing rights. Briefly, Fi | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
A recent article sheds some light on the arbitrariness of $p$-values; the selection of two thresholds was motivated, at least in part, as a work-around to a dispute over publishing rights. Briefly, Fisher sought to use continuous-valued $p$-values as a characterizat... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
A recent article sheds some light on the arbitrariness of $p$-values; the selection of two thresholds was motivated, at least in part, as a work-around to a dispute over publishing rights. Briefly, Fi |
2,436 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | This is an area of hypothesis testing that has always fascinated me. Specifically because one day someone decided on some arbitrary number that dichotomized the testing procedure and since then people rarely question it.
I remember having a lecturer tell us not to put too much faith in the the Staiger and Stock test o... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | This is an area of hypothesis testing that has always fascinated me. Specifically because one day someone decided on some arbitrary number that dichotomized the testing procedure and since then people | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
This is an area of hypothesis testing that has always fascinated me. Specifically because one day someone decided on some arbitrary number that dichotomized the testing procedure and since then people rarely question it.
I remember having a lecturer tell us not to ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
This is an area of hypothesis testing that has always fascinated me. Specifically because one day someone decided on some arbitrary number that dichotomized the testing procedure and since then people |
2,437 | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | Why 1 and 5? Because they feel right.
I'm sure there are studies on the emotional value and cognitive salience of specific numbers, but we can understand the choice of 1 and 5 without having to resort to research.
The people that created today's statistics were born, raised and live in a decimal world. Of course there ... | Regarding p-values, why 1% and 5%? Why not 6% or 10%? | Why 1 and 5? Because they feel right.
I'm sure there are studies on the emotional value and cognitive salience of specific numbers, but we can understand the choice of 1 and 5 without having to resort | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
Why 1 and 5? Because they feel right.
I'm sure there are studies on the emotional value and cognitive salience of specific numbers, but we can understand the choice of 1 and 5 without having to resort to research.
The people that created today's statistics were born... | Regarding p-values, why 1% and 5%? Why not 6% or 10%?
Why 1 and 5? Because they feel right.
I'm sure there are studies on the emotional value and cognitive salience of specific numbers, but we can understand the choice of 1 and 5 without having to resort |
2,438 | Please explain the waiting paradox | As Glen_b pointed out, if the buses arrive every $15$ minutes without any uncertainty whatsoever, we know that the maximum possible waiting time is $15$ minutes. If from our part we arrive "at random", we feel that "on average" we will wait half the maximum possible waiting time. And the maximum possible waiting time i... | Please explain the waiting paradox | As Glen_b pointed out, if the buses arrive every $15$ minutes without any uncertainty whatsoever, we know that the maximum possible waiting time is $15$ minutes. If from our part we arrive "at random" | Please explain the waiting paradox
As Glen_b pointed out, if the buses arrive every $15$ minutes without any uncertainty whatsoever, we know that the maximum possible waiting time is $15$ minutes. If from our part we arrive "at random", we feel that "on average" we will wait half the maximum possible waiting time. And ... | Please explain the waiting paradox
As Glen_b pointed out, if the buses arrive every $15$ minutes without any uncertainty whatsoever, we know that the maximum possible waiting time is $15$ minutes. If from our part we arrive "at random" |
2,439 | Please explain the waiting paradox | If the bus arrives "every 15 minutes" (i.e. on a schedule) then the (randomly arriving) passenger's average wait is indeed only 7.5 minutes, because it will be uniformly distributed in that 15 minute gap.
--
If, on the other hand, the bus arrives randomly at the average rate of 4 per hour (i.e. according to a Poisson p... | Please explain the waiting paradox | If the bus arrives "every 15 minutes" (i.e. on a schedule) then the (randomly arriving) passenger's average wait is indeed only 7.5 minutes, because it will be uniformly distributed in that 15 minute | Please explain the waiting paradox
If the bus arrives "every 15 minutes" (i.e. on a schedule) then the (randomly arriving) passenger's average wait is indeed only 7.5 minutes, because it will be uniformly distributed in that 15 minute gap.
--
If, on the other hand, the bus arrives randomly at the average rate of 4 per ... | Please explain the waiting paradox
If the bus arrives "every 15 minutes" (i.e. on a schedule) then the (randomly arriving) passenger's average wait is indeed only 7.5 minutes, because it will be uniformly distributed in that 15 minute |
2,440 | Please explain the waiting paradox | More on buses... Sorry to butt into the conversation so late in the discussion, but I have been looking at Poisson processes lately... So before it slips out of my mind, here is a pictorial representation of the inspection paradox:
The fallacy stems from the assumption that since buses follow a certain pattern of arriv... | Please explain the waiting paradox | More on buses... Sorry to butt into the conversation so late in the discussion, but I have been looking at Poisson processes lately... So before it slips out of my mind, here is a pictorial representa | Please explain the waiting paradox
More on buses... Sorry to butt into the conversation so late in the discussion, but I have been looking at Poisson processes lately... So before it slips out of my mind, here is a pictorial representation of the inspection paradox:
The fallacy stems from the assumption that since buse... | Please explain the waiting paradox
More on buses... Sorry to butt into the conversation so late in the discussion, but I have been looking at Poisson processes lately... So before it slips out of my mind, here is a pictorial representa |
2,441 | Please explain the waiting paradox | There is a simple explanation which resolves the different answers which one gets from calculating expected waiting time for buses arriving per a Poisson Process with given mean interarrival time (in this case 15 minutes), whose interarrival times are therefore i.i.d. exponential with mean of 15 minutes.
Method 1) Beca... | Please explain the waiting paradox | There is a simple explanation which resolves the different answers which one gets from calculating expected waiting time for buses arriving per a Poisson Process with given mean interarrival time (in | Please explain the waiting paradox
There is a simple explanation which resolves the different answers which one gets from calculating expected waiting time for buses arriving per a Poisson Process with given mean interarrival time (in this case 15 minutes), whose interarrival times are therefore i.i.d. exponential with... | Please explain the waiting paradox
There is a simple explanation which resolves the different answers which one gets from calculating expected waiting time for buses arriving per a Poisson Process with given mean interarrival time (in |
2,442 | Please explain the waiting paradox | The question as posed was "...a bus arrives at the bus stop every 15 minutes and a passenger arrives at random." If the bus arrives every 15 minutes then its not random; it arrives every 15 minutes so the correct answer is 7.5 minutes. Either the source was incorrectly quoted or the writer of the source was sloppy.
O... | Please explain the waiting paradox | The question as posed was "...a bus arrives at the bus stop every 15 minutes and a passenger arrives at random." If the bus arrives every 15 minutes then its not random; it arrives every 15 minutes s | Please explain the waiting paradox
The question as posed was "...a bus arrives at the bus stop every 15 minutes and a passenger arrives at random." If the bus arrives every 15 minutes then its not random; it arrives every 15 minutes so the correct answer is 7.5 minutes. Either the source was incorrectly quoted or the... | Please explain the waiting paradox
The question as posed was "...a bus arrives at the bus stop every 15 minutes and a passenger arrives at random." If the bus arrives every 15 minutes then its not random; it arrives every 15 minutes s |
2,443 | Mathematician wants the equivalent knowledge to a quality stats degree | (Very) short story
Long story short, in some sense, statistics is like any other technical field: There is no fast track.
Long story
Bachelor's degree programs in statistics are relatively rare in the U.S. One reason I believe this is true is that it is quite hard to pack all that is necessary to learn statistics well ... | Mathematician wants the equivalent knowledge to a quality stats degree | (Very) short story
Long story short, in some sense, statistics is like any other technical field: There is no fast track.
Long story
Bachelor's degree programs in statistics are relatively rare in the | Mathematician wants the equivalent knowledge to a quality stats degree
(Very) short story
Long story short, in some sense, statistics is like any other technical field: There is no fast track.
Long story
Bachelor's degree programs in statistics are relatively rare in the U.S. One reason I believe this is true is that i... | Mathematician wants the equivalent knowledge to a quality stats degree
(Very) short story
Long story short, in some sense, statistics is like any other technical field: There is no fast track.
