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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8,801 | What's the difference between a probability and a proportion? | I don't know if there is a difference, but probabilities are not % they range from 0 to 1. I mean if you multiply a probability by 100 you get %. If your question is what's the difference between probability and % then this would be my answer, but this is not your question. The definition of probability assumes an in... | What's the difference between a probability and a proportion? | I don't know if there is a difference, but probabilities are not % they range from 0 to 1. I mean if you multiply a probability by 100 you get %. If your question is what's the difference between pro | What's the difference between a probability and a proportion?
I don't know if there is a difference, but probabilities are not % they range from 0 to 1. I mean if you multiply a probability by 100 you get %. If your question is what's the difference between probability and % then this would be my answer, but this is n... | What's the difference between a probability and a proportion?
I don't know if there is a difference, but probabilities are not % they range from 0 to 1. I mean if you multiply a probability by 100 you get %. If your question is what's the difference between pro |
8,802 | What is the proper name for a "river plot" visualisation [duplicate] | It is a map, and so cartographers would likely refer to it as a thematic map (as opposed to a topographical map). The fact that many statistical diagrams have unique names (e.g. a bar chart, a scatterplot, a dotplot) as opposed to just describing their contents can sometime be a hindrance. Both because not everything i... | What is the proper name for a "river plot" visualisation [duplicate] | It is a map, and so cartographers would likely refer to it as a thematic map (as opposed to a topographical map). The fact that many statistical diagrams have unique names (e.g. a bar chart, a scatter | What is the proper name for a "river plot" visualisation [duplicate]
It is a map, and so cartographers would likely refer to it as a thematic map (as opposed to a topographical map). The fact that many statistical diagrams have unique names (e.g. a bar chart, a scatterplot, a dotplot) as opposed to just describing thei... | What is the proper name for a "river plot" visualisation [duplicate]
It is a map, and so cartographers would likely refer to it as a thematic map (as opposed to a topographical map). The fact that many statistical diagrams have unique names (e.g. a bar chart, a scatter |
8,803 | What is the proper name for a "river plot" visualisation [duplicate] | I have found it. What I was looking for is called a "Sankey diagram". Although there seems to be a tutorial on generating these graphs using rCharts, apparently there is no R-only package for this type of graphs yet on CRAN. | What is the proper name for a "river plot" visualisation [duplicate] | I have found it. What I was looking for is called a "Sankey diagram". Although there seems to be a tutorial on generating these graphs using rCharts, apparently there is no R-only package for this typ | What is the proper name for a "river plot" visualisation [duplicate]
I have found it. What I was looking for is called a "Sankey diagram". Although there seems to be a tutorial on generating these graphs using rCharts, apparently there is no R-only package for this type of graphs yet on CRAN. | What is the proper name for a "river plot" visualisation [duplicate]
I have found it. What I was looking for is called a "Sankey diagram". Although there seems to be a tutorial on generating these graphs using rCharts, apparently there is no R-only package for this typ |
8,804 | What is the proper name for a "river plot" visualisation [duplicate] | I don't think so. It includes so many elements I doubt it lends itself a single canonical name. That said, you could look for ribbon plot, parallel coordinates plot, and (thanks to the comment above from user603) flow map (and searching for flow maps certainly seems the way to proceed). A web search for "replicate Char... | What is the proper name for a "river plot" visualisation [duplicate] | I don't think so. It includes so many elements I doubt it lends itself a single canonical name. That said, you could look for ribbon plot, parallel coordinates plot, and (thanks to the comment above f | What is the proper name for a "river plot" visualisation [duplicate]
I don't think so. It includes so many elements I doubt it lends itself a single canonical name. That said, you could look for ribbon plot, parallel coordinates plot, and (thanks to the comment above from user603) flow map (and searching for flow maps ... | What is the proper name for a "river plot" visualisation [duplicate]
I don't think so. It includes so many elements I doubt it lends itself a single canonical name. That said, you could look for ribbon plot, parallel coordinates plot, and (thanks to the comment above f |
8,805 | Cross-validation including training, validation, and testing. Why do we need three subsets? | The training set is used to choose the optimum parameters for a given model. Note that evaluating some given set of parameters using the training set should give you an unbiased estimate of your cost function - it is the act of choosing the parameters which optimise the estimate of your cost function based on the train... | Cross-validation including training, validation, and testing. Why do we need three subsets? | The training set is used to choose the optimum parameters for a given model. Note that evaluating some given set of parameters using the training set should give you an unbiased estimate of your cost | Cross-validation including training, validation, and testing. Why do we need three subsets?
The training set is used to choose the optimum parameters for a given model. Note that evaluating some given set of parameters using the training set should give you an unbiased estimate of your cost function - it is the act of ... | Cross-validation including training, validation, and testing. Why do we need three subsets?
The training set is used to choose the optimum parameters for a given model. Note that evaluating some given set of parameters using the training set should give you an unbiased estimate of your cost |
8,806 | Cross-validation including training, validation, and testing. Why do we need three subsets? | If I have already found minimum Cost Function on Validation subset, why would I need to test it again on Test subset
Because of random error: Usually you only have a finite number of cases.
Optimization of the validation (inner test) performance means that you may be overfitting to that inner test set. The inner test... | Cross-validation including training, validation, and testing. Why do we need three subsets? | If I have already found minimum Cost Function on Validation subset, why would I need to test it again on Test subset
Because of random error: Usually you only have a finite number of cases.
Optimiza | Cross-validation including training, validation, and testing. Why do we need three subsets?
If I have already found minimum Cost Function on Validation subset, why would I need to test it again on Test subset
Because of random error: Usually you only have a finite number of cases.
Optimization of the validation (inne... | Cross-validation including training, validation, and testing. Why do we need three subsets?
If I have already found minimum Cost Function on Validation subset, why would I need to test it again on Test subset
Because of random error: Usually you only have a finite number of cases.
Optimiza |
8,807 | Cross-validation including training, validation, and testing. Why do we need three subsets? | While training the model one must select meta parameters for the model (for example, regularization parameter) or even choose from several models. In this case validation subset is used for parameter choosing, but test subset for final prediction estimation. | Cross-validation including training, validation, and testing. Why do we need three subsets? | While training the model one must select meta parameters for the model (for example, regularization parameter) or even choose from several models. In this case validation subset is used for parameter | Cross-validation including training, validation, and testing. Why do we need three subsets?
While training the model one must select meta parameters for the model (for example, regularization parameter) or even choose from several models. In this case validation subset is used for parameter choosing, but test subset fo... | Cross-validation including training, validation, and testing. Why do we need three subsets?
While training the model one must select meta parameters for the model (for example, regularization parameter) or even choose from several models. In this case validation subset is used for parameter |
8,808 | Why is softmax function used to calculate probabilities although we can divide each value by the sum of the vector? | The function you propose has a singularity whenever the sum of the elements is zero.
Suppose your vector is $[-1, \frac{1}{3}, \frac{2}{3}]$. This vector has a sum of 0, so division is not defined. The function is not differentiable here.
Additionally, if one or more of the elements of the vector is negative but the su... | Why is softmax function used to calculate probabilities although we can divide each value by the sum | The function you propose has a singularity whenever the sum of the elements is zero.
Suppose your vector is $[-1, \frac{1}{3}, \frac{2}{3}]$. This vector has a sum of 0, so division is not defined. Th | Why is softmax function used to calculate probabilities although we can divide each value by the sum of the vector?
The function you propose has a singularity whenever the sum of the elements is zero.
Suppose your vector is $[-1, \frac{1}{3}, \frac{2}{3}]$. This vector has a sum of 0, so division is not defined. The fu... | Why is softmax function used to calculate probabilities although we can divide each value by the sum
The function you propose has a singularity whenever the sum of the elements is zero.
Suppose your vector is $[-1, \frac{1}{3}, \frac{2}{3}]$. This vector has a sum of 0, so division is not defined. Th |
8,809 | Why is softmax function used to calculate probabilities although we can divide each value by the sum of the vector? | Softmax has two components:
Transform the components to e^x. This allows the neural network to work with logarithmic probabilities, instead of ordinary probabilities. This turns the common operation of multiplying probabilities into addition, which is far more natural for the linear algebra based structure of neural n... | Why is softmax function used to calculate probabilities although we can divide each value by the sum | Softmax has two components:
Transform the components to e^x. This allows the neural network to work with logarithmic probabilities, instead of ordinary probabilities. This turns the common operation | Why is softmax function used to calculate probabilities although we can divide each value by the sum of the vector?
Softmax has two components:
Transform the components to e^x. This allows the neural network to work with logarithmic probabilities, instead of ordinary probabilities. This turns the common operation of m... | Why is softmax function used to calculate probabilities although we can divide each value by the sum
Softmax has two components:
Transform the components to e^x. This allows the neural network to work with logarithmic probabilities, instead of ordinary probabilities. This turns the common operation |
8,810 | Why is softmax function used to calculate probabilities although we can divide each value by the sum of the vector? | In addition to previous suggestion, the softmax function allows for an additional parameter $\beta$, often named temperature $t=1/\beta$ from statistical mechanics, that allows to modulate how much the output probability distribution is concentrated around the positions with larger input value versus smaller ones.
$$
... | Why is softmax function used to calculate probabilities although we can divide each value by the sum | In addition to previous suggestion, the softmax function allows for an additional parameter $\beta$, often named temperature $t=1/\beta$ from statistical mechanics, that allows to modulate how much t | Why is softmax function used to calculate probabilities although we can divide each value by the sum of the vector?
In addition to previous suggestion, the softmax function allows for an additional parameter $\beta$, often named temperature $t=1/\beta$ from statistical mechanics, that allows to modulate how much the o... | Why is softmax function used to calculate probabilities although we can divide each value by the sum
In addition to previous suggestion, the softmax function allows for an additional parameter $\beta$, often named temperature $t=1/\beta$ from statistical mechanics, that allows to modulate how much t |
8,811 | Is it true that Bayesian methods don't overfit? | No, it is not true. Bayesian methods will certainly overfit the data. There are a couple of things that make Bayesian methods more robust against overfitting and you can make them more fragile as well.
The combinatoric nature of Bayesian hypotheses, rather than binary hypotheses allows for multiple comparisons when s... | Is it true that Bayesian methods don't overfit? | No, it is not true. Bayesian methods will certainly overfit the data. There are a couple of things that make Bayesian methods more robust against overfitting and you can make them more fragile as we | Is it true that Bayesian methods don't overfit?
No, it is not true. Bayesian methods will certainly overfit the data. There are a couple of things that make Bayesian methods more robust against overfitting and you can make them more fragile as well.
The combinatoric nature of Bayesian hypotheses, rather than binary h... | Is it true that Bayesian methods don't overfit?
No, it is not true. Bayesian methods will certainly overfit the data. There are a couple of things that make Bayesian methods more robust against overfitting and you can make them more fragile as we |
8,812 | Is it true that Bayesian methods don't overfit? | Something to be aware of is that like practically everywhere else, a significant problem in Bayesian methods can be model misspecification.
This is an obvious point, but I thought I'd still share a story.
A vignette from back in undergrad...
A classic application of Bayesian particle filtering is to track the location ... | Is it true that Bayesian methods don't overfit? | Something to be aware of is that like practically everywhere else, a significant problem in Bayesian methods can be model misspecification.
This is an obvious point, but I thought I'd still share a st | Is it true that Bayesian methods don't overfit?
Something to be aware of is that like practically everywhere else, a significant problem in Bayesian methods can be model misspecification.
This is an obvious point, but I thought I'd still share a story.
A vignette from back in undergrad...
A classic application of Bayes... | Is it true that Bayesian methods don't overfit?
Something to be aware of is that like practically everywhere else, a significant problem in Bayesian methods can be model misspecification.