Long story
Bachelor's degree programs in statistics are relatively rare in the |
2,444 | Mathematician wants the equivalent knowledge to a quality stats degree | I can't speak for the more rigorous schools, but I am doing a B.S. in General Statistics (the most rigorous at my school) at University of California, Davis, and there is a fairly heavy amount of reliance on rigor and derivation. A doctorate in math will be helpful, insomuch as you will have a very strong background in... | Mathematician wants the equivalent knowledge to a quality stats degree | I can't speak for the more rigorous schools, but I am doing a B.S. in General Statistics (the most rigorous at my school) at University of California, Davis, and there is a fairly heavy amount of reli | Mathematician wants the equivalent knowledge to a quality stats degree
I can't speak for the more rigorous schools, but I am doing a B.S. in General Statistics (the most rigorous at my school) at University of California, Davis, and there is a fairly heavy amount of reliance on rigor and derivation. A doctorate in math... | Mathematician wants the equivalent knowledge to a quality stats degree
I can't speak for the more rigorous schools, but I am doing a B.S. in General Statistics (the most rigorous at my school) at University of California, Davis, and there is a fairly heavy amount of reli |
2,445 | Mathematician wants the equivalent knowledge to a quality stats degree | The Royal Statistical Society in the UK offers the Graduate Diploma in Statistics, which is at the level of a good Bachelor's degree. A syllabus, reading list, & past papers are available from their website. I've known mathematicians use it to get up to speed in Statistics. Taking the exams (officially, or in the comfo... | Mathematician wants the equivalent knowledge to a quality stats degree | The Royal Statistical Society in the UK offers the Graduate Diploma in Statistics, which is at the level of a good Bachelor's degree. A syllabus, reading list, & past papers are available from their w | Mathematician wants the equivalent knowledge to a quality stats degree
The Royal Statistical Society in the UK offers the Graduate Diploma in Statistics, which is at the level of a good Bachelor's degree. A syllabus, reading list, & past papers are available from their website. I've known mathematicians use it to get u... | Mathematician wants the equivalent knowledge to a quality stats degree
The Royal Statistical Society in the UK offers the Graduate Diploma in Statistics, which is at the level of a good Bachelor's degree. A syllabus, reading list, & past papers are available from their w |
2,446 | Mathematician wants the equivalent knowledge to a quality stats degree | I would go to the curriculum websites of the top stats schools, write down the books they use in their undergrad courses, see which ones are highly rated on Amazon, and order them at your public/university library.
Some schools to consider:
MIT - technically, cross-taught with Harvard.
Caltech
Carnegie Mellon
Stanfor... | Mathematician wants the equivalent knowledge to a quality stats degree | I would go to the curriculum websites of the top stats schools, write down the books they use in their undergrad courses, see which ones are highly rated on Amazon, and order them at your public/unive | Mathematician wants the equivalent knowledge to a quality stats degree
I would go to the curriculum websites of the top stats schools, write down the books they use in their undergrad courses, see which ones are highly rated on Amazon, and order them at your public/university library.
Some schools to consider:
MIT - t... | Mathematician wants the equivalent knowledge to a quality stats degree
I would go to the curriculum websites of the top stats schools, write down the books they use in their undergrad courses, see which ones are highly rated on Amazon, and order them at your public/unive |
2,447 | Mathematician wants the equivalent knowledge to a quality stats degree | I have seen Statistical Inference, by Silvey, used by mathematicians who needed some workaday grasp of statistics. It's a small book, and should by rights be cheap. Looking at http://www.amazon.com/Statistical-Inference-Monographs-Statistics-Probability/dp/0412138204/ref=sr_1_1?ie=UTF8&s=books&qid=1298750064&sr=1-1, it... | Mathematician wants the equivalent knowledge to a quality stats degree | I have seen Statistical Inference, by Silvey, used by mathematicians who needed some workaday grasp of statistics. It's a small book, and should by rights be cheap. Looking at http://www.amazon.com/St | Mathematician wants the equivalent knowledge to a quality stats degree
I have seen Statistical Inference, by Silvey, used by mathematicians who needed some workaday grasp of statistics. It's a small book, and should by rights be cheap. Looking at http://www.amazon.com/Statistical-Inference-Monographs-Statistics-Probabi... | Mathematician wants the equivalent knowledge to a quality stats degree
I have seen Statistical Inference, by Silvey, used by mathematicians who needed some workaday grasp of statistics. It's a small book, and should by rights be cheap. Looking at http://www.amazon.com/St |
2,448 | Mathematician wants the equivalent knowledge to a quality stats degree | Regarding the measurement of your knowledge: You could attend some data mining / data analysis competitions, such as 1, 2, 3, 4, and see how you score compared to others.
There are a lot of pointers to textbooks on mathematical statistics in the answers. I would like to add as relevant topics:
the empirical social res... | Mathematician wants the equivalent knowledge to a quality stats degree | Regarding the measurement of your knowledge: You could attend some data mining / data analysis competitions, such as 1, 2, 3, 4, and see how you score compared to others.
There are a lot of pointers t | Mathematician wants the equivalent knowledge to a quality stats degree
Regarding the measurement of your knowledge: You could attend some data mining / data analysis competitions, such as 1, 2, 3, 4, and see how you score compared to others.
There are a lot of pointers to textbooks on mathematical statistics in the ans... | Mathematician wants the equivalent knowledge to a quality stats degree
Regarding the measurement of your knowledge: You could attend some data mining / data analysis competitions, such as 1, 2, 3, 4, and see how you score compared to others.
There are a lot of pointers t |
2,449 | Mathematician wants the equivalent knowledge to a quality stats degree | E.T. Jaynes "Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1", Cambridge University Press, 2003 is pretty much a must-read for the Bayesian side of statistics, at about the right level. I'm looking forward to recommendations for the frequentist side of things (I have loads of mon... | Mathematician wants the equivalent knowledge to a quality stats degree | E.T. Jaynes "Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1", Cambridge University Press, 2003 is pretty much a must-read for the Bayesian side of statistics, a | Mathematician wants the equivalent knowledge to a quality stats degree
E.T. Jaynes "Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1", Cambridge University Press, 2003 is pretty much a must-read for the Bayesian side of statistics, at about the right level. I'm looking forward to ... | Mathematician wants the equivalent knowledge to a quality stats degree
E.T. Jaynes "Probability Theory: The Logic of Science: Principles and Elementary Applications Vol 1", Cambridge University Press, 2003 is pretty much a must-read for the Bayesian side of statistics, a |
2,450 | Mathematician wants the equivalent knowledge to a quality stats degree | I come from a computer science background focusing on machine learning.
However, I really started to understand (and more important to apply) statistics after taking a Pattern Recognition course using Bishop's Book
https://www.microsoft.com/en-us/research/people/cmbishop/#!prml-book
here are some course slides from MI... | Mathematician wants the equivalent knowledge to a quality stats degree | I come from a computer science background focusing on machine learning.
However, I really started to understand (and more important to apply) statistics after taking a Pattern Recognition course usin | Mathematician wants the equivalent knowledge to a quality stats degree
I come from a computer science background focusing on machine learning.
However, I really started to understand (and more important to apply) statistics after taking a Pattern Recognition course using Bishop's Book
https://www.microsoft.com/en-us/r... | Mathematician wants the equivalent knowledge to a quality stats degree
I come from a computer science background focusing on machine learning.
However, I really started to understand (and more important to apply) statistics after taking a Pattern Recognition course usin |
2,451 | Mathematician wants the equivalent knowledge to a quality stats degree | I think Stanford provides the best resources when it comes to flexibility. They even have a machine learning course online that would provide you with a respectable base of knowledge when it comes to designing algorithms in R. Search it up on Google and it will redirect you to their Lagunita page where they have some i... | Mathematician wants the equivalent knowledge to a quality stats degree | I think Stanford provides the best resources when it comes to flexibility. They even have a machine learning course online that would provide you with a respectable base of knowledge when it comes to | Mathematician wants the equivalent knowledge to a quality stats degree
I think Stanford provides the best resources when it comes to flexibility. They even have a machine learning course online that would provide you with a respectable base of knowledge when it comes to designing algorithms in R. Search it up on Google... | Mathematician wants the equivalent knowledge to a quality stats degree
I think Stanford provides the best resources when it comes to flexibility. They even have a machine learning course online that would provide you with a respectable base of knowledge when it comes to |
2,452 | Basic question about Fisher Information matrix and relationship to Hessian and standard errors | Yudi Pawitan writes in his book In All Likelihood that the second derivative of the log-likelihood evaluated at the maximum likelihood estimates (MLE) is the observed Fisher information (see also this document, page 1). This is exactly what most optimization algorithms like optim in R return: the Hessian evaluated at t... | Basic question about Fisher Information matrix and relationship to Hessian and standard errors | Yudi Pawitan writes in his book In All Likelihood that the second derivative of the log-likelihood evaluated at the maximum likelihood estimates (MLE) is the observed Fisher information (see also this | Basic question about Fisher Information matrix and relationship to Hessian and standard errors
Yudi Pawitan writes in his book In All Likelihood that the second derivative of the log-likelihood evaluated at the maximum likelihood estimates (MLE) is the observed Fisher information (see also this document, page 1). This ... | Basic question about Fisher Information matrix and relationship to Hessian and standard errors
Yudi Pawitan writes in his book In All Likelihood that the second derivative of the log-likelihood evaluated at the maximum likelihood estimates (MLE) is the observed Fisher information (see also this |
2,453 | Basic question about Fisher Information matrix and relationship to Hessian and standard errors | Estimating likelihood functions entails a two-step process.
First, one declares the log-likelihood function. Then one optimizes the log-likelihood functions. That's fine.
Writing the log-likelihood functions in R, we ask for $-1*l$ (where $l$ represents the log - likelihood function) because the optim command in R mini... | Basic question about Fisher Information matrix and relationship to Hessian and standard errors | Estimating likelihood functions entails a two-step process.
First, one declares the log-likelihood function. Then one optimizes the log-likelihood functions. That's fine.
Writing the log-likelihood fu | Basic question about Fisher Information matrix and relationship to Hessian and standard errors
Estimating likelihood functions entails a two-step process.
First, one declares the log-likelihood function. Then one optimizes the log-likelihood functions. That's fine.
Writing the log-likelihood functions in R, we ask for ... | Basic question about Fisher Information matrix and relationship to Hessian and standard errors
Estimating likelihood functions entails a two-step process.
First, one declares the log-likelihood function. Then one optimizes the log-likelihood functions. That's fine.
Writing the log-likelihood fu |
2,454 | What are the 'big problems' in statistics? | A big question should involve key issues of statistical methodology or, because statistics is entirely about applications, it should concern how statistics is used with problems important to society.
This characterization suggests the following should be included in any consideration of big problems:
How best to condu... | What are the 'big problems' in statistics? | A big question should involve key issues of statistical methodology or, because statistics is entirely about applications, it should concern how statistics is used with problems important to society.
| What are the 'big problems' in statistics?
A big question should involve key issues of statistical methodology or, because statistics is entirely about applications, it should concern how statistics is used with problems important to society.
This characterization suggests the following should be included in any consid... | What are the 'big problems' in statistics?
A big question should involve key issues of statistical methodology or, because statistics is entirely about applications, it should concern how statistics is used with problems important to society.
|
2,455 | What are the 'big problems' in statistics? | Michael Jordan has a short article called What are the Open Problems in Bayesian Statistics?, in which he polled a bunch of statisticians for their views on the open problems in statistics. I'll summarize (aka, copy-and-paste) a bit here, but it's probably best just to read the original.
Nonparametrics and semiparametr... | What are the 'big problems' in statistics? | Michael Jordan has a short article called What are the Open Problems in Bayesian Statistics?, in which he polled a bunch of statisticians for their views on the open problems in statistics. I'll summa | What are the 'big problems' in statistics?
Michael Jordan has a short article called What are the Open Problems in Bayesian Statistics?, in which he polled a bunch of statisticians for their views on the open problems in statistics. I'll summarize (aka, copy-and-paste) a bit here, but it's probably best just to read th... | What are the 'big problems' in statistics?
Michael Jordan has a short article called What are the Open Problems in Bayesian Statistics?, in which he polled a bunch of statisticians for their views on the open problems in statistics. I'll summa |
2,456 | What are the 'big problems' in statistics? | I'm not sure how big they are, but there is a Wikipedia page for unsolved problems in statistics. Their list includes:
Inference and testing
Systematic errors
Admissability of the Graybill–Deal estimator
Combining dependent p-values in Meta-analysis
Behrens–Fisher problem
Multiple comparisons
Open problems in Baye... | What are the 'big problems' in statistics? | I'm not sure how big they are, but there is a Wikipedia page for unsolved problems in statistics. Their list includes:
Inference and testing
Systematic errors
Admissability of the Graybill–Deal e | What are the 'big problems' in statistics?
I'm not sure how big they are, but there is a Wikipedia page for unsolved problems in statistics. Their list includes:
Inference and testing
Systematic errors
Admissability of the Graybill–Deal estimator
Combining dependent p-values in Meta-analysis
Behrens–Fisher problem... | What are the 'big problems' in statistics?
I'm not sure how big they are, but there is a Wikipedia page for unsolved problems in statistics. Their list includes:
Inference and testing
Systematic errors
Admissability of the Graybill–Deal e |
2,457 | What are the 'big problems' in statistics? | As an example of the general spirit (if not quite specificity) of answer I'm looking for, I found a "Hilbert's 23"-inspired lecture by David Donoho at a "Math Challenges of the 21st Century" conference:
High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality | What are the 'big problems' in statistics? | As an example of the general spirit (if not quite specificity) of answer I'm looking for, I found a "Hilbert's 23"-inspired lecture by David Donoho at a "Math Challenges of the 21st Century" conferenc | What are the 'big problems' in statistics?
As an example of the general spirit (if not quite specificity) of answer I'm looking for, I found a "Hilbert's 23"-inspired lecture by David Donoho at a "Math Challenges of the 21st Century" conference:
High-Dimensional Data Analysis: The Curses and Blessings of Dimensionality | What are the 'big problems' in statistics?
As an example of the general spirit (if not quite specificity) of answer I'm looking for, I found a "Hilbert's 23"-inspired lecture by David Donoho at a "Math Challenges of the 21st Century" conferenc |
2,458 | What are the 'big problems' in statistics? | Mathoverflow has a similar question about big problems in probability theory.
It would appear from that page that the biggest questions are to do with self avoiding random walks and percolations. | What are the 'big problems' in statistics? | Mathoverflow has a similar question about big problems in probability theory.
It would appear from that page that the biggest questions are to do with self avoiding random walks and percolations. | What are the 'big problems' in statistics?
Mathoverflow has a similar question about big problems in probability theory.
It would appear from that page that the biggest questions are to do with self avoiding random walks and percolations. | What are the 'big problems' in statistics?
Mathoverflow has a similar question about big problems in probability theory.
It would appear from that page that the biggest questions are to do with self avoiding random walks and percolations. |
2,459 | What are the 'big problems' in statistics? | You might check out Harvard's "Hard Problems in the Social Sciences' colloquium held earlier this year. Several of these talks offer issues in the use of statistics and modeling in the social sciences. | What are the 'big problems' in statistics? | You might check out Harvard's "Hard Problems in the Social Sciences' colloquium held earlier this year. Several of these talks offer issues in the use of statistics and modeling in the social sciences | What are the 'big problems' in statistics?
You might check out Harvard's "Hard Problems in the Social Sciences' colloquium held earlier this year. Several of these talks offer issues in the use of statistics and modeling in the social sciences. | What are the 'big problems' in statistics?
You might check out Harvard's "Hard Problems in the Social Sciences' colloquium held earlier this year. Several of these talks offer issues in the use of statistics and modeling in the social sciences |
2,460 | What are the 'big problems' in statistics? | My answer would be the struggle between frequentist and Bayesian statistics. When people ask you which you "believe in", this is not good! Especially for a scientific discipline. | What are the 'big problems' in statistics? | My answer would be the struggle between frequentist and Bayesian statistics. When people ask you which you "believe in", this is not good! Especially for a scientific discipline. | What are the 'big problems' in statistics?
My answer would be the struggle between frequentist and Bayesian statistics. When people ask you which you "believe in", this is not good! Especially for a scientific discipline. | What are the 'big problems' in statistics?
My answer would be the struggle between frequentist and Bayesian statistics. When people ask you which you "believe in", this is not good! Especially for a scientific discipline. |
2,461 | Likelihood ratio vs Bayes Factor | apparently the Bayes factor somehow uses likelihoods that represent the likelihood of each model integrated over it's entire parameter space (i.e. not just at the MLE). How is this integration actually achieved typically? Does one really just try to calculate the likelihood at each of thousands (millions?) of random sa... | Likelihood ratio vs Bayes Factor | apparently the Bayes factor somehow uses likelihoods that represent the likelihood of each model integrated over it's entire parameter space (i.e. not just at the MLE). How is this integration actuall | Likelihood ratio vs Bayes Factor
apparently the Bayes factor somehow uses likelihoods that represent the likelihood of each model integrated over it's entire parameter space (i.e. not just at the MLE). How is this integration actually achieved typically? Does one really just try to calculate the likelihood at each of t... | Likelihood ratio vs Bayes Factor
apparently the Bayes factor somehow uses likelihoods that represent the likelihood of each model integrated over it's entire parameter space (i.e. not just at the MLE). How is this integration actuall |
2,462 | Likelihood ratio vs Bayes Factor | In understanding the difference between likelihood ratios and Bayes factors, it is useful to consider one key feature of Bayes factors in more detail:
How do Bayes factors manage to automatically account for the complexity of the underlying models?