This is an obvious point, but I thought I'd still share a st |
8,813 | How to increase longer term reproducibility of research (particularly using R and Sweave) | At some level, this becomes impossible. Consider the case of the famous Pentium floating point bug: you not only need to conserve your models, your data, your parameters, your packages, all external packages, the host system or language (say, R) as well as the OS ... plus potentially the hardware it all ran on. Now c... | How to increase longer term reproducibility of research (particularly using R and Sweave) | At some level, this becomes impossible. Consider the case of the famous Pentium floating point bug: you not only need to conserve your models, your data, your parameters, your packages, all external | How to increase longer term reproducibility of research (particularly using R and Sweave)
At some level, this becomes impossible. Consider the case of the famous Pentium floating point bug: you not only need to conserve your models, your data, your parameters, your packages, all external packages, the host system or l... | How to increase longer term reproducibility of research (particularly using R and Sweave)
At some level, this becomes impossible. Consider the case of the famous Pentium floating point bug: you not only need to conserve your models, your data, your parameters, your packages, all external |
8,814 | How to increase longer term reproducibility of research (particularly using R and Sweave) | The first step in reproducibility is making sure the data are in a format that is easy for future researchers to read. Flat files are the clear choice here (Fairbairn in press).
To make the code useful over the long term, perhaps the best thing to do is write clear documentation that explains both what the code does an... | How to increase longer term reproducibility of research (particularly using R and Sweave) | The first step in reproducibility is making sure the data are in a format that is easy for future researchers to read. Flat files are the clear choice here (Fairbairn in press).
To make the code usefu | How to increase longer term reproducibility of research (particularly using R and Sweave)
The first step in reproducibility is making sure the data are in a format that is easy for future researchers to read. Flat files are the clear choice here (Fairbairn in press).
To make the code useful over the long term, perhaps ... | How to increase longer term reproducibility of research (particularly using R and Sweave)
The first step in reproducibility is making sure the data are in a format that is easy for future researchers to read. Flat files are the clear choice here (Fairbairn in press).
To make the code usefu |
8,815 | How to increase longer term reproducibility of research (particularly using R and Sweave) | One strategy involves using the cacher package.
Peng RD, Eckel SP (2009). "Distributed reproducible research using cached computations," IEEE Computing in Science and Engineering, 11 (1), 28–34. (PDF online)
also see more articles on
Roger Peng's website
Further discussion and examples can be found in the book:
Stat... | How to increase longer term reproducibility of research (particularly using R and Sweave) | One strategy involves using the cacher package.
Peng RD, Eckel SP (2009). "Distributed reproducible research using cached computations," IEEE Computing in Science and Engineering, 11 (1), 28–34. (PDF | How to increase longer term reproducibility of research (particularly using R and Sweave)
One strategy involves using the cacher package.
Peng RD, Eckel SP (2009). "Distributed reproducible research using cached computations," IEEE Computing in Science and Engineering, 11 (1), 28–34. (PDF online)
also see more article... | How to increase longer term reproducibility of research (particularly using R and Sweave)
One strategy involves using the cacher package.
Peng RD, Eckel SP (2009). "Distributed reproducible research using cached computations," IEEE Computing in Science and Engineering, 11 (1), 28–34. (PDF |
8,816 | How to increase longer term reproducibility of research (particularly using R and Sweave) | If you are interested in the virtual machine route, I think it would be doable via a small linux distribution with the specific version of R and packages installed. Data is included, along with scripts, and package the whole thing in a virtual box file.
This does not get around hardware problems mentioned earlier such... | How to increase longer term reproducibility of research (particularly using R and Sweave) | If you are interested in the virtual machine route, I think it would be doable via a small linux distribution with the specific version of R and packages installed. Data is included, along with scrip | How to increase longer term reproducibility of research (particularly using R and Sweave)
If you are interested in the virtual machine route, I think it would be doable via a small linux distribution with the specific version of R and packages installed. Data is included, along with scripts, and package the whole thin... | How to increase longer term reproducibility of research (particularly using R and Sweave)
If you are interested in the virtual machine route, I think it would be doable via a small linux distribution with the specific version of R and packages installed. Data is included, along with scrip |
8,817 | How to increase longer term reproducibility of research (particularly using R and Sweave) | I would recomend two things in addition to the excellent answers already present;
At Key points in your code, dump out the current data as a flat file, suitably named and described in comments, thus highlighting if one package has produced differing results where the differences have been introduced. These data files... | How to increase longer term reproducibility of research (particularly using R and Sweave) | I would recomend two things in addition to the excellent answers already present;
At Key points in your code, dump out the current data as a flat file, suitably named and described in comments, thus | How to increase longer term reproducibility of research (particularly using R and Sweave)
I would recomend two things in addition to the excellent answers already present;
At Key points in your code, dump out the current data as a flat file, suitably named and described in comments, thus highlighting if one package ha... | How to increase longer term reproducibility of research (particularly using R and Sweave)
I would recomend two things in addition to the excellent answers already present;
At Key points in your code, dump out the current data as a flat file, suitably named and described in comments, thus |
8,818 | How to increase longer term reproducibility of research (particularly using R and Sweave) | Good suggestions, I've got plenty of things to look into now.
Remember, one extremely important consideration is making sure that the work is "correct" in the first place. This is the role that tools like Sweave play, by increasing the chances that what you did, and what you said you did, are the same thing. | How to increase longer term reproducibility of research (particularly using R and Sweave) | Good suggestions, I've got plenty of things to look into now.
Remember, one extremely important consideration is making sure that the work is "correct" in the first place. This is the role that too | How to increase longer term reproducibility of research (particularly using R and Sweave)
Good suggestions, I've got plenty of things to look into now.
Remember, one extremely important consideration is making sure that the work is "correct" in the first place. This is the role that tools like Sweave play, by increa... | How to increase longer term reproducibility of research (particularly using R and Sweave)
Good suggestions, I've got plenty of things to look into now.
Remember, one extremely important consideration is making sure that the work is "correct" in the first place. This is the role that too |
8,819 | What does "normalization" mean and how to verify that a sample or a distribution is normalized? | Unfortunately, terms are used differently in different fields, by different people within the same field, etc., so I'm not sure how well this can be answered for you here. You should make sure you know the definition that your instructor / the textbook is using for "normalized". However, here are some common definiti... | What does "normalization" mean and how to verify that a sample or a distribution is normalized? | Unfortunately, terms are used differently in different fields, by different people within the same field, etc., so I'm not sure how well this can be answered for you here. You should make sure you kn | What does "normalization" mean and how to verify that a sample or a distribution is normalized?
Unfortunately, terms are used differently in different fields, by different people within the same field, etc., so I'm not sure how well this can be answered for you here. You should make sure you know the definition that y... | What does "normalization" mean and how to verify that a sample or a distribution is normalized?
Unfortunately, terms are used differently in different fields, by different people within the same field, etc., so I'm not sure how well this can be answered for you here. You should make sure you kn |
8,820 | What does "normalization" mean and how to verify that a sample or a distribution is normalized? | By using the formula you provided on each score in your sample, you are converting them all to z-scores.
To verify that you computed all the z-scores correctly, find the new mean and standard deviation of your sample. If the mean is $0$ and the standard deviation is $1$, you've done everything correctly.
The purpose o... | What does "normalization" mean and how to verify that a sample or a distribution is normalized? | By using the formula you provided on each score in your sample, you are converting them all to z-scores.
To verify that you computed all the z-scores correctly, find the new mean and standard deviati | What does "normalization" mean and how to verify that a sample or a distribution is normalized?
By using the formula you provided on each score in your sample, you are converting them all to z-scores.
To verify that you computed all the z-scores correctly, find the new mean and standard deviation of your sample. If th... | What does "normalization" mean and how to verify that a sample or a distribution is normalized?
By using the formula you provided on each score in your sample, you are converting them all to z-scores.
To verify that you computed all the z-scores correctly, find the new mean and standard deviati |
8,821 | What does "normalization" mean and how to verify that a sample or a distribution is normalized? | After consulting the TA, what the question was asking was whether if
$$
\int_{-\infty}^{\infty}f(x)dx=1
$$
where $f(x)$ in this case is the density of the uniform(a,b). | What does "normalization" mean and how to verify that a sample or a distribution is normalized? | After consulting the TA, what the question was asking was whether if
$$
\int_{-\infty}^{\infty}f(x)dx=1
$$
where $f(x)$ in this case is the density of the uniform(a,b). | What does "normalization" mean and how to verify that a sample or a distribution is normalized?
After consulting the TA, what the question was asking was whether if
$$
\int_{-\infty}^{\infty}f(x)dx=1
$$
where $f(x)$ in this case is the density of the uniform(a,b). | What does "normalization" mean and how to verify that a sample or a distribution is normalized?
After consulting the TA, what the question was asking was whether if
$$
\int_{-\infty}^{\infty}f(x)dx=1
$$
where $f(x)$ in this case is the density of the uniform(a,b). |
8,822 | Test for finite variance? | No, this is not possible, because a finite sample of size $n$ cannot reliably distinguish between, say, a normal population and a normal population contaminated by a $1/N$ amount of a Cauchy distribution where $N$ >> $n$. (Of course the former has finite variance and the latter has infinite variance.) Thus any fully ... | Test for finite variance? | No, this is not possible, because a finite sample of size $n$ cannot reliably distinguish between, say, a normal population and a normal population contaminated by a $1/N$ amount of a Cauchy distribut | Test for finite variance?
No, this is not possible, because a finite sample of size $n$ cannot reliably distinguish between, say, a normal population and a normal population contaminated by a $1/N$ amount of a Cauchy distribution where $N$ >> $n$. (Of course the former has finite variance and the latter has infinite v... | Test for finite variance?
No, this is not possible, because a finite sample of size $n$ cannot reliably distinguish between, say, a normal population and a normal population contaminated by a $1/N$ amount of a Cauchy distribut |
8,823 | Test for finite variance? | You cannot be certain without knowing the distribution. But there are certain things you can do, such as looking at what might be called the "partial variance", i.e. if you have a sample of size $N$, you draw the variance estimated from the first $n$ terms, with $n$ running from 2 to $N$.
With a finite population vari... | Test for finite variance? | You cannot be certain without knowing the distribution. But there are certain things you can do, such as looking at what might be called the "partial variance", i.e. if you have a sample of size $N$, | Test for finite variance?
You cannot be certain without knowing the distribution. But there are certain things you can do, such as looking at what might be called the "partial variance", i.e. if you have a sample of size $N$, you draw the variance estimated from the first $n$ terms, with $n$ running from 2 to $N$.
Wit... | Test for finite variance?
You cannot be certain without knowing the distribution. But there are certain things you can do, such as looking at what might be called the "partial variance", i.e. if you have a sample of size $N$, |
8,824 | Test for finite variance? | Here's another answer. Suppose you could parametrize the problem, something like this:
$$
H_{0}:\ X \sim t(\mathtt{df}=3)\mathrm{\ versus\ } H_{1}:\ X \sim t(\mathtt{df}=1).
$$
Then you could do an ordinary Neyman-Pearson likelihood ratio test of $H_{0}$ versus $H_{1}$. Note that $H_{1}$ is Cauchy (infinite varian... | Test for finite variance? | Here's another answer. Suppose you could parametrize the problem, something like this:
$$
H_{0}:\ X \sim t(\mathtt{df}=3)\mathrm{\ versus\ } H_{1}:\ X \sim t(\mathtt{df}=1).
$$
Then you could do a | Test for finite variance?
Here's another answer. Suppose you could parametrize the problem, something like this:
$$
H_{0}:\ X \sim t(\mathtt{df}=3)\mathrm{\ versus\ } H_{1}:\ X \sim t(\mathtt{df}=1).
$$
Then you could do an ordinary Neyman-Pearson likelihood ratio test of $H_{0}$ versus $H_{1}$. Note that $H_{1}$ ... | Test for finite variance?