One perspective on this question is to consider methods for determinist... | Likelihood ratio vs Bayes Factor | In understanding the difference between likelihood ratios and Bayes factors, it is useful to consider one key feature of Bayes factors in more detail:
How do Bayes factors manage to automatically acco | Likelihood ratio vs Bayes Factor
In understanding the difference between likelihood ratios and Bayes factors, it is useful to consider one key feature of Bayes factors in more detail:
How do Bayes factors manage to automatically account for the complexity of the underlying models?
One perspective on this question is to... | Likelihood ratio vs Bayes Factor
In understanding the difference between likelihood ratios and Bayes factors, it is useful to consider one key feature of Bayes factors in more detail:
How do Bayes factors manage to automatically acco |
2,463 | Central limit theorem for sample medians | If you work in terms of indicator variables (i.e. $Z_i = 1$ if $X_i \leq x$ and $0$ otherwise), you can directly apply the Central limit theorem to a mean of $Z$'s, and by using the Delta method, turn that into an asymptotic normal distribution for $F_X^{-1}(\bar{Z})$, which in turn means that you get asymptotic normal... | Central limit theorem for sample medians | If you work in terms of indicator variables (i.e. $Z_i = 1$ if $X_i \leq x$ and $0$ otherwise), you can directly apply the Central limit theorem to a mean of $Z$'s, and by using the Delta method, turn | Central limit theorem for sample medians
If you work in terms of indicator variables (i.e. $Z_i = 1$ if $X_i \leq x$ and $0$ otherwise), you can directly apply the Central limit theorem to a mean of $Z$'s, and by using the Delta method, turn that into an asymptotic normal distribution for $F_X^{-1}(\bar{Z})$, which in ... | Central limit theorem for sample medians
If you work in terms of indicator variables (i.e. $Z_i = 1$ if $X_i \leq x$ and $0$ otherwise), you can directly apply the Central limit theorem to a mean of $Z$'s, and by using the Delta method, turn |
2,464 | Central limit theorem for sample medians | The key idea is that the sampling distribution of the median is simple to express in terms of the distribution function but more complicated to express in terms of the median value. Once we understand how the distribution function can re-express values as probabilities and back again, it is easy to derive the exact sa... | Central limit theorem for sample medians | The key idea is that the sampling distribution of the median is simple to express in terms of the distribution function but more complicated to express in terms of the median value. Once we understan | Central limit theorem for sample medians
The key idea is that the sampling distribution of the median is simple to express in terms of the distribution function but more complicated to express in terms of the median value. Once we understand how the distribution function can re-express values as probabilities and back... | Central limit theorem for sample medians
The key idea is that the sampling distribution of the median is simple to express in terms of the distribution function but more complicated to express in terms of the median value. Once we understan |
2,465 | Central limit theorem for sample medians | @EngrStudent illuminating answer tells us that we should expect different results when the distribution is continuous, and when it is discrete (the "red" graphs, where the asymptotic distribution of the sample median fails spectacularly to look like normal, correspond to the distributions Binomial(3), Geometric(11), Hy... | Central limit theorem for sample medians | @EngrStudent illuminating answer tells us that we should expect different results when the distribution is continuous, and when it is discrete (the "red" graphs, where the asymptotic distribution of t | Central limit theorem for sample medians
@EngrStudent illuminating answer tells us that we should expect different results when the distribution is continuous, and when it is discrete (the "red" graphs, where the asymptotic distribution of the sample median fails spectacularly to look like normal, correspond to the dis... | Central limit theorem for sample medians
@EngrStudent illuminating answer tells us that we should expect different results when the distribution is continuous, and when it is discrete (the "red" graphs, where the asymptotic distribution of t |
2,466 | Central limit theorem for sample medians | I like the analytic answer given by Glen_b. It is a good answer.
It needs a picture. I like pictures.
Here are areas of elasticity in an answer to the question:
There are lots of distributions in the world. Mileage is likely to vary.
Sufficient has different meanings. For a counter-example to a theory, sometimes a... | Central limit theorem for sample medians | I like the analytic answer given by Glen_b. It is a good answer.
It needs a picture. I like pictures.
Here are areas of elasticity in an answer to the question:
There are lots of distributions in t | Central limit theorem for sample medians
I like the analytic answer given by Glen_b. It is a good answer.
It needs a picture. I like pictures.
Here are areas of elasticity in an answer to the question:
There are lots of distributions in the world. Mileage is likely to vary.
Sufficient has different meanings. For a... | Central limit theorem for sample medians
I like the analytic answer given by Glen_b. It is a good answer.
It needs a picture. I like pictures.
Here are areas of elasticity in an answer to the question:
There are lots of distributions in t |
2,467 | Central limit theorem for sample medians | Yes it is, and not just for the median, but for any sample quantile. Copying from this paper, written by T.S. Ferguson, a professor at UCLA (his page is here), which interestingly deals with the joint distribution of sample mean and sample quantiles, we have:
Let $X_1, . . . ,X_n$ be i.i.d. with distribution function... | Central limit theorem for sample medians | Yes it is, and not just for the median, but for any sample quantile. Copying from this paper, written by T.S. Ferguson, a professor at UCLA (his page is here), which interestingly deals with the joi | Central limit theorem for sample medians
Yes it is, and not just for the median, but for any sample quantile. Copying from this paper, written by T.S. Ferguson, a professor at UCLA (his page is here), which interestingly deals with the joint distribution of sample mean and sample quantiles, we have:
Let $X_1, . . . ,... | Central limit theorem for sample medians
Yes it is, and not just for the median, but for any sample quantile. Copying from this paper, written by T.S. Ferguson, a professor at UCLA (his page is here), which interestingly deals with the joi |
2,468 | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation? | The correction is called Bessel's correction and it has a mathematical proof. Personally, I was taught it the easy way: using $n-1$ is how you correct the bias of $E[\frac{1}{n}\sum_1^n(x_i - \bar x)^2]$ (see here).
You can also explain the correction based on the concept of degrees of freedom, simulation isn't strictl... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance | The correction is called Bessel's correction and it has a mathematical proof. Personally, I was taught it the easy way: using $n-1$ is how you correct the bias of $E[\frac{1}{n}\sum_1^n(x_i - \bar x)^ | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?
The correction is called Bessel's correction and it has a mathematical proof. Personally, I was taught it the easy way: using $n-1$ is how you correct the bias of $E[\frac{1}{n}\sum_1^n(x_i - \bar x)... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance
The correction is called Bessel's correction and it has a mathematical proof. Personally, I was taught it the easy way: using $n-1$ is how you correct the bias of $E[\frac{1}{n}\sum_1^n(x_i - \bar x)^ |
2,469 | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation? | Most proofs I have seen are simple enough that Gauss (however he did it) probably found it pretty easy to prove.
I've been looking for a derivation on CV that I could link you to (there are a number of links to proofs off-site, including at least one in answers here), but I haven't found one here on CV in a couple of s... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance | Most proofs I have seen are simple enough that Gauss (however he did it) probably found it pretty easy to prove.
I've been looking for a derivation on CV that I could link you to (there are a number o | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?
Most proofs I have seen are simple enough that Gauss (however he did it) probably found it pretty easy to prove.
I've been looking for a derivation on CV that I could link you to (there are a number ... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance
Most proofs I have seen are simple enough that Gauss (however he did it) probably found it pretty easy to prove.
I've been looking for a derivation on CV that I could link you to (there are a number o |
2,470 | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation? | According to Weisstein's World of Mathematics, it was first proved by Gauss in 1823. The reference is volume 4 of Gauss' Werke, which can be read at https://archive.org/details/werkecarlf04gausrich. The relevant pages seem to be 47-49. It seems that Gauss investigated the question and came up with a proof. I don't read... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance | According to Weisstein's World of Mathematics, it was first proved by Gauss in 1823. The reference is volume 4 of Gauss' Werke, which can be read at https://archive.org/details/werkecarlf04gausrich. T | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?
According to Weisstein's World of Mathematics, it was first proved by Gauss in 1823. The reference is volume 4 of Gauss' Werke, which can be read at https://archive.org/details/werkecarlf04gausrich. ... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance
According to Weisstein's World of Mathematics, it was first proved by Gauss in 1823. The reference is volume 4 of Gauss' Werke, which can be read at https://archive.org/details/werkecarlf04gausrich. T |
2,471 | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation? | For me one piece of intuition is that
$$\begin{array}{c}
\mbox{The degree to which}\\
X_{i}\mbox{ varies from }\bar{X}
\end{array}+\begin{array}{c}
\mbox{The degree to which}\\
\bar{X}\mbox{ varies from }\mu
\end{array}=\begin{array}{c}
\mbox{The degree to which }\\
X_{i}\mbox{ varies from }\mu.
\end{array}$$
That is, ... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance | For me one piece of intuition is that
$$\begin{array}{c}
\mbox{The degree to which}\\
X_{i}\mbox{ varies from }\bar{X}
\end{array}+\begin{array}{c}
\mbox{The degree to which}\\
\bar{X}\mbox{ varies fr | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?
For me one piece of intuition is that
$$\begin{array}{c}
\mbox{The degree to which}\\
X_{i}\mbox{ varies from }\bar{X}
\end{array}+\begin{array}{c}
\mbox{The degree to which}\\
\bar{X}\mbox{ varies f... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance
For me one piece of intuition is that
$$\begin{array}{c}
\mbox{The degree to which}\\
X_{i}\mbox{ varies from }\bar{X}
\end{array}+\begin{array}{c}
\mbox{The degree to which}\\
\bar{X}\mbox{ varies fr |
2,472 | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation? | Most of the answers have already elaborately explained it but apart from those there's one simple illustration that one could find helpful:
Suppose you are given that $n=4$ and the first three numbers are:
$8,4,6$,_
Now the fourth number can be anything since there are no constraints. Now consider the situation when yo... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance | Most of the answers have already elaborately explained it but apart from those there's one simple illustration that one could find helpful:
Suppose you are given that $n=4$ and the first three numbers | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance without simulation?
Most of the answers have already elaborately explained it but apart from those there's one simple illustration that one could find helpful:
Suppose you are given that $n=4$ and the first three number... | How exactly did statisticians agree to using (n-1) as the unbiased estimator for population variance
Most of the answers have already elaborately explained it but apart from those there's one simple illustration that one could find helpful:
Suppose you are given that $n=4$ and the first three numbers |
2,473 | When (if ever) is a frequentist approach substantively better than a Bayesian? | Here's five reasons why frequentists methods may be preferred:
Faster. Given that Bayesian statistics often give nearly identical answers to frequentist answers (and when they don't, it's not 100% clear that Bayesian is always the way to go), the fact that frequentist statistics can be obtained often several orders o... | When (if ever) is a frequentist approach substantively better than a Bayesian? | Here's five reasons why frequentists methods may be preferred:
Faster. Given that Bayesian statistics often give nearly identical answers to frequentist answers (and when they don't, it's not 100% c | When (if ever) is a frequentist approach substantively better than a Bayesian?
Here's five reasons why frequentists methods may be preferred:
Faster. Given that Bayesian statistics often give nearly identical answers to frequentist answers (and when they don't, it's not 100% clear that Bayesian is always the way to g... | When (if ever) is a frequentist approach substantively better than a Bayesian?
Here's five reasons why frequentists methods may be preferred:
Faster. Given that Bayesian statistics often give nearly identical answers to frequentist answers (and when they don't, it's not 100% c |
2,474 | When (if ever) is a frequentist approach substantively better than a Bayesian? | A few concrete advantages of frequentist statistics:
There are often closed-form solutions to frequentist problems whereas you would need a conjugate prior to have a closed form solution in the Bayesian analogue. This is useful for a number of reasons - one of which is computation time.
A reason that'll, hopefully, ev... | When (if ever) is a frequentist approach substantively better than a Bayesian? | A few concrete advantages of frequentist statistics:
There are often closed-form solutions to frequentist problems whereas you would need a conjugate prior to have a closed form solution in the Bayes | When (if ever) is a frequentist approach substantively better than a Bayesian?
A few concrete advantages of frequentist statistics:
There are often closed-form solutions to frequentist problems whereas you would need a conjugate prior to have a closed form solution in the Bayesian analogue. This is useful for a number... | When (if ever) is a frequentist approach substantively better than a Bayesian?
A few concrete advantages of frequentist statistics:
There are often closed-form solutions to frequentist problems whereas you would need a conjugate prior to have a closed form solution in the Bayes |
2,475 | When (if ever) is a frequentist approach substantively better than a Bayesian? | The most important reason to use Frequentist approaches, which has surprisingly not yet been mentioned, is error control. Very often, research leads to dichotomous interpretations (should I do a study building on this, or not? Should be implement an intervention, or not?). Frequentist approaches allow you to strictly c... | When (if ever) is a frequentist approach substantively better than a Bayesian? | The most important reason to use Frequentist approaches, which has surprisingly not yet been mentioned, is error control. Very often, research leads to dichotomous interpretations (should I do a study | When (if ever) is a frequentist approach substantively better than a Bayesian?
The most important reason to use Frequentist approaches, which has surprisingly not yet been mentioned, is error control. Very often, research leads to dichotomous interpretations (should I do a study building on this, or not? Should be impl... | When (if ever) is a frequentist approach substantively better than a Bayesian?
The most important reason to use Frequentist approaches, which has surprisingly not yet been mentioned, is error control. Very often, research leads to dichotomous interpretations (should I do a study |
2,476 | When (if ever) is a frequentist approach substantively better than a Bayesian? | I think one of the biggest questions, as a statistican, you have to ask yourself is whether or not you believe in, or want to adhere to, the likelihood principle. If you don't believe in the likelihood principle then I think the frequentist paradigm to statistics can be extremely powerful, however, if you do believe in... | When (if ever) is a frequentist approach substantively better than a Bayesian? | I think one of the biggest questions, as a statistican, you have to ask yourself is whether or not you believe in, or want to adhere to, the likelihood principle. If you don't believe in the likelihoo | When (if ever) is a frequentist approach substantively better than a Bayesian?
I think one of the biggest questions, as a statistican, you have to ask yourself is whether or not you believe in, or want to adhere to, the likelihood principle. If you don't believe in the likelihood principle then I think the frequentist ... | When (if ever) is a frequentist approach substantively better than a Bayesian?
I think one of the biggest questions, as a statistican, you have to ask yourself is whether or not you believe in, or want to adhere to, the likelihood principle. If you don't believe in the likelihoo |
2,477 | When (if ever) is a frequentist approach substantively better than a Bayesian? | Personally I'm having difficulty thinking of a situation where the frequentist answer would be preferred over a Bayesian one. My thinking is detailed here and in other blog articles on fharrell.com about problems with p-values and null hypothesis testing. Frequentists tend to ignore a few fundamental problems. Here ... | When (if ever) is a frequentist approach substantively better than a Bayesian? | Personally I'm having difficulty thinking of a situation where the frequentist answer would be preferred over a Bayesian one. My thinking is detailed here and in other blog articles on fharrell.com a | When (if ever) is a frequentist approach substantively better than a Bayesian?
Personally I'm having difficulty thinking of a situation where the frequentist answer would be preferred over a Bayesian one. My thinking is detailed here and in other blog articles on fharrell.com about problems with p-values and null hypo... | When (if ever) is a frequentist approach substantively better than a Bayesian?
Personally I'm having difficulty thinking of a situation where the frequentist answer would be preferred over a Bayesian one. My thinking is detailed here and in other blog articles on fharrell.com a |
2,478 | When (if ever) is a frequentist approach substantively better than a Bayesian? | You and I are both scientists, and as scientists, are chiefly interested in questions of evidence. For that reason, I think Bayesian approaches, when feasible, are preferable.
Bayesian approaches answer our question: What is the strength of evidence for one hypothesis over another? Frequentist approaches, on the other... | When (if ever) is a frequentist approach substantively better than a Bayesian? | You and I are both scientists, and as scientists, are chiefly interested in questions of evidence. For that reason, I think Bayesian approaches, when feasible, are preferable.
Bayesian approaches ans | When (if ever) is a frequentist approach substantively better than a Bayesian?