Here's another answer. Suppose you could parametrize the problem, something like this:
$$
H_{0}:\ X \sim t(\mathtt{df}=3)\mathrm{\ versus\ } H_{1}:\ X \sim t(\mathtt{df}=1).
$$
Then you could do a |
8,825 | Test for finite variance? | In order to test such a vague hypothesis, you need to average out over all densities with finite variance, and all densities with infinite variance. This is likely to be impossible, you basically need to be more specific. One more specific version of this and have two hypothesis for a sample $D\equiv Y_{1},Y_{2},\dot... | Test for finite variance? | In order to test such a vague hypothesis, you need to average out over all densities with finite variance, and all densities with infinite variance. This is likely to be impossible, you basically nee | Test for finite variance?
In order to test such a vague hypothesis, you need to average out over all densities with finite variance, and all densities with infinite variance. This is likely to be impossible, you basically need to be more specific. One more specific version of this and have two hypothesis for a sample... | Test for finite variance?
In order to test such a vague hypothesis, you need to average out over all densities with finite variance, and all densities with infinite variance. This is likely to be impossible, you basically nee |
8,826 | Test for finite variance? | The counterexample is not relevant to the question asked. You want to test the null hypothesis that a sample of i.i.d. random variables is drawn from a distribution having finite variance, at a given significance level. I recommend a good reference text like "Statistical Inference" by Casella to understand the use and ... | Test for finite variance? | The counterexample is not relevant to the question asked. You want to test the null hypothesis that a sample of i.i.d. random variables is drawn from a distribution having finite variance, at a given | Test for finite variance?
The counterexample is not relevant to the question asked. You want to test the null hypothesis that a sample of i.i.d. random variables is drawn from a distribution having finite variance, at a given significance level. I recommend a good reference text like "Statistical Inference" by Casella ... | Test for finite variance?
The counterexample is not relevant to the question asked. You want to test the null hypothesis that a sample of i.i.d. random variables is drawn from a distribution having finite variance, at a given |
8,827 | Test for finite variance? | One approach that had been suggested to me was via the Central Limit Theorem.
This is a old question, but I want to propose a way to use the CLT to test for large tails.
Let $X = \{X_1,\ldots,X_n\}$ be our sample. If the sample is a i.i.d. realization from a light tail distribution, then the CLT theorem holds. It foll... | Test for finite variance? | One approach that had been suggested to me was via the Central Limit Theorem.
This is a old question, but I want to propose a way to use the CLT to test for large tails.
Let $X = \{X_1,\ldots,X_n\}$ | Test for finite variance?
One approach that had been suggested to me was via the Central Limit Theorem.
This is a old question, but I want to propose a way to use the CLT to test for large tails.
Let $X = \{X_1,\ldots,X_n\}$ be our sample. If the sample is a i.i.d. realization from a light tail distribution, then the ... | Test for finite variance?
One approach that had been suggested to me was via the Central Limit Theorem.
This is a old question, but I want to propose a way to use the CLT to test for large tails.
Let $X = \{X_1,\ldots,X_n\}$ |
8,828 | Difference Between ANOVA and Kruskal-Wallis test | There are differences in the assumptions and the hypotheses that are tested.
The ANOVA (and t-test) is explicitly a test of equality of means of values. The Kruskal-Wallis (and Mann-Whitney) can be seen technically as a comparison of the mean ranks.
Hence, in terms of original values, the Kruskal-Wallis is more genera... | Difference Between ANOVA and Kruskal-Wallis test | There are differences in the assumptions and the hypotheses that are tested.
The ANOVA (and t-test) is explicitly a test of equality of means of values. The Kruskal-Wallis (and Mann-Whitney) can be se | Difference Between ANOVA and Kruskal-Wallis test
There are differences in the assumptions and the hypotheses that are tested.
The ANOVA (and t-test) is explicitly a test of equality of means of values. The Kruskal-Wallis (and Mann-Whitney) can be seen technically as a comparison of the mean ranks.
Hence, in terms of o... | Difference Between ANOVA and Kruskal-Wallis test
There are differences in the assumptions and the hypotheses that are tested.
The ANOVA (and t-test) is explicitly a test of equality of means of values. The Kruskal-Wallis (and Mann-Whitney) can be se |
8,829 | Difference Between ANOVA and Kruskal-Wallis test | Yes there is. The anova is a parametric approach while kruskal.test is a non parametric approach. So kruskal.test does not need any distributional assumption.
From practical point of view, when your data is skewed, then anova would not a be good approach to use. Have a look at this question for example. | Difference Between ANOVA and Kruskal-Wallis test | Yes there is. The anova is a parametric approach while kruskal.test is a non parametric approach. So kruskal.test does not need any distributional assumption.
From practical point of view, when your | Difference Between ANOVA and Kruskal-Wallis test
Yes there is. The anova is a parametric approach while kruskal.test is a non parametric approach. So kruskal.test does not need any distributional assumption.
From practical point of view, when your data is skewed, then anova would not a be good approach to use. Have a ... | Difference Between ANOVA and Kruskal-Wallis test
Yes there is. The anova is a parametric approach while kruskal.test is a non parametric approach. So kruskal.test does not need any distributional assumption.
From practical point of view, when your |
8,830 | Difference Between ANOVA and Kruskal-Wallis test | As far as I know (but please correct me if I'm wrong cause I'm not sure), the Kruskal-Wallis test is constructed in order to detect a difference between two distributions having the same shape and the same dispersion, that is, one is obtained by translating the other by a difference $\Delta$, such as:
Let's call $(*)$... | Difference Between ANOVA and Kruskal-Wallis test | As far as I know (but please correct me if I'm wrong cause I'm not sure), the Kruskal-Wallis test is constructed in order to detect a difference between two distributions having the same shape and the | Difference Between ANOVA and Kruskal-Wallis test
As far as I know (but please correct me if I'm wrong cause I'm not sure), the Kruskal-Wallis test is constructed in order to detect a difference between two distributions having the same shape and the same dispersion, that is, one is obtained by translating the other by ... | Difference Between ANOVA and Kruskal-Wallis test
As far as I know (but please correct me if I'm wrong cause I'm not sure), the Kruskal-Wallis test is constructed in order to detect a difference between two distributions having the same shape and the |
8,831 | Difference Between ANOVA and Kruskal-Wallis test | Kruskal-Wallis is rank based, rather than value-based. This can make a big difference if there are skewed distributions or if there are extreme cases | Difference Between ANOVA and Kruskal-Wallis test | Kruskal-Wallis is rank based, rather than value-based. This can make a big difference if there are skewed distributions or if there are extreme cases | Difference Between ANOVA and Kruskal-Wallis test
Kruskal-Wallis is rank based, rather than value-based. This can make a big difference if there are skewed distributions or if there are extreme cases | Difference Between ANOVA and Kruskal-Wallis test
Kruskal-Wallis is rank based, rather than value-based. This can make a big difference if there are skewed distributions or if there are extreme cases |
8,832 | Explanation of Spikes in training loss vs. iterations with Adam Optimizer | The spikes are an unavoidable consequence of Mini-Batch Gradient Descent in Adam (batch_size=32).
Some mini-batches have 'by chance' unlucky data for the optimization, inducing those spikes you see in your cost function using Adam. If you try stochastic gradient descent (same as using batch_size=1) you will see that t... | Explanation of Spikes in training loss vs. iterations with Adam Optimizer | The spikes are an unavoidable consequence of Mini-Batch Gradient Descent in Adam (batch_size=32).
Some mini-batches have 'by chance' unlucky data for the optimization, inducing those spikes you see i | Explanation of Spikes in training loss vs. iterations with Adam Optimizer
The spikes are an unavoidable consequence of Mini-Batch Gradient Descent in Adam (batch_size=32).
Some mini-batches have 'by chance' unlucky data for the optimization, inducing those spikes you see in your cost function using Adam. If you try st... | Explanation of Spikes in training loss vs. iterations with Adam Optimizer
The spikes are an unavoidable consequence of Mini-Batch Gradient Descent in Adam (batch_size=32).
Some mini-batches have 'by chance' unlucky data for the optimization, inducing those spikes you see i |
8,833 | Explanation of Spikes in training loss vs. iterations with Adam Optimizer | I've spent insane amount of time debugging exploding gradients and similar behaviour. Your answer will be dependent on loss function, data, architecture etc. There's hundreds of reasons. I'll name a few.
Loss-dependent. Loglikelihood-losses needs to be clipped, if not, it may evaluate near log(0) for bad predictions/o... | Explanation of Spikes in training loss vs. iterations with Adam Optimizer | I've spent insane amount of time debugging exploding gradients and similar behaviour. Your answer will be dependent on loss function, data, architecture etc. There's hundreds of reasons. I'll name a f | Explanation of Spikes in training loss vs. iterations with Adam Optimizer
I've spent insane amount of time debugging exploding gradients and similar behaviour. Your answer will be dependent on loss function, data, architecture etc. There's hundreds of reasons. I'll name a few.
Loss-dependent. Loglikelihood-losses need... | Explanation of Spikes in training loss vs. iterations with Adam Optimizer
I've spent insane amount of time debugging exploding gradients and similar behaviour. Your answer will be dependent on loss function, data, architecture etc. There's hundreds of reasons. I'll name a f |
8,834 | Why is xgboost overfitting in my task? Is it fine to accept this overfitting? | Is overfitting so bad that you should not pick a model that does overfit, even though its test error is smaller? No. But you should have a justification for choosing it.
This behavior is not restricted to XGBoost. It is a common thread among all machine learning techniques; finding the right tradeoff between underfitti... | Why is xgboost overfitting in my task? Is it fine to accept this overfitting? | Is overfitting so bad that you should not pick a model that does overfit, even though its test error is smaller? No. But you should have a justification for choosing it.
This behavior is not restricte | Why is xgboost overfitting in my task? Is it fine to accept this overfitting?
Is overfitting so bad that you should not pick a model that does overfit, even though its test error is smaller? No. But you should have a justification for choosing it.
This behavior is not restricted to XGBoost. It is a common thread among ... | Why is xgboost overfitting in my task? Is it fine to accept this overfitting?
Is overfitting so bad that you should not pick a model that does overfit, even though its test error is smaller? No. But you should have a justification for choosing it.
This behavior is not restricte |
8,835 | Where's the graph theory in graphical models? | There is very little true mathematical graph theory in probabilistic graphical models, where by true mathematical graph theory I mean proofs about cliques, vertex orders, max-flow min-cut theorems, and so on. Even something as fundamental as Euler's Theorem and Handshaking Lemma are not used, though I suppose one migh... | Where's the graph theory in graphical models? | There is very little true mathematical graph theory in probabilistic graphical models, where by true mathematical graph theory I mean proofs about cliques, vertex orders, max-flow min-cut theorems, an | Where's the graph theory in graphical models?
There is very little true mathematical graph theory in probabilistic graphical models, where by true mathematical graph theory I mean proofs about cliques, vertex orders, max-flow min-cut theorems, and so on. Even something as fundamental as Euler's Theorem and Handshaking... | Where's the graph theory in graphical models?
There is very little true mathematical graph theory in probabilistic graphical models, where by true mathematical graph theory I mean proofs about cliques, vertex orders, max-flow min-cut theorems, an |
8,836 | Where's the graph theory in graphical models? | In a strict sense, graph theory seems loosely connected to PGMs. However, graph algorithms come in handy. PGMs started with message-passing inference, which is a subset of general class of message-passing algorithms on graphs (may be, that is the reason for the word “graphical” in them). Graph-cut algorithms are widely... | Where's the graph theory in graphical models? | In a strict sense, graph theory seems loosely connected to PGMs. However, graph algorithms come in handy. PGMs started with message-passing inference, which is a subset of general class of message-pas | Where's the graph theory in graphical models?