You and I are both scientists, and as scientists, are chiefly interested in questions of evidence. For that reason, I think Bayesian approaches, when feasible, are preferable.
Bayesian approaches answer our question: What is the strength of... | When (if ever) is a frequentist approach substantively better than a Bayesian?
You and I are both scientists, and as scientists, are chiefly interested in questions of evidence. For that reason, I think Bayesian approaches, when feasible, are preferable.
Bayesian approaches ans |
2,479 | When (if ever) is a frequentist approach substantively better than a Bayesian? | Many people do not seem aware of a third philosophical school: likelihoodism. AWF Edwards's book, Likelihood, is probably the best place to read up on it. Here is a short article he wrote.
Likelihoodism eschews p-values, like Bayesianism, but also eschews the Bayesian's often dubious prior. There is an intro treatment ... | When (if ever) is a frequentist approach substantively better than a Bayesian? | Many people do not seem aware of a third philosophical school: likelihoodism. AWF Edwards's book, Likelihood, is probably the best place to read up on it. Here is a short article he wrote.
Likelihoodi | When (if ever) is a frequentist approach substantively better than a Bayesian?
Many people do not seem aware of a third philosophical school: likelihoodism. AWF Edwards's book, Likelihood, is probably the best place to read up on it. Here is a short article he wrote.
Likelihoodism eschews p-values, like Bayesianism, bu... | When (if ever) is a frequentist approach substantively better than a Bayesian?
Many people do not seem aware of a third philosophical school: likelihoodism. AWF Edwards's book, Likelihood, is probably the best place to read up on it. Here is a short article he wrote.
Likelihoodi |
2,480 | When (if ever) is a frequentist approach substantively better than a Bayesian? | One of the biggest disadvantages of frequentist approaches to model building has always been, as TrynnaDoStats notes in his first point, the challenges involved with inverting big closed-form solutions. Closed-form matrix inversion requires that the entire matrix be resident in RAM, a significant limitation on single C... | When (if ever) is a frequentist approach substantively better than a Bayesian? | One of the biggest disadvantages of frequentist approaches to model building has always been, as TrynnaDoStats notes in his first point, the challenges involved with inverting big closed-form solution | When (if ever) is a frequentist approach substantively better than a Bayesian?
One of the biggest disadvantages of frequentist approaches to model building has always been, as TrynnaDoStats notes in his first point, the challenges involved with inverting big closed-form solutions. Closed-form matrix inversion requires ... | When (if ever) is a frequentist approach substantively better than a Bayesian?
One of the biggest disadvantages of frequentist approaches to model building has always been, as TrynnaDoStats notes in his first point, the challenges involved with inverting big closed-form solution |
2,481 | When (if ever) is a frequentist approach substantively better than a Bayesian? | Several comments:
The fundamental difference between the bayesian and frequentist statistician is that the bayesian is willing to extend the tools of probability to situations where the frequentist wouldn't.
More specifically, the bayesian is willing to use probability to model the uncertainty in her own mind over v... | When (if ever) is a frequentist approach substantively better than a Bayesian? | Several comments:
The fundamental difference between the bayesian and frequentist statistician is that the bayesian is willing to extend the tools of probability to situations where the frequentist w | When (if ever) is a frequentist approach substantively better than a Bayesian?
Several comments:
The fundamental difference between the bayesian and frequentist statistician is that the bayesian is willing to extend the tools of probability to situations where the frequentist wouldn't.
More specifically, the bayesia... | When (if ever) is a frequentist approach substantively better than a Bayesian?
Several comments:
The fundamental difference between the bayesian and frequentist statistician is that the bayesian is willing to extend the tools of probability to situations where the frequentist w |
2,482 | When (if ever) is a frequentist approach substantively better than a Bayesian? | Frequentist tests focus on falsifying the null hypothesis. However, Null Hypothesis Significance Testing (NHST) can also be done from a Bayesian perspective, because in all cases NHST is simply a calculation of P( Observed Effect | Effect = 0 ). So, it's hard to identify a time when it would be necessary to conduct NHS... | When (if ever) is a frequentist approach substantively better than a Bayesian? | Frequentist tests focus on falsifying the null hypothesis. However, Null Hypothesis Significance Testing (NHST) can also be done from a Bayesian perspective, because in all cases NHST is simply a calc | When (if ever) is a frequentist approach substantively better than a Bayesian?
Frequentist tests focus on falsifying the null hypothesis. However, Null Hypothesis Significance Testing (NHST) can also be done from a Bayesian perspective, because in all cases NHST is simply a calculation of P( Observed Effect | Effect = ... | When (if ever) is a frequentist approach substantively better than a Bayesian?
Frequentist tests focus on falsifying the null hypothesis. However, Null Hypothesis Significance Testing (NHST) can also be done from a Bayesian perspective, because in all cases NHST is simply a calc |
2,483 | When (if ever) is a frequentist approach substantively better than a Bayesian? | The goal of much research is not to reach a final conclusion, but just to obtain a little more evidence to incrementally push the community's sense of a question in one direction.
Bayesian statistics are indispensable when what you need is to evaluate a decision or conclusion in light of the available evidence. Quality... | When (if ever) is a frequentist approach substantively better than a Bayesian? | The goal of much research is not to reach a final conclusion, but just to obtain a little more evidence to incrementally push the community's sense of a question in one direction.
Bayesian statistics | When (if ever) is a frequentist approach substantively better than a Bayesian?
The goal of much research is not to reach a final conclusion, but just to obtain a little more evidence to incrementally push the community's sense of a question in one direction.
Bayesian statistics are indispensable when what you need is t... | When (if ever) is a frequentist approach substantively better than a Bayesian?
The goal of much research is not to reach a final conclusion, but just to obtain a little more evidence to incrementally push the community's sense of a question in one direction.
Bayesian statistics |
2,484 | When (if ever) is a frequentist approach substantively better than a Bayesian? | The actual execution of a Bayesian method is more technical than that of a Frequentist. By "more technical" I mean things like: 1) choosing priors, 2) programming your model in a BUGS/JAGS/STAN, and 3) thinking about sampling and convergence.
Obviously, #1 is pretty much not optional, by definition of Bayesian. Though ... | When (if ever) is a frequentist approach substantively better than a Bayesian? | The actual execution of a Bayesian method is more technical than that of a Frequentist. By "more technical" I mean things like: 1) choosing priors, 2) programming your model in a BUGS/JAGS/STAN, and 3 | When (if ever) is a frequentist approach substantively better than a Bayesian?
The actual execution of a Bayesian method is more technical than that of a Frequentist. By "more technical" I mean things like: 1) choosing priors, 2) programming your model in a BUGS/JAGS/STAN, and 3) thinking about sampling and convergence... | When (if ever) is a frequentist approach substantively better than a Bayesian?
The actual execution of a Bayesian method is more technical than that of a Frequentist. By "more technical" I mean things like: 1) choosing priors, 2) programming your model in a BUGS/JAGS/STAN, and 3 |
2,485 | When (if ever) is a frequentist approach substantively better than a Bayesian? | One type of problem in which a particular Frequentist based approach has essentially dominated any Bayesian is that of prediction in the M-open case.
What does M-open mean?
M-open implies that the true model that generates the data does not appear in the set of models we are considering. For example, if the true mean ... | When (if ever) is a frequentist approach substantively better than a Bayesian? | One type of problem in which a particular Frequentist based approach has essentially dominated any Bayesian is that of prediction in the M-open case.
What does M-open mean?
M-open implies that the tr | When (if ever) is a frequentist approach substantively better than a Bayesian?
One type of problem in which a particular Frequentist based approach has essentially dominated any Bayesian is that of prediction in the M-open case.
What does M-open mean?
M-open implies that the true model that generates the data does not... | When (if ever) is a frequentist approach substantively better than a Bayesian?
One type of problem in which a particular Frequentist based approach has essentially dominated any Bayesian is that of prediction in the M-open case.
What does M-open mean?
M-open implies that the tr |
2,486 | When (if ever) is a frequentist approach substantively better than a Bayesian? | Conceptually: I don't know. I believe Bayesian statistics is the most logical way to think but I coudn't justify why.
The advantage of frequentist is that it is easier for most people at elementary level. But for me it was strange. It took years until I could really clarify intellectually what a confidence interval is.... | When (if ever) is a frequentist approach substantively better than a Bayesian? | Conceptually: I don't know. I believe Bayesian statistics is the most logical way to think but I coudn't justify why.