In a strict sense, graph theory seems loosely connected to PGMs. However, graph algorithms come in handy. PGMs started with message-passing inference, which is a subset of general class of message-passing algorithms on graphs (may be, that is the reason for the word “graphi... | Where's the graph theory in graphical models?
In a strict sense, graph theory seems loosely connected to PGMs. However, graph algorithms come in handy. PGMs started with message-passing inference, which is a subset of general class of message-pas |
8,837 | Where's the graph theory in graphical models? | There has been some work investigating the link between the ease of decoding of Low Density Parity Check codes (which gets excellent results when you consider it a probablistic graph and apply Loopy Belief Propagation), and the girth of the graph formed by the parity check matrix. This link to girth goes right the way ... | Where's the graph theory in graphical models? | There has been some work investigating the link between the ease of decoding of Low Density Parity Check codes (which gets excellent results when you consider it a probablistic graph and apply Loopy B | Where's the graph theory in graphical models?
There has been some work investigating the link between the ease of decoding of Low Density Parity Check codes (which gets excellent results when you consider it a probablistic graph and apply Loopy Belief Propagation), and the girth of the graph formed by the parity check ... | Where's the graph theory in graphical models?
There has been some work investigating the link between the ease of decoding of Low Density Parity Check codes (which gets excellent results when you consider it a probablistic graph and apply Loopy B |
8,838 | Where's the graph theory in graphical models? | One successful application of graph algorithms to probabilistic graphical models is the Chow-Liu algorithm. It solves the problem of finding the optimum (tree) graph structure and is based on maximum spanning trees (MST) algorithm.
A joint probability over a tree graphical model can be written as:
\begin{equation}
... | Where's the graph theory in graphical models? | One successful application of graph algorithms to probabilistic graphical models is the Chow-Liu algorithm. It solves the problem of finding the optimum (tree) graph structure and is based on maximum | Where's the graph theory in graphical models?
One successful application of graph algorithms to probabilistic graphical models is the Chow-Liu algorithm. It solves the problem of finding the optimum (tree) graph structure and is based on maximum spanning trees (MST) algorithm.
A joint probability over a tree graphical ... | Where's the graph theory in graphical models?
One successful application of graph algorithms to probabilistic graphical models is the Chow-Liu algorithm. It solves the problem of finding the optimum (tree) graph structure and is based on maximum |
8,839 | Open source tools for visualizing multi-dimensional data? | How about R with ggplot2?
Other tools that I really like:
Processing
Prefuse
Protovis | Open source tools for visualizing multi-dimensional data? | How about R with ggplot2?
Other tools that I really like:
Processing
Prefuse
Protovis | Open source tools for visualizing multi-dimensional data?
How about R with ggplot2?
Other tools that I really like:
Processing
Prefuse
Protovis | Open source tools for visualizing multi-dimensional data?
How about R with ggplot2?
Other tools that I really like:
Processing
Prefuse
Protovis |
8,840 | Open source tools for visualizing multi-dimensional data? | Mondrian: Exploratory data analysis with focus on large data and databases.
iPlots: a package for the R statistical environment which provides high interaction statistical graphics, written in Java. | Open source tools for visualizing multi-dimensional data? | Mondrian: Exploratory data analysis with focus on large data and databases.
iPlots: a package for the R statistical environment which provides high interaction statistical graphics, written in Java. | Open source tools for visualizing multi-dimensional data?
Mondrian: Exploratory data analysis with focus on large data and databases.
iPlots: a package for the R statistical environment which provides high interaction statistical graphics, written in Java. | Open source tools for visualizing multi-dimensional data?
Mondrian: Exploratory data analysis with focus on large data and databases.
iPlots: a package for the R statistical environment which provides high interaction statistical graphics, written in Java. |
8,841 | Open source tools for visualizing multi-dimensional data? | The lattice package in R.
Lattice is a powerful and elegant high-level data visualization
system, with an emphasis on multivariate data,that is sufficient for
typical graphics needs, and is also flexible enough to handle most
nonstandard requirements.
Quick-R has a quick introduction. | Open source tools for visualizing multi-dimensional data? | The lattice package in R.
Lattice is a powerful and elegant high-level data visualization
system, with an emphasis on multivariate data,that is sufficient for
typical graphics needs, and is also fl | Open source tools for visualizing multi-dimensional data?
The lattice package in R.
Lattice is a powerful and elegant high-level data visualization
system, with an emphasis on multivariate data,that is sufficient for
typical graphics needs, and is also flexible enough to handle most
nonstandard requirements.
Quic... | Open source tools for visualizing multi-dimensional data?
The lattice package in R.
Lattice is a powerful and elegant high-level data visualization
system, with an emphasis on multivariate data,that is sufficient for
typical graphics needs, and is also fl |
8,842 | Open source tools for visualizing multi-dimensional data? | ggobi and the R links to Ggobi are really rather good for this. There are simpler visualisations (iPlots is very nice, also interactive, as mentioned).
But it depends whether you are doing something more specialised. For example TreeView lets you visualise the kind of cluster dendrograms you get out of microarrays. | Open source tools for visualizing multi-dimensional data? | ggobi and the R links to Ggobi are really rather good for this. There are simpler visualisations (iPlots is very nice, also interactive, as mentioned).
But it depends whether you are doing something | Open source tools for visualizing multi-dimensional data?
ggobi and the R links to Ggobi are really rather good for this. There are simpler visualisations (iPlots is very nice, also interactive, as mentioned).
But it depends whether you are doing something more specialised. For example TreeView lets you visualise t... | Open source tools for visualizing multi-dimensional data?
ggobi and the R links to Ggobi are really rather good for this. There are simpler visualisations (iPlots is very nice, also interactive, as mentioned).
But it depends whether you are doing something |
8,843 | Open source tools for visualizing multi-dimensional data? | Python's matplotlib | Open source tools for visualizing multi-dimensional data? | Python's matplotlib | Open source tools for visualizing multi-dimensional data?
Python's matplotlib | Open source tools for visualizing multi-dimensional data?
Python's matplotlib |
8,844 | Open source tools for visualizing multi-dimensional data? | Viewpoints is useful for multi-variate data sets. | Open source tools for visualizing multi-dimensional data? | Viewpoints is useful for multi-variate data sets. | Open source tools for visualizing multi-dimensional data?
Viewpoints is useful for multi-variate data sets. | Open source tools for visualizing multi-dimensional data?
Viewpoints is useful for multi-variate data sets. |
8,845 | Open source tools for visualizing multi-dimensional data? | t-SNE has many open source implementations. One of the easiest to use is probably sklearn.manifold.TSNE. sklearn.manifold contains other manifold learning methods to plot your data to 2D: | Open source tools for visualizing multi-dimensional data? | t-SNE has many open source implementations. One of the easiest to use is probably sklearn.manifold.TSNE. sklearn.manifold contains other manifold learning methods to plot your data to 2D: | Open source tools for visualizing multi-dimensional data?
t-SNE has many open source implementations. One of the easiest to use is probably sklearn.manifold.TSNE. sklearn.manifold contains other manifold learning methods to plot your data to 2D: | Open source tools for visualizing multi-dimensional data?
t-SNE has many open source implementations. One of the easiest to use is probably sklearn.manifold.TSNE. sklearn.manifold contains other manifold learning methods to plot your data to 2D: |
8,846 | Open source tools for visualizing multi-dimensional data? | Look also SCaVis data plotting library. It works on any platform since Java.
It supports many data containers and plot styles (2D, 3D etc.) | Open source tools for visualizing multi-dimensional data? | Look also SCaVis data plotting library. It works on any platform since Java.
It supports many data containers and plot styles (2D, 3D etc.) | Open source tools for visualizing multi-dimensional data?
Look also SCaVis data plotting library. It works on any platform since Java.
It supports many data containers and plot styles (2D, 3D etc.) | Open source tools for visualizing multi-dimensional data?
Look also SCaVis data plotting library. It works on any platform since Java.
It supports many data containers and plot styles (2D, 3D etc.) |
8,847 | Best bandit algorithm? | A paper from NIPS 2011 ("An empirical evaluation of Thompson Sampling") shows, in experiments, that Thompson Sampling beats UCB. UCB is based on choosing the lever that promises the highest reward under optimistic assumptions (i.e. the variance of your estimate of the expected reward is high, therefore you pull levers ... | Best bandit algorithm? | A paper from NIPS 2011 ("An empirical evaluation of Thompson Sampling") shows, in experiments, that Thompson Sampling beats UCB. UCB is based on choosing the lever that promises the highest reward und | Best bandit algorithm?
A paper from NIPS 2011 ("An empirical evaluation of Thompson Sampling") shows, in experiments, that Thompson Sampling beats UCB. UCB is based on choosing the lever that promises the highest reward under optimistic assumptions (i.e. the variance of your estimate of the expected reward is high, the... | Best bandit algorithm?
A paper from NIPS 2011 ("An empirical evaluation of Thompson Sampling") shows, in experiments, that Thompson Sampling beats UCB. UCB is based on choosing the lever that promises the highest reward und |
8,848 | Best bandit algorithm? | UCB is indeed near optimal in the stochastic case (up to a log T factor for a T round game), and up to a gap in Pinsker's inequality in a more problem dependent sense. Recent paper of Audibert and Bubeck removes this log dependence in the worst case, but has a worse bound in the favorable case when different arms have ... | Best bandit algorithm? | UCB is indeed near optimal in the stochastic case (up to a log T factor for a T round game), and up to a gap in Pinsker's inequality in a more problem dependent sense. Recent paper of Audibert and Bub | Best bandit algorithm?
UCB is indeed near optimal in the stochastic case (up to a log T factor for a T round game), and up to a gap in Pinsker's inequality in a more problem dependent sense. Recent paper of Audibert and Bubeck removes this log dependence in the worst case, but has a worse bound in the favorable case wh... | Best bandit algorithm?
UCB is indeed near optimal in the stochastic case (up to a log T factor for a T round game), and up to a gap in Pinsker's inequality in a more problem dependent sense. Recent paper of Audibert and Bub |
8,849 | Best bandit algorithm? | The current state of the art could be summed up like this:
stochastic: UCB and variants (regret in $R_T = O(\frac{K \log T}{\Delta})$)
adversarial: EXP3 and variants (regret in $\tilde{R}_T = O(\sqrt{T K \log K})$)
contextual: it's complicated
with $T$ is the number of rounds, $K$ the number of arms, $\Delta$ the tru... | Best bandit algorithm? | The current state of the art could be summed up like this:
stochastic: UCB and variants (regret in $R_T = O(\frac{K \log T}{\Delta})$)
adversarial: EXP3 and variants (regret in $\tilde{R}_T = O(\sqrt | Best bandit algorithm?
The current state of the art could be summed up like this:
stochastic: UCB and variants (regret in $R_T = O(\frac{K \log T}{\Delta})$)
adversarial: EXP3 and variants (regret in $\tilde{R}_T = O(\sqrt{T K \log K})$)
contextual: it's complicated
with $T$ is the number of rounds, $K$ the number of... | Best bandit algorithm?
The current state of the art could be summed up like this:
stochastic: UCB and variants (regret in $R_T = O(\frac{K \log T}{\Delta})$)
adversarial: EXP3 and variants (regret in $\tilde{R}_T = O(\sqrt |
8,850 | Calculating PCA variance explained [duplicate] | Yes, that's correct. summary.prcomp brings that information as well:
summary(pca)
#Importance of components:
# PC1 PC2 PC3 PC4
#Standard deviation 1.5749 0.9949 0.59713 0.41645
#Proportion of Variance 0.6201 0.2474 0.08914 0.04336
#Cumulative Proportion 0.6201 0.8675 0.95664 1.0... | Calculating PCA variance explained [duplicate] | Yes, that's correct. summary.prcomp brings that information as well:
summary(pca)
#Importance of components:
# PC1 PC2 PC3 PC4
#Standard deviation 1.5749 0.9949 | Calculating PCA variance explained [duplicate]
Yes, that's correct. summary.prcomp brings that information as well:
summary(pca)
#Importance of components:
# PC1 PC2 PC3 PC4
#Standard deviation 1.5749 0.9949 0.59713 0.41645
#Proportion of Variance 0.6201 0.2474 0.08914 0.04336
#C... | Calculating PCA variance explained [duplicate]
Yes, that's correct. summary.prcomp brings that information as well:
summary(pca)
#Importance of components:
# PC1 PC2 PC3 PC4
#Standard deviation 1.5749 0.9949 |
8,851 | REML or ML to compare two mixed effects models with differing fixed effects, but with the same random effect? | Zuur et al., and Faraway (from @janhove's comment above) are right; using likelihood-based methods (including AIC) to compare two models with different fixed effects that are fitted by REML will generally lead to nonsense.
Faraway (2006) Extending the linear model with R (p. 156):
The reason is that REML estimates the... | REML or ML to compare two mixed effects models with differing fixed effects, but with the same rando | Zuur et al., and Faraway (from @janhove's comment above) are right; using likelihood-based methods (including AIC) to compare two models with different fixed effects that are fitted by REML will gener | REML or ML to compare two mixed effects models with differing fixed effects, but with the same random effect?
Zuur et al., and Faraway (from @janhove's comment above) are right; using likelihood-based methods (including AIC) to compare two models with different fixed effects that are fitted by REML will generally lead ... | REML or ML to compare two mixed effects models with differing fixed effects, but with the same rando
Zuur et al., and Faraway (from @janhove's comment above) are right; using likelihood-based methods (including AIC) to compare two models with different fixed effects that are fitted by REML will gener |
8,852 | REML or ML to compare two mixed effects models with differing fixed effects, but with the same random effect? | I'll give an example to illustrate why the REML likelihood cannot be used for things like AIC comparisons. Imagine that we a normal mixed effects model. Let $X$ denote the design matrix and assume that this matrix has full rank. We can find a reparametrization of the mean value space, given by the matrix $\tilde{X}$. T... | REML or ML to compare two mixed effects models with differing fixed effects, but with the same rando | I'll give an example to illustrate why the REML likelihood cannot be used for things like AIC comparisons. Imagine that we a normal mixed effects model. Let $X$ denote the design matrix and assume tha | REML or ML to compare two mixed effects models with differing fixed effects, but with the same random effect?
I'll give an example to illustrate why the REML likelihood cannot be used for things like AIC comparisons. Imagine that we a normal mixed effects model. Let $X$ denote the design matrix and assume that this mat... | REML or ML to compare two mixed effects models with differing fixed effects, but with the same rando
I'll give an example to illustrate why the REML likelihood cannot be used for things like AIC comparisons. Imagine that we a normal mixed effects model. Let $X$ denote the design matrix and assume tha |
8,853 | Who invented the decision tree? | Good question. @G5W is on the right track in referencing Wei-Yin Loh's paper. Loh's paper discusses the statistical antecedents of decision trees and, correctly, traces their locus back to Fisher's (1936) paper on discriminant analysis -- essentially regression classifying multiple groups as the dependent variable -- a... | Who invented the decision tree? | Good question. @G5W is on the right track in referencing Wei-Yin Loh's paper. Loh's paper discusses the statistical antecedents of decision trees and, correctly, traces their locus back to Fisher's (1 | Who invented the decision tree?
Good question. @G5W is on the right track in referencing Wei-Yin Loh's paper. Loh's paper discusses the statistical antecedents of decision trees and, correctly, traces their locus back to Fisher's (1936) paper on discriminant analysis -- essentially regression classifying multiple group... | Who invented the decision tree?
Good question. @G5W is on the right track in referencing Wei-Yin Loh's paper. Loh's paper discusses the statistical antecedents of decision trees and, correctly, traces their locus back to Fisher's (1 |
8,854 | Who invented the decision tree? | The big reference on CART is:
Classification and Regression Trees
Leo Breiman, Jerome Friedman, Charles J. Stone, R.A. Olshen (1984)
but that certainly was not the earliest work on the subject.
In his 1986 paper Induction of Decision Trees, Quinlan himself identifies Hunt's Concept Learning
System (CLS) as a pre... | Who invented the decision tree? | The big reference on CART is:
Classification and Regression Trees
Leo Breiman, Jerome Friedman, Charles J. Stone, R.A. Olshen (1984)
but that certainly was not the earliest work on the subject.
I | Who invented the decision tree?
The big reference on CART is:
Classification and Regression Trees
Leo Breiman, Jerome Friedman, Charles J. Stone, R.A. Olshen (1984)
but that certainly was not the earliest work on the subject.
In his 1986 paper Induction of Decision Trees, Quinlan himself identifies Hunt's Concept... | Who invented the decision tree?
The big reference on CART is:
Classification and Regression Trees
Leo Breiman, Jerome Friedman, Charles J. Stone, R.A. Olshen (1984)
but that certainly was not the earliest work on the subject.
I |
8,855 | Feature selection & model with glmnet on Methylation data (p>>N) | Part 1
In the elastic net two types of constraints on the parameters are employed
Lasso constraints (i.e. on the size of the absolute values of $\beta_j$)
Ridge constraints (i.e. on the size of the squared values of $\beta_j$)
$\alpha$ controls the relative weighting of the two types. The Lasso constraints allow for ... | Feature selection & model with glmnet on Methylation data (p>>N) | Part 1
In the elastic net two types of constraints on the parameters are employed
Lasso constraints (i.e. on the size of the absolute values of $\beta_j$)
Ridge constraints (i.e. on the size of the s | Feature selection & model with glmnet on Methylation data (p>>N)
Part 1
In the elastic net two types of constraints on the parameters are employed
Lasso constraints (i.e. on the size of the absolute values of $\beta_j$)
Ridge constraints (i.e. on the size of the squared values of $\beta_j$)
$\alpha$ controls the rela... | Feature selection & model with glmnet on Methylation data (p>>N)
Part 1
In the elastic net two types of constraints on the parameters are employed
Lasso constraints (i.e. on the size of the absolute values of $\beta_j$)
Ridge constraints (i.e. on the size of the s |
8,856 | What are some interesting and well-written applied statistics papers? | It's a bit difficult for me to see what paper might be of interest to you, so let me try and suggest the following ones, from the psychometric literature:
Borsboom, D. (2006). The attack of
the psychometricians.
Psychometrika, 71, 425-440.
for dressing the scene (Why do we need to use statistical models that bett... | What are some interesting and well-written applied statistics papers? | It's a bit difficult for me to see what paper might be of interest to you, so let me try and suggest the following ones, from the psychometric literature:
Borsboom, D. (2006). The attack of
the psy | What are some interesting and well-written applied statistics papers?
It's a bit difficult for me to see what paper might be of interest to you, so let me try and suggest the following ones, from the psychometric literature:
Borsboom, D. (2006). The attack of
the psychometricians.
Psychometrika, 71, 425-440.
for ... | What are some interesting and well-written applied statistics papers?
It's a bit difficult for me to see what paper might be of interest to you, so let me try and suggest the following ones, from the psychometric literature:
Borsboom, D. (2006). The attack of
the psy |
8,857 | What are some interesting and well-written applied statistics papers? | Here are five highly-cited papers from the last 40 years of the Journal of the Royal Statistical Society, Series C: Applied Statistics with a clear application in the title that caught my eye while scanning through the Web of Knowledge search results:
Sheila M. Gore, Stuart J. Pocock and Gillian R. Kerr (1984). Regres... | What are some interesting and well-written applied statistics papers? | Here are five highly-cited papers from the last 40 years of the Journal of the Royal Statistical Society, Series C: Applied Statistics with a clear application in the title that caught my eye while sc | What are some interesting and well-written applied statistics papers?
Here are five highly-cited papers from the last 40 years of the Journal of the Royal Statistical Society, Series C: Applied Statistics with a clear application in the title that caught my eye while scanning through the Web of Knowledge search results... | What are some interesting and well-written applied statistics papers?
Here are five highly-cited papers from the last 40 years of the Journal of the Royal Statistical Society, Series C: Applied Statistics with a clear application in the title that caught my eye while sc |
8,858 | What are some interesting and well-written applied statistics papers? | On a wider level I would recommend the ["Statistical Modeling: The Two Cultures"][1] paper by Leo Breiman in 2001 (cited 515) I know it was covered by the journal club recently and I found it to be really interesting. I've c&p'd the abstract.
Abstract. There are two cultures in
the use of statistical modeling to
r... | What are some interesting and well-written applied statistics papers? | On a wider level I would recommend the ["Statistical Modeling: The Two Cultures"][1] paper by Leo Breiman in 2001 (cited 515) I know it was covered by the journal club recently and I found it to be re | What are some interesting and well-written applied statistics papers?
On a wider level I would recommend the ["Statistical Modeling: The Two Cultures"][1] paper by Leo Breiman in 2001 (cited 515) I know it was covered by the journal club recently and I found it to be really interesting. I've c&p'd the abstract.
Abstra... | What are some interesting and well-written applied statistics papers?
On a wider level I would recommend the ["Statistical Modeling: The Two Cultures"][1] paper by Leo Breiman in 2001 (cited 515) I know it was covered by the journal club recently and I found it to be re |
8,859 | What are some interesting and well-written applied statistics papers? | From a genetic epidemiology perspective, I would now recommend the following series of papers about genome-wide association studies:
Cordell, H.J. and Clayton, D.G. (2005). Genetic association studies. Lancet 366, 1121-1131.
Cantor, R.M., Lange, K., and Sinsheimer, J.S. (2010). Prioritizing GWAS results: A review of s... | What are some interesting and well-written applied statistics papers? | From a genetic epidemiology perspective, I would now recommend the following series of papers about genome-wide association studies:
Cordell, H.J. and Clayton, D.G. (2005). Genetic association studie | What are some interesting and well-written applied statistics papers?
From a genetic epidemiology perspective, I would now recommend the following series of papers about genome-wide association studies:
Cordell, H.J. and Clayton, D.G. (2005). Genetic association studies. Lancet 366, 1121-1131.
Cantor, R.M., Lange, K.,... | What are some interesting and well-written applied statistics papers?
From a genetic epidemiology perspective, I would now recommend the following series of papers about genome-wide association studies:
Cordell, H.J. and Clayton, D.G. (2005). Genetic association studie |
8,860 | What are some interesting and well-written applied statistics papers? | Jim Berger's review articles: http://www.stat.duke.edu/~berger/papers.html
You might start with Could Fisher, Jeffreys and Neyman have agreed upon testing? | What are some interesting and well-written applied statistics papers? | Jim Berger's review articles: http://www.stat.duke.edu/~berger/papers.html
You might start with Could Fisher, Jeffreys and Neyman have agreed upon testing? | What are some interesting and well-written applied statistics papers?
Jim Berger's review articles: http://www.stat.duke.edu/~berger/papers.html
You might start with Could Fisher, Jeffreys and Neyman have agreed upon testing? | What are some interesting and well-written applied statistics papers?
Jim Berger's review articles: http://www.stat.duke.edu/~berger/papers.html
You might start with Could Fisher, Jeffreys and Neyman have agreed upon testing? |
8,861 | What are some interesting and well-written applied statistics papers? | An article with early impact regarding statistical bioinformatics research:
Jelizarow et al. Over-optimism in bioinformatics: an illustration. Bioinformatics, 2010
It makes for an interesting discussion on bias sources, overfitting, and fishing for significance. | What are some interesting and well-written applied statistics papers? | An article with early impact regarding statistical bioinformatics research:
Jelizarow et al. Over-optimism in bioinformatics: an illustration. Bioinformatics, 2010
It makes for an interesting discussi | What are some interesting and well-written applied statistics papers?