The advantage of frequentist is that it is easier for most people at elementary le | When (if ever) is a frequentist approach substantively better than a Bayesian?
Conceptually: I don't know. I believe Bayesian statistics is the most logical way to think but I coudn't justify why.
The advantage of frequentist is that it is easier for most people at elementary level. But for me it was strange. It took y... | When (if ever) is a frequentist approach substantively better than a Bayesian?
Conceptually: I don't know. I believe Bayesian statistics is the most logical way to think but I coudn't justify why.
The advantage of frequentist is that it is easier for most people at elementary le |
2,487 | Bayes regression: how is it done in comparison to standard regression? | The simple linear regression model
$$ y_i = \alpha + \beta x_i + \varepsilon $$
can be written in terms of the probabilistic model behind it
$$
\mu_i = \alpha + \beta x_i \\
y_i \sim \mathcal{N}(\mu_i, \sigma)
$$
i.e. dependent variable $Y$ follows normal distribution parametrized by mean $\mu_i$, that is a linear fun... | Bayes regression: how is it done in comparison to standard regression? | The simple linear regression model
$$ y_i = \alpha + \beta x_i + \varepsilon $$
can be written in terms of the probabilistic model behind it
$$
\mu_i = \alpha + \beta x_i \\
y_i \sim \mathcal{N}(\mu_ | Bayes regression: how is it done in comparison to standard regression?
The simple linear regression model
$$ y_i = \alpha + \beta x_i + \varepsilon $$
can be written in terms of the probabilistic model behind it
$$
\mu_i = \alpha + \beta x_i \\
y_i \sim \mathcal{N}(\mu_i, \sigma)
$$
i.e. dependent variable $Y$ follows... | Bayes regression: how is it done in comparison to standard regression?
The simple linear regression model
$$ y_i = \alpha + \beta x_i + \varepsilon $$
can be written in terms of the probabilistic model behind it
$$
\mu_i = \alpha + \beta x_i \\
y_i \sim \mathcal{N}(\mu_ |
2,488 | Bayes regression: how is it done in comparison to standard regression? | Given a data set $D = (x_1,y_1), \ldots, (x_N,y_N)$ where $x \in \mathbb{R}^d, y \in \mathbb{R}$, a Bayesian Linear Regression models the problem in the following way:
Prior: $$w \sim \mathcal{N}(0, \sigma_w^2 I_d)$$
$w$ is vector $(w_1, \ldots, w_d)^T$, so the previous distribution is a multivariate Gaussian; and $I_d... | Bayes regression: how is it done in comparison to standard regression? | Given a data set $D = (x_1,y_1), \ldots, (x_N,y_N)$ where $x \in \mathbb{R}^d, y \in \mathbb{R}$, a Bayesian Linear Regression models the problem in the following way:
Prior: $$w \sim \mathcal{N}(0, \ | Bayes regression: how is it done in comparison to standard regression?
Given a data set $D = (x_1,y_1), \ldots, (x_N,y_N)$ where $x \in \mathbb{R}^d, y \in \mathbb{R}$, a Bayesian Linear Regression models the problem in the following way:
Prior: $$w \sim \mathcal{N}(0, \sigma_w^2 I_d)$$
$w$ is vector $(w_1, \ldots, w_d... | Bayes regression: how is it done in comparison to standard regression?
Given a data set $D = (x_1,y_1), \ldots, (x_N,y_N)$ where $x \in \mathbb{R}^d, y \in \mathbb{R}$, a Bayesian Linear Regression models the problem in the following way:
Prior: $$w \sim \mathcal{N}(0, \ |
2,489 | When to use generalized estimating equations vs. mixed effects models? | Use GEE when you're interested in uncovering the population average effect of a covariate vs. the individual specific effect. These two things are only equivalent in linear models, but not in non-linear (e.g. logistic). To see this, take, for example the random effects logistic model of the $j$'th observation of the $i... | When to use generalized estimating equations vs. mixed effects models? | Use GEE when you're interested in uncovering the population average effect of a covariate vs. the individual specific effect. These two things are only equivalent in linear models, but not in non-line | When to use generalized estimating equations vs. mixed effects models?
Use GEE when you're interested in uncovering the population average effect of a covariate vs. the individual specific effect. These two things are only equivalent in linear models, but not in non-linear (e.g. logistic). To see this, take, for exampl... | When to use generalized estimating equations vs. mixed effects models?
Use GEE when you're interested in uncovering the population average effect of a covariate vs. the individual specific effect. These two things are only equivalent in linear models, but not in non-line |
2,490 | When to use generalized estimating equations vs. mixed effects models? | GEE in my mind is most useful when we are not using Bayesian modeling and when a full likelihood solution is not available. Also, GEE may require larger sample sizes in order to be sufficiently accurate, and it is very non-robust to non-randomly missing longitudinal data. GEE assumes missing completely at random wher... | When to use generalized estimating equations vs. mixed effects models? | GEE in my mind is most useful when we are not using Bayesian modeling and when a full likelihood solution is not available. Also, GEE may require larger sample sizes in order to be sufficiently accur | When to use generalized estimating equations vs. mixed effects models?
GEE in my mind is most useful when we are not using Bayesian modeling and when a full likelihood solution is not available. Also, GEE may require larger sample sizes in order to be sufficiently accurate, and it is very non-robust to non-randomly mi... | When to use generalized estimating equations vs. mixed effects models?
GEE in my mind is most useful when we are not using Bayesian modeling and when a full likelihood solution is not available. Also, GEE may require larger sample sizes in order to be sufficiently accur |
2,491 | When to use generalized estimating equations vs. mixed effects models? | You can find a thorough discussion and concrete examples in Fitzmaurice, Laird and Ware, Applied Longitudinal Analysis, John Wiley & Sons, 2011, 2nd edition, Chapters 11-16.
As to the examples, you can find datasets and SAS/Stata/R programs in the companion website. | When to use generalized estimating equations vs. mixed effects models? | You can find a thorough discussion and concrete examples in Fitzmaurice, Laird and Ware, Applied Longitudinal Analysis, John Wiley & Sons, 2011, 2nd edition, Chapters 11-16.
As to the examples, you ca | When to use generalized estimating equations vs. mixed effects models?
You can find a thorough discussion and concrete examples in Fitzmaurice, Laird and Ware, Applied Longitudinal Analysis, John Wiley & Sons, 2011, 2nd edition, Chapters 11-16.
As to the examples, you can find datasets and SAS/Stata/R programs in the c... | When to use generalized estimating equations vs. mixed effects models?
You can find a thorough discussion and concrete examples in Fitzmaurice, Laird and Ware, Applied Longitudinal Analysis, John Wiley & Sons, 2011, 2nd edition, Chapters 11-16.
As to the examples, you ca |
2,492 | What is a "kernel" in plain English? | In both statistics (kernel density estimation or kernel smoothing) and machine learning (kernel methods) literature, kernel is used as a measure of similarity. In particular, the kernel function $k(x,.)$ defines the distribution of similarities of points around a given point $x$. $k(x,y)$ denotes the similarity of poin... | What is a "kernel" in plain English? | In both statistics (kernel density estimation or kernel smoothing) and machine learning (kernel methods) literature, kernel is used as a measure of similarity. In particular, the kernel function $k(x, | What is a "kernel" in plain English?
In both statistics (kernel density estimation or kernel smoothing) and machine learning (kernel methods) literature, kernel is used as a measure of similarity. In particular, the kernel function $k(x,.)$ defines the distribution of similarities of points around a given point $x$. $k... | What is a "kernel" in plain English?
In both statistics (kernel density estimation or kernel smoothing) and machine learning (kernel methods) literature, kernel is used as a measure of similarity. In particular, the kernel function $k(x, |
2,493 | What is a "kernel" in plain English? | There appear to be at least two different meanings of "kernel": one more commonly used in statistics; the other in machine learning.
In statistics "kernel" is most commonly used to refer to kernel density estimation and kernel smoothing.
A straightforward explanation of kernels in density estimation can be found (here)... | What is a "kernel" in plain English? | There appear to be at least two different meanings of "kernel": one more commonly used in statistics; the other in machine learning.
In statistics "kernel" is most commonly used to refer to kernel den | What is a "kernel" in plain English?
There appear to be at least two different meanings of "kernel": one more commonly used in statistics; the other in machine learning.
In statistics "kernel" is most commonly used to refer to kernel density estimation and kernel smoothing.
A straightforward explanation of kernels in d... | What is a "kernel" in plain English?