An article with early impact regarding statistical bioinformatics research:
Jelizarow et al. Over-optimism in bioinformatics: an illustration. Bioinformatics, 2010
It makes for an interesting discussion on bias sources, overfitting, and fishing for s... | What are some interesting and well-written applied statistics papers?
An article with early impact regarding statistical bioinformatics research:
Jelizarow et al. Over-optimism in bioinformatics: an illustration. Bioinformatics, 2010
It makes for an interesting discussi |
8,862 | In layman's terms, what is the difference between a model and a distribution? | Probability distribution is a mathematical function that describes a random variable. A little bit more precisely, it is a function that assigns probabilities to numbers and it's output has to agree with axioms of probability.
Statistical model is an abstract, idealized description of some phenomenon in mathematical te... | In layman's terms, what is the difference between a model and a distribution? | Probability distribution is a mathematical function that describes a random variable. A little bit more precisely, it is a function that assigns probabilities to numbers and it's output has to agree w | In layman's terms, what is the difference between a model and a distribution?
Probability distribution is a mathematical function that describes a random variable. A little bit more precisely, it is a function that assigns probabilities to numbers and it's output has to agree with axioms of probability.
Statistical mod... | In layman's terms, what is the difference between a model and a distribution?
Probability distribution is a mathematical function that describes a random variable. A little bit more precisely, it is a function that assigns probabilities to numbers and it's output has to agree w |
8,863 | In layman's terms, what is the difference between a model and a distribution? | Think of $\mathcal{S}$ as a set of tickets. You can write stuff on a ticket. Usually a ticket starts out with the name of some real-world person or object that it "represents" or "models." There's lots of blank space on each ticket for writing other things.
You can make as many copies of each ticket as you want. A ... | In layman's terms, what is the difference between a model and a distribution? | Think of $\mathcal{S}$ as a set of tickets. You can write stuff on a ticket. Usually a ticket starts out with the name of some real-world person or object that it "represents" or "models." There's | In layman's terms, what is the difference between a model and a distribution?
Think of $\mathcal{S}$ as a set of tickets. You can write stuff on a ticket. Usually a ticket starts out with the name of some real-world person or object that it "represents" or "models." There's lots of blank space on each ticket for wri... | In layman's terms, what is the difference between a model and a distribution?
Think of $\mathcal{S}$ as a set of tickets. You can write stuff on a ticket. Usually a ticket starts out with the name of some real-world person or object that it "represents" or "models." There's |
8,864 | In layman's terms, what is the difference between a model and a distribution? | The definition of a distribution as assigning probabilities to each possible event works for discrete distribution, but becomes trickier for continuous distributions, where e.g. any number on the real line could be the outcome. Very often when talking about distributions, we think of them as having fixed parameters suc... | In layman's terms, what is the difference between a model and a distribution? | The definition of a distribution as assigning probabilities to each possible event works for discrete distribution, but becomes trickier for continuous distributions, where e.g. any number on the real | In layman's terms, what is the difference between a model and a distribution?
The definition of a distribution as assigning probabilities to each possible event works for discrete distribution, but becomes trickier for continuous distributions, where e.g. any number on the real line could be the outcome. Very often whe... | In layman's terms, what is the difference between a model and a distribution?
The definition of a distribution as assigning probabilities to each possible event works for discrete distribution, but becomes trickier for continuous distributions, where e.g. any number on the real |
8,865 | In layman's terms, what is the difference between a model and a distribution? | A probability distribution gives all the information about how a random quantity fluctuates. In practice we usually do not have the full probability distribution of our quantity of interest. We may know or assume something about it without knowing or assuming that we know everything about it. For example, we might assu... | In layman's terms, what is the difference between a model and a distribution? | A probability distribution gives all the information about how a random quantity fluctuates. In practice we usually do not have the full probability distribution of our quantity of interest. We may kn | In layman's terms, what is the difference between a model and a distribution?
A probability distribution gives all the information about how a random quantity fluctuates. In practice we usually do not have the full probability distribution of our quantity of interest. We may know or assume something about it without kn... | In layman's terms, what is the difference between a model and a distribution?
A probability distribution gives all the information about how a random quantity fluctuates. In practice we usually do not have the full probability distribution of our quantity of interest. We may kn |
8,866 | In layman's terms, what is the difference between a model and a distribution? | You ask a very important question, Alan, and have received some fine answers above. I would like to offer a simpler answer, and also indicate an additional dimension to the distinction that the above answers have not addressed. For simplicity, everything I'll say here relates to parametric statistical models.
First of ... | In layman's terms, what is the difference between a model and a distribution? | You ask a very important question, Alan, and have received some fine answers above. I would like to offer a simpler answer, and also indicate an additional dimension to the distinction that the above | In layman's terms, what is the difference between a model and a distribution?
You ask a very important question, Alan, and have received some fine answers above. I would like to offer a simpler answer, and also indicate an additional dimension to the distinction that the above answers have not addressed. For simplicity... | In layman's terms, what is the difference between a model and a distribution?
You ask a very important question, Alan, and have received some fine answers above. I would like to offer a simpler answer, and also indicate an additional dimension to the distinction that the above |
8,867 | In layman's terms, what is the difference between a model and a distribution? | A model is specified by a PDF, but it is not a PDF.
Probability distribution (PDF) is a function that assigns probabilities to numbers and its output has to agree with axioms of probability, like Tim explained.
A model is fully defined by a probability distribution, but it is more than that. In the coin tossing example... | In layman's terms, what is the difference between a model and a distribution? | A model is specified by a PDF, but it is not a PDF.
Probability distribution (PDF) is a function that assigns probabilities to numbers and its output has to agree with axioms of probability, like Tim | In layman's terms, what is the difference between a model and a distribution?
A model is specified by a PDF, but it is not a PDF.
Probability distribution (PDF) is a function that assigns probabilities to numbers and its output has to agree with axioms of probability, like Tim explained.
A model is fully defined by a p... | In layman's terms, what is the difference between a model and a distribution?
A model is specified by a PDF, but it is not a PDF.
Probability distribution (PDF) is a function that assigns probabilities to numbers and its output has to agree with axioms of probability, like Tim |
8,868 | A statistical approach to determine if data are missing at random | I found the information I was talking about in my comment.
From van Buurens book, page 31, he writes
"Several tests have been proposed to test MCAR versus MAR. These tests
are not widely used, and their practical value is unclear. See Enders (2010, pp. 17–21) for an evaluation of two procedures. It is not possible to t... | A statistical approach to determine if data are missing at random | I found the information I was talking about in my comment.
From van Buurens book, page 31, he writes
"Several tests have been proposed to test MCAR versus MAR. These tests
are not widely used, and the | A statistical approach to determine if data are missing at random
I found the information I was talking about in my comment.
From van Buurens book, page 31, he writes
"Several tests have been proposed to test MCAR versus MAR. These tests
are not widely used, and their practical value is unclear. See Enders (2010, pp. 1... | A statistical approach to determine if data are missing at random
I found the information I was talking about in my comment.
From van Buurens book, page 31, he writes
"Several tests have been proposed to test MCAR versus MAR. These tests
are not widely used, and the |
8,869 | A statistical approach to determine if data are missing at random | This is not possible, unless you managed to retrieve missing data. You cannot determine from the observed data whether the missing data is missing at random (MAR) or not at random (MNAR). You can only tell whether the data is clearly not missing completely at random (MCAR). Beyond that only appeal to plausibility of MC... | A statistical approach to determine if data are missing at random | This is not possible, unless you managed to retrieve missing data. You cannot determine from the observed data whether the missing data is missing at random (MAR) or not at random (MNAR). You can only | A statistical approach to determine if data are missing at random
This is not possible, unless you managed to retrieve missing data. You cannot determine from the observed data whether the missing data is missing at random (MAR) or not at random (MNAR). You can only tell whether the data is clearly not missing complete... | A statistical approach to determine if data are missing at random
This is not possible, unless you managed to retrieve missing data. You cannot determine from the observed data whether the missing data is missing at random (MAR) or not at random (MNAR). You can only |
8,870 | A statistical approach to determine if data are missing at random | A method I use is a shadow matrix, in which the dataset consists of indicator variables where a 1 is given if a value is present, and 0 if it isn't. Correlating these with each other and the original data can help determine if variables tend to be missing together (MAR) or not (MCAR). Using R for an example (borrowing ... | A statistical approach to determine if data are missing at random | A method I use is a shadow matrix, in which the dataset consists of indicator variables where a 1 is given if a value is present, and 0 if it isn't. Correlating these with each other and the original | A statistical approach to determine if data are missing at random
A method I use is a shadow matrix, in which the dataset consists of indicator variables where a 1 is given if a value is present, and 0 if it isn't. Correlating these with each other and the original data can help determine if variables tend to be missin... | A statistical approach to determine if data are missing at random
A method I use is a shadow matrix, in which the dataset consists of indicator variables where a 1 is given if a value is present, and 0 if it isn't. Correlating these with each other and the original |
8,871 | A statistical approach to determine if data are missing at random | This sounds quite doable from a classification standpoint.
You want to classify missing versus non-missing data using all other features. If you get significantly better than random results, then your data aren't missing at random. | A statistical approach to determine if data are missing at random | This sounds quite doable from a classification standpoint.
You want to classify missing versus non-missing data using all other features. If you get significantly better than random results, then your | A statistical approach to determine if data are missing at random
This sounds quite doable from a classification standpoint.
You want to classify missing versus non-missing data using all other features. If you get significantly better than random results, then your data aren't missing at random. | A statistical approach to determine if data are missing at random
This sounds quite doable from a classification standpoint.
You want to classify missing versus non-missing data using all other features. If you get significantly better than random results, then your |
8,872 | A statistical approach to determine if data are missing at random | You want to know whether there is some correlation of a value being missed in feature and the value of any other of the features.
For each of the features, create a new feature indicating whether the value is missing or not (let's call them "is_missing" feature).
Compute your favourite correlation measure (I suggest us... | A statistical approach to determine if data are missing at random | You want to know whether there is some correlation of a value being missed in feature and the value of any other of the features.
For each of the features, create a new feature indicating whether the | A statistical approach to determine if data are missing at random
You want to know whether there is some correlation of a value being missed in feature and the value of any other of the features.
For each of the features, create a new feature indicating whether the value is missing or not (let's call them "is_missing" ... | A statistical approach to determine if data are missing at random
You want to know whether there is some correlation of a value being missed in feature and the value of any other of the features.
For each of the features, create a new feature indicating whether the |
8,873 | A statistical approach to determine if data are missing at random | There is a useful package called finalfit check here it has a missing_pairs(outcome VAR, explanatory Vars) were you can explore patterns of missingness and decide whether data is MCAR or MAR. It produces pairs plots to show relationships between missing values and observed values in all variables. | A statistical approach to determine if data are missing at random | There is a useful package called finalfit check here it has a missing_pairs(outcome VAR, explanatory Vars) were you can explore patterns of missingness and decide whether data is MCAR or MAR. It produ | A statistical approach to determine if data are missing at random
There is a useful package called finalfit check here it has a missing_pairs(outcome VAR, explanatory Vars) were you can explore patterns of missingness and decide whether data is MCAR or MAR. It produces pairs plots to show relationships between missing ... | A statistical approach to determine if data are missing at random
There is a useful package called finalfit check here it has a missing_pairs(outcome VAR, explanatory Vars) were you can explore patterns of missingness and decide whether data is MCAR or MAR. It produ |
8,874 | What does a non positive definite covariance matrix tell me about my data? | The covariance matrix is not positive definite because it is singular. That means that at least one of your variables can be expressed as a linear combination of the others. You do not need all the variables as the value of at least one can be determined from a subset of the others. I would suggest adding variables ... | What does a non positive definite covariance matrix tell me about my data? | The covariance matrix is not positive definite because it is singular. That means that at least one of your variables can be expressed as a linear combination of the others. You do not need all the | What does a non positive definite covariance matrix tell me about my data?