There appear to be at least two different meanings of "kernel": one more commonly used in statistics; the other in machine learning.
In statistics "kernel" is most commonly used to refer to kernel den |
2,494 | Intuition on the Kullback–Leibler (KL) Divergence | A (metric) distance $D$ must be symmetric, i.e. $D(P,Q) = D(Q,P)$.
But, from definition, $KL$ is not.
Example: $\Omega = \{A,B\}$, $P(A) = 0.2, P(B) = 0.8$, $Q(A) = Q(B) = 0.5$.
We have:
$$KL(P,Q) = P(A)\log \frac{P(A)}{Q(A)} + P(B) \log \frac{P(B)}{Q(B)} \approx 0.19$$
and
$$KL(Q,P) = Q(A)\log \frac{Q(A)}{P(A)} + Q(B)... | Intuition on the Kullback–Leibler (KL) Divergence | A (metric) distance $D$ must be symmetric, i.e. $D(P,Q) = D(Q,P)$.
But, from definition, $KL$ is not.
Example: $\Omega = \{A,B\}$, $P(A) = 0.2, P(B) = 0.8$, $Q(A) = Q(B) = 0.5$.
We have:
$$KL(P,Q) = P | Intuition on the Kullback–Leibler (KL) Divergence
A (metric) distance $D$ must be symmetric, i.e. $D(P,Q) = D(Q,P)$.
But, from definition, $KL$ is not.
Example: $\Omega = \{A,B\}$, $P(A) = 0.2, P(B) = 0.8$, $Q(A) = Q(B) = 0.5$.
We have:
$$KL(P,Q) = P(A)\log \frac{P(A)}{Q(A)} + P(B) \log \frac{P(B)}{Q(B)} \approx 0.19$$... | Intuition on the Kullback–Leibler (KL) Divergence
A (metric) distance $D$ must be symmetric, i.e. $D(P,Q) = D(Q,P)$.
But, from definition, $KL$ is not.
Example: $\Omega = \{A,B\}$, $P(A) = 0.2, P(B) = 0.8$, $Q(A) = Q(B) = 0.5$.
We have:
$$KL(P,Q) = P |
2,495 | Intuition on the Kullback–Leibler (KL) Divergence | Adding to the other excellent answers, an answer with another viewpoint which maybe can add some more intuition, which was asked for.
The Kullback-Leibler divergence is
$$ \DeclareMathOperator{\KL}{KL}
\KL(P || Q) = \int_{-\infty}^\infty p(x) \log \frac{p(x)}{q(x)} \; dx
$$
If you have two hypothesis regarding which di... | Intuition on the Kullback–Leibler (KL) Divergence | Adding to the other excellent answers, an answer with another viewpoint which maybe can add some more intuition, which was asked for.
The Kullback-Leibler divergence is
$$ \DeclareMathOperator{\KL}{KL | Intuition on the Kullback–Leibler (KL) Divergence
Adding to the other excellent answers, an answer with another viewpoint which maybe can add some more intuition, which was asked for.
The Kullback-Leibler divergence is
$$ \DeclareMathOperator{\KL}{KL}
\KL(P || Q) = \int_{-\infty}^\infty p(x) \log \frac{p(x)}{q(x)} \; d... | Intuition on the Kullback–Leibler (KL) Divergence
Adding to the other excellent answers, an answer with another viewpoint which maybe can add some more intuition, which was asked for.
The Kullback-Leibler divergence is
$$ \DeclareMathOperator{\KL}{KL |
2,496 | Intuition on the Kullback–Leibler (KL) Divergence | First of all, the violation of the symmetry condition is the smallest problem with Kullback-Leibler divergence. $D(P||Q)$ also violates triangle inequality. You can simply introduce the symmetric version as $$ SKL(P, Q) = D(P||Q) + D(Q||P) $$, but that's still not metric, because both $D(P||Q)$ and $SKL(P, Q)$ violates... | Intuition on the Kullback–Leibler (KL) Divergence | First of all, the violation of the symmetry condition is the smallest problem with Kullback-Leibler divergence. $D(P||Q)$ also violates triangle inequality. You can simply introduce the symmetric vers | Intuition on the Kullback–Leibler (KL) Divergence
First of all, the violation of the symmetry condition is the smallest problem with Kullback-Leibler divergence. $D(P||Q)$ also violates triangle inequality. You can simply introduce the symmetric version as $$ SKL(P, Q) = D(P||Q) + D(Q||P) $$, but that's still not metri... | Intuition on the Kullback–Leibler (KL) Divergence
First of all, the violation of the symmetry condition is the smallest problem with Kullback-Leibler divergence. $D(P||Q)$ also violates triangle inequality. You can simply introduce the symmetric vers |
2,497 | Intuition on the Kullback–Leibler (KL) Divergence | I am tempted here to give a purely intuitive answer to your question. Rephrasing what you say, the KL divergence is a way to measure to the distance between two distributions as you would compute the distance between two data sets in a Hilbert space, but some caution should be taken.
Why? The KL divergence is not a dis... | Intuition on the Kullback–Leibler (KL) Divergence | I am tempted here to give a purely intuitive answer to your question. Rephrasing what you say, the KL divergence is a way to measure to the distance between two distributions as you would compute the | Intuition on the Kullback–Leibler (KL) Divergence
I am tempted here to give a purely intuitive answer to your question. Rephrasing what you say, the KL divergence is a way to measure to the distance between two distributions as you would compute the distance between two data sets in a Hilbert space, but some caution sh... | Intuition on the Kullback–Leibler (KL) Divergence
I am tempted here to give a purely intuitive answer to your question. Rephrasing what you say, the KL divergence is a way to measure to the distance between two distributions as you would compute the |
2,498 | Intuition on the Kullback–Leibler (KL) Divergence | The textbook Elements of Information Theory gives us an example:
For example, if we knew the true distribution p of the random
variable, we could construct a code with average description length
H(p). If, instead, we used the code for a distribution q, we would
need H(p) + D(p||q) bits on the average to descri... | Intuition on the Kullback–Leibler (KL) Divergence | The textbook Elements of Information Theory gives us an example:
For example, if we knew the true distribution p of the random
variable, we could construct a code with average description length
| Intuition on the Kullback–Leibler (KL) Divergence
The textbook Elements of Information Theory gives us an example:
For example, if we knew the true distribution p of the random
variable, we could construct a code with average description length
H(p). If, instead, we used the code for a distribution q, we would
... | Intuition on the Kullback–Leibler (KL) Divergence
The textbook Elements of Information Theory gives us an example:
For example, if we knew the true distribution p of the random
variable, we could construct a code with average description length
|
2,499 | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysis? | Disclaimer: @ttnphns is very knowledgeable about both PCA and FA, and I respect his opinion and have learned a lot from many of his great answers on the topic. However, I tend to disagree with his reply here, as well as with other (numerous) posts on this topic here on CV, not only his; or rather, I think they have lim... | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysi | Disclaimer: @ttnphns is very knowledgeable about both PCA and FA, and I respect his opinion and have learned a lot from many of his great answers on the topic. However, I tend to disagree with his rep | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysis?
Disclaimer: @ttnphns is very knowledgeable about both PCA and FA, and I respect his opinion and have learned a lot from many of his great answers on the topic. However, I tend to disagree with his reply here, as well ... | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysi
Disclaimer: @ttnphns is very knowledgeable about both PCA and FA, and I respect his opinion and have learned a lot from many of his great answers on the topic. However, I tend to disagree with his rep |
2,500 | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysis? | As you said, you are familiar with relevant answers; see also: So, as long as "Factor analysis..." + a couple of last paragraphs; and the bottom list here. In short, PCA is mostly a data reduction technique whereas FA is a modeling-of-latent-traits technique. Sometimes they happen to give similar results; but in your c... | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysi | As you said, you are familiar with relevant answers; see also: So, as long as "Factor analysis..." + a couple of last paragraphs; and the bottom list here. In short, PCA is mostly a data reduction tec | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysis?
As you said, you are familiar with relevant answers; see also: So, as long as "Factor analysis..." + a couple of last paragraphs; and the bottom list here. In short, PCA is mostly a data reduction technique whereas FA... | Is there any good reason to use PCA instead of EFA? Also, can PCA be a substitute for factor analysi
As you said, you are familiar with relevant answers; see also: So, as long as "Factor analysis..." + a couple of last paragraphs; and the bottom list here. In short, PCA is mostly a data reduction tec |
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