The covariance matrix is not positive definite because it is singular. That means that at least one of your variables can be expressed as a linear combination of the others. You do not need all the variables as the value of at least one can be... | What does a non positive definite covariance matrix tell me about my data?
The covariance matrix is not positive definite because it is singular. That means that at least one of your variables can be expressed as a linear combination of the others. You do not need all the |
8,875 | What does a non positive definite covariance matrix tell me about my data? | One point that I don't think is addressed above is that it IS possible to calculate a non-positive definite covariance matrix from empirical data even if your variables are not perfectly linearly related. If you don't have sufficient data (particularly if you are trying to construct a high-dimensional covariance matrix... | What does a non positive definite covariance matrix tell me about my data? | One point that I don't think is addressed above is that it IS possible to calculate a non-positive definite covariance matrix from empirical data even if your variables are not perfectly linearly rela | What does a non positive definite covariance matrix tell me about my data?
One point that I don't think is addressed above is that it IS possible to calculate a non-positive definite covariance matrix from empirical data even if your variables are not perfectly linearly related. If you don't have sufficient data (parti... | What does a non positive definite covariance matrix tell me about my data?
One point that I don't think is addressed above is that it IS possible to calculate a non-positive definite covariance matrix from empirical data even if your variables are not perfectly linearly rela |
8,876 | What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it? | I will try to add to the other answer. First, completeness is a technical condition which is justified mainly by the theorems that use it. So let us start with some related concepts and theorems where they occur.
Let $X=(X_1,X_2,\dotsc,X_n)$ represent a vector of iid data, which we model as having a distribution $f(x;\... | What is the intuition behind defining completeness in a statistic as being impossible to form an unb | I will try to add to the other answer. First, completeness is a technical condition which is justified mainly by the theorems that use it. So let us start with some related concepts and theorems where | What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it?
I will try to add to the other answer. First, completeness is a technical condition which is justified mainly by the theorems that use it. So let us start with some related concepts and th... | What is the intuition behind defining completeness in a statistic as being impossible to form an unb
I will try to add to the other answer. First, completeness is a technical condition which is justified mainly by the theorems that use it. So let us start with some related concepts and theorems where |
8,877 | What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it? | Some intuition may be available from the theory of best (minimum variance) unbiased estimators (Casella and Berger's Statistical Inference (2002), Theorem 7.3.20).
If $E_\theta W=\tau(\theta)$ then $W$ is a best unbiased estimator of $\tau(\theta)$ iff $W$ is uncorrelated with all other unbiased estimators of zero.
Pro... | What is the intuition behind defining completeness in a statistic as being impossible to form an unb | Some intuition may be available from the theory of best (minimum variance) unbiased estimators (Casella and Berger's Statistical Inference (2002), Theorem 7.3.20).
If $E_\theta W=\tau(\theta)$ then $W | What is the intuition behind defining completeness in a statistic as being impossible to form an unbiased estimator of $0$ from it?
Some intuition may be available from the theory of best (minimum variance) unbiased estimators (Casella and Berger's Statistical Inference (2002), Theorem 7.3.20).
If $E_\theta W=\tau(\the... | What is the intuition behind defining completeness in a statistic as being impossible to form an unb
Some intuition may be available from the theory of best (minimum variance) unbiased estimators (Casella and Berger's Statistical Inference (2002), Theorem 7.3.20).
If $E_\theta W=\tau(\theta)$ then $W |
8,878 | Estimating parameters of Student's t-distribution | Closed form does not exist for T, but a very intuitive and stable approach is via the EM algorithm. Now because student is a scale mixture of normals, you can write your model as
$$y_i=\mu+e_i$$
where $e_i|\sigma,w_i \sim N(0,\sigma^2w_i^{-1})$ and $w_i\sim Ga(\frac{\nu}{2}, \frac{\nu}{2})$. This means that condition... | Estimating parameters of Student's t-distribution | Closed form does not exist for T, but a very intuitive and stable approach is via the EM algorithm. Now because student is a scale mixture of normals, you can write your model as
$$y_i=\mu+e_i$$
wher | Estimating parameters of Student's t-distribution
Closed form does not exist for T, but a very intuitive and stable approach is via the EM algorithm. Now because student is a scale mixture of normals, you can write your model as
$$y_i=\mu+e_i$$
where $e_i|\sigma,w_i \sim N(0,\sigma^2w_i^{-1})$ and $w_i\sim Ga(\frac{\n... | Estimating parameters of Student's t-distribution
Closed form does not exist for T, but a very intuitive and stable approach is via the EM algorithm. Now because student is a scale mixture of normals, you can write your model as
$$y_i=\mu+e_i$$
wher |
8,879 | Estimating parameters of Student's t-distribution | The following paper addresses exactly the problem you posted.
Liu C. and Rubin D.B. 1995. "ML estimation of the t distribution using
EM and its extensions, ECM and ECME." Statistica Sinica 5:19–39.
It provides a general multivariate t-distribution parameter estimation, with or without the knowledge of the degree of fre... | Estimating parameters of Student's t-distribution | The following paper addresses exactly the problem you posted.
Liu C. and Rubin D.B. 1995. "ML estimation of the t distribution using
EM and its extensions, ECM and ECME." Statistica Sinica 5:19–39.
It | Estimating parameters of Student's t-distribution
The following paper addresses exactly the problem you posted.
Liu C. and Rubin D.B. 1995. "ML estimation of the t distribution using
EM and its extensions, ECM and ECME." Statistica Sinica 5:19–39.
It provides a general multivariate t-distribution parameter estimation, ... | Estimating parameters of Student's t-distribution
The following paper addresses exactly the problem you posted.
Liu C. and Rubin D.B. 1995. "ML estimation of the t distribution using
EM and its extensions, ECM and ECME." Statistica Sinica 5:19–39.
It |
8,880 | Estimating parameters of Student's t-distribution | I doubt that it exists in closed form: if you write any one of the factors of the likelihood as $$\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{t^2}{\nu} \right)^{-\frac{\nu+1}{2}} = \frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \exp \left \{ \left [ \ln \le... | Estimating parameters of Student's t-distribution | I doubt that it exists in closed form: if you write any one of the factors of the likelihood as $$\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{t^2}{\nu} \right)^ | Estimating parameters of Student's t-distribution
I doubt that it exists in closed form: if you write any one of the factors of the likelihood as $$\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{t^2}{\nu} \right)^{-\frac{\nu+1}{2}} = \frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\G... | Estimating parameters of Student's t-distribution
I doubt that it exists in closed form: if you write any one of the factors of the likelihood as $$\frac{\Gamma(\frac{\nu+1}{2})} {\sqrt{\nu\pi}\,\Gamma(\frac{\nu}{2})} \left(1+\frac{t^2}{\nu} \right)^ |
8,881 | Estimating parameters of Student's t-distribution | Does a closed-form maximum-likelihood estimator for the Student's t distribution exist? The answer is now YES!! During the COVID pandemic, I dug into this problem and discovered a method I call Independent Approximators (IAs). This new algorithm provides a closed-form estimate of the location, scale, and shape that a... | Estimating parameters of Student's t-distribution | Does a closed-form maximum-likelihood estimator for the Student's t distribution exist? The answer is now YES!! During the COVID pandemic, I dug into this problem and discovered a method I call Indep | Estimating parameters of Student's t-distribution
Does a closed-form maximum-likelihood estimator for the Student's t distribution exist? The answer is now YES!! During the COVID pandemic, I dug into this problem and discovered a method I call Independent Approximators (IAs). This new algorithm provides a closed-form... | Estimating parameters of Student's t-distribution
Does a closed-form maximum-likelihood estimator for the Student's t distribution exist? The answer is now YES!! During the COVID pandemic, I dug into this problem and discovered a method I call Indep |
8,882 | Transforming variables for multiple regression in R | John Fox's book An R companion to applied regression is an excellent ressource on applied regression modelling with R. The package car which I use throughout in this answer is the accompanying package. The book also has as website with additional chapters.
Transforming the response (aka dependent variable, outcome)
Bo... | Transforming variables for multiple regression in R | John Fox's book An R companion to applied regression is an excellent ressource on applied regression modelling with R. The package car which I use throughout in this answer is the accompanying package | Transforming variables for multiple regression in R
John Fox's book An R companion to applied regression is an excellent ressource on applied regression modelling with R. The package car which I use throughout in this answer is the accompanying package. The book also has as website with additional chapters.
Transformi... | Transforming variables for multiple regression in R
John Fox's book An R companion to applied regression is an excellent ressource on applied regression modelling with R. The package car which I use throughout in this answer is the accompanying package |
8,883 | Transforming variables for multiple regression in R | You should tell us more about the nature of your response (outcome, dependent) variable. From your first plot it is strongly positively skewed with many values near zero and some negative. From that it is possible, but not inevitable, that transformation would help you, but the most important question is whether transf... | Transforming variables for multiple regression in R | You should tell us more about the nature of your response (outcome, dependent) variable. From your first plot it is strongly positively skewed with many values near zero and some negative. From that i | Transforming variables for multiple regression in R
You should tell us more about the nature of your response (outcome, dependent) variable. From your first plot it is strongly positively skewed with many values near zero and some negative. From that it is possible, but not inevitable, that transformation would help yo... | Transforming variables for multiple regression in R
You should tell us more about the nature of your response (outcome, dependent) variable. From your first plot it is strongly positively skewed with many values near zero and some negative. From that i |
8,884 | Specifying multiple (separate) random effects in lme [closed] | After many struggles I found a solution for my problem, which I am posting here in case somebody will have similar questions:
fit <- lme(Y ~ time, random=list(year=~1, date=~time), data=X, weights=varIdent(form=~1|year)) | Specifying multiple (separate) random effects in lme [closed] | After many struggles I found a solution for my problem, which I am posting here in case somebody will have similar questions:
fit <- lme(Y ~ time, random=list(year=~1, date=~time), data=X, weights=var | Specifying multiple (separate) random effects in lme [closed]
After many struggles I found a solution for my problem, which I am posting here in case somebody will have similar questions:
fit <- lme(Y ~ time, random=list(year=~1, date=~time), data=X, weights=varIdent(form=~1|year)) | Specifying multiple (separate) random effects in lme [closed]
After many struggles I found a solution for my problem, which I am posting here in case somebody will have similar questions:
fit <- lme(Y ~ time, random=list(year=~1, date=~time), data=X, weights=var |
8,885 | What is the best method for checking convergence in MCMC? | I use the Gelman-Rubin convergence diagnostic as well. A potential problem with Gelman-Rubin is that it may mis-diagnose convergence if the shrink factor happens to be close to 1 by chance, in which case you can use a Gelman-Rubin-Brooks plot. See the "General Methods for Monitoring Convergence of Iterative Simulatio... | What is the best method for checking convergence in MCMC? | I use the Gelman-Rubin convergence diagnostic as well. A potential problem with Gelman-Rubin is that it may mis-diagnose convergence if the shrink factor happens to be close to 1 by chance, in which | What is the best method for checking convergence in MCMC?
I use the Gelman-Rubin convergence diagnostic as well. A potential problem with Gelman-Rubin is that it may mis-diagnose convergence if the shrink factor happens to be close to 1 by chance, in which case you can use a Gelman-Rubin-Brooks plot. See the "General... | What is the best method for checking convergence in MCMC?
I use the Gelman-Rubin convergence diagnostic as well. A potential problem with Gelman-Rubin is that it may mis-diagnose convergence if the shrink factor happens to be close to 1 by chance, in which |
8,886 | What is the best method for checking convergence in MCMC? | Rather than using the Gelman-Rubin statistic, which is a nice aid but not perfect (as with all convergence diagnostics), I simply use the same idea and plot the results for a visual graphical assessment. In almost all cases I have considered (which is a very large number), graphing the trace plots of multiple MCMC chai... | What is the best method for checking convergence in MCMC? | Rather than using the Gelman-Rubin statistic, which is a nice aid but not perfect (as with all convergence diagnostics), I simply use the same idea and plot the results for a visual graphical assessme | What is the best method for checking convergence in MCMC?
Rather than using the Gelman-Rubin statistic, which is a nice aid but not perfect (as with all convergence diagnostics), I simply use the same idea and plot the results for a visual graphical assessment. In almost all cases I have considered (which is a very lar... | What is the best method for checking convergence in MCMC?
Rather than using the Gelman-Rubin statistic, which is a nice aid but not perfect (as with all convergence diagnostics), I simply use the same idea and plot the results for a visual graphical assessme |
8,887 | What is the best method for checking convergence in MCMC? | This is a wee late into the debate, but we have a whole chapter in our 2007 book Introducing Monte Carlo Methods with R dealing with this issue. You can also download the CODA package from CRAN to this effect. | What is the best method for checking convergence in MCMC? | This is a wee late into the debate, but we have a whole chapter in our 2007 book Introducing Monte Carlo Methods with R dealing with this issue. You can also download the CODA package from CRAN to th | What is the best method for checking convergence in MCMC?
This is a wee late into the debate, but we have a whole chapter in our 2007 book Introducing Monte Carlo Methods with R dealing with this issue. You can also download the CODA package from CRAN to this effect. | What is the best method for checking convergence in MCMC?
This is a wee late into the debate, but we have a whole chapter in our 2007 book Introducing Monte Carlo Methods with R dealing with this issue. You can also download the CODA package from CRAN to th |
8,888 | What is the best method for checking convergence in MCMC? | I like to do trace plots primarily and sometimes I use the Gelman-Rubin convergence diagnostic. | What is the best method for checking convergence in MCMC? | I like to do trace plots primarily and sometimes I use the Gelman-Rubin convergence diagnostic. | What is the best method for checking convergence in MCMC?
I like to do trace plots primarily and sometimes I use the Gelman-Rubin convergence diagnostic. | What is the best method for checking convergence in MCMC?
I like to do trace plots primarily and sometimes I use the Gelman-Rubin convergence diagnostic. |
8,889 | Can non-random samples be analyzed using standard statistical tests? | There are two general models to testing. The first one, based on the assumption of random sampling from a population, is usually called the "population model".
For example, for the two-independent samples t-test, we assume that the two groups we want to compare are random samples from the respective populations. Assumi... | Can non-random samples be analyzed using standard statistical tests? | There are two general models to testing. The first one, based on the assumption of random sampling from a population, is usually called the "population model".
For example, for the two-independent sam | Can non-random samples be analyzed using standard statistical tests?
There are two general models to testing. The first one, based on the assumption of random sampling from a population, is usually called the "population model".
For example, for the two-independent samples t-test, we assume that the two groups we want ... | Can non-random samples be analyzed using standard statistical tests?
There are two general models to testing. The first one, based on the assumption of random sampling from a population, is usually called the "population model".
For example, for the two-independent sam |
8,890 | Can non-random samples be analyzed using standard statistical tests? | Your question is very good, but it doesn't have a straightforward answer.
Most tests like those you mention are based on the assumption that a sample is a random sample, because a random sample is likely to be representative of the sampled population. If the assumption is invalid then any interpretation of the results ... | Can non-random samples be analyzed using standard statistical tests? | Your question is very good, but it doesn't have a straightforward answer.
Most tests like those you mention are based on the assumption that a sample is a random sample, because a random sample is lik | Can non-random samples be analyzed using standard statistical tests?
Your question is very good, but it doesn't have a straightforward answer.
Most tests like those you mention are based on the assumption that a sample is a random sample, because a random sample is likely to be representative of the sampled population.... | Can non-random samples be analyzed using standard statistical tests?
Your question is very good, but it doesn't have a straightforward answer.
Most tests like those you mention are based on the assumption that a sample is a random sample, because a random sample is lik |
8,891 | Can non-random samples be analyzed using standard statistical tests? | You ask a very general question, so the answer can't be suitable for all cases. However, I can clarify. Statistical tests generally have to do with the distribution observed versus a hypothetical distribution (so-called null distribution or null hypothesis; or, in some cases, an alternative distribution). Samples ma... | Can non-random samples be analyzed using standard statistical tests? | You ask a very general question, so the answer can't be suitable for all cases. However, I can clarify. Statistical tests generally have to do with the distribution observed versus a hypothetical di | Can non-random samples be analyzed using standard statistical tests?
You ask a very general question, so the answer can't be suitable for all cases. However, I can clarify. Statistical tests generally have to do with the distribution observed versus a hypothetical distribution (so-called null distribution or null hyp... | Can non-random samples be analyzed using standard statistical tests?
You ask a very general question, so the answer can't be suitable for all cases. However, I can clarify. Statistical tests generally have to do with the distribution observed versus a hypothetical di |
8,892 | Different covariance types for Gaussian Mixture Models | A Gaussian distribution is completely determined by its covariance matrix and its mean (a location in space). The covariance matrix of a Gaussian distribution determines the directions and lengths of the axes of its density contours, all of which are ellipsoids.
These four types of mixture models can be illustrated in... | Different covariance types for Gaussian Mixture Models | A Gaussian distribution is completely determined by its covariance matrix and its mean (a location in space). The covariance matrix of a Gaussian distribution determines the directions and lengths of | Different covariance types for Gaussian Mixture Models
A Gaussian distribution is completely determined by its covariance matrix and its mean (a location in space). The covariance matrix of a Gaussian distribution determines the directions and lengths of the axes of its density contours, all of which are ellipsoids.
T... | Different covariance types for Gaussian Mixture Models
A Gaussian distribution is completely determined by its covariance matrix and its mean (a location in space). The covariance matrix of a Gaussian distribution determines the directions and lengths of |
8,893 | Residual plots: why plot versus fitted values, not observed $Y$ values? | By construction the error term in an OLS model is uncorrelated with the observed values of the X covariates. This will always be true for the observed data even if the model is yielding biased estimates that do not reflect the true values of a parameter because an assumption of the model is violated (like an omitted va... | Residual plots: why plot versus fitted values, not observed $Y$ values? | By construction the error term in an OLS model is uncorrelated with the observed values of the X covariates. This will always be true for the observed data even if the model is yielding biased estimat | Residual plots: why plot versus fitted values, not observed $Y$ values?
By construction the error term in an OLS model is uncorrelated with the observed values of the X covariates. This will always be true for the observed data even if the model is yielding biased estimates that do not reflect the true values of a para... | Residual plots: why plot versus fitted values, not observed $Y$ values?
By construction the error term in an OLS model is uncorrelated with the observed values of the X covariates. This will always be true for the observed data even if the model is yielding biased estimat |
8,894 | Residual plots: why plot versus fitted values, not observed $Y$ values? | Two facts which I assume you're happy with me just stating:
i. $y_i = \hat{y}_i+\hat{e}_i$
ii. $\text{Cov}(\hat{y}_i,\hat{e}_i)=0$
Then:
$\text{Cov}(y_i,\hat{e}_i)=\text{Cov}(\hat{y}_i+\hat{e}_i,\hat{e}_i)$
$\qquad=\text{Cov}(\hat{y}_i,\hat{e}_i) +\text{Cov}(\hat{e}_i,\hat{e}_i)$
$\qquad=0 +\sigma^2_e$
$\qquad=\sigma^2... | Residual plots: why plot versus fitted values, not observed $Y$ values? | Two facts which I assume you're happy with me just stating:
i. $y_i = \hat{y}_i+\hat{e}_i$
ii. $\text{Cov}(\hat{y}_i,\hat{e}_i)=0$
Then:
$\text{Cov}(y_i,\hat{e}_i)=\text{Cov}(\hat{y}_i+\hat{e}_i,\hat{ | Residual plots: why plot versus fitted values, not observed $Y$ values?
Two facts which I assume you're happy with me just stating:
i. $y_i = \hat{y}_i+\hat{e}_i$
ii. $\text{Cov}(\hat{y}_i,\hat{e}_i)=0$
Then:
$\text{Cov}(y_i,\hat{e}_i)=\text{Cov}(\hat{y}_i+\hat{e}_i,\hat{e}_i)$
$\qquad=\text{Cov}(\hat{y}_i,\hat{e}_i) +... | Residual plots: why plot versus fitted values, not observed $Y$ values?
Two facts which I assume you're happy with me just stating:
i. $y_i = \hat{y}_i+\hat{e}_i$
ii. $\text{Cov}(\hat{y}_i,\hat{e}_i)=0$
Then:
$\text{Cov}(y_i,\hat{e}_i)=\text{Cov}(\hat{y}_i+\hat{e}_i,\hat{ |
8,895 | Does the order of explanatory variables matter when calculating their regression coefficients? | I believe the confusion may be arising from something a bit simpler, but it provides a nice opportunity to review some related matters.
Note that the text is not claiming that all of the regression coefficients $\newcommand{\bhat}{\hat{\beta}}\newcommand{\m}{\mathbf}\newcommand{\z}{\m{z}}\bhat_i$ can be calculated via ... | Does the order of explanatory variables matter when calculating their regression coefficients? | I believe the confusion may be arising from something a bit simpler, but it provides a nice opportunity to review some related matters.
Note that the text is not claiming that all of the regression co | Does the order of explanatory variables matter when calculating their regression coefficients?
I believe the confusion may be arising from something a bit simpler, but it provides a nice opportunity to review some related matters.
Note that the text is not claiming that all of the regression coefficients $\newcommand{\... | Does the order of explanatory variables matter when calculating their regression coefficients?
I believe the confusion may be arising from something a bit simpler, but it provides a nice opportunity to review some related matters.
Note that the text is not claiming that all of the regression co |
8,896 | Does the order of explanatory variables matter when calculating their regression coefficients? | I had a look through the book and it looks like exercise 3.4 might be useful in understanding the concept of using GS to find all the regression coefficients $\beta_j$ (not just the final coefficient $\beta_p$ - so I typed up a solution. Hope this is useful.
Exercise 3.4 in ESL
Show how the vector of least square coe... | Does the order of explanatory variables matter when calculating their regression coefficients? | I had a look through the book and it looks like exercise 3.4 might be useful in understanding the concept of using GS to find all the regression coefficients $\beta_j$ (not just the final coefficient | Does the order of explanatory variables matter when calculating their regression coefficients?
I had a look through the book and it looks like exercise 3.4 might be useful in understanding the concept of using GS to find all the regression coefficients $\beta_j$ (not just the final coefficient $\beta_p$ - so I typed up... | Does the order of explanatory variables matter when calculating their regression coefficients?
I had a look through the book and it looks like exercise 3.4 might be useful in understanding the concept of using GS to find all the regression coefficients $\beta_j$ (not just the final coefficient |
8,897 | Does the order of explanatory variables matter when calculating their regression coefficients? | Why not try it and compare? Fit a set of regression coefficients, then change the order and fit them again and see if they differ (other than possible round-off error).
As @mpiktas points out it is not exactly clear what you are doing.
I can see using GS to solve for $B$ in the least squares equation $(x'x)B=(x'y)$.... | Does the order of explanatory variables matter when calculating their regression coefficients? | Why not try it and compare? Fit a set of regression coefficients, then change the order and fit them again and see if they differ (other than possible round-off error).
As @mpiktas points out it is n | Does the order of explanatory variables matter when calculating their regression coefficients?
Why not try it and compare? Fit a set of regression coefficients, then change the order and fit them again and see if they differ (other than possible round-off error).
As @mpiktas points out it is not exactly clear what you... | Does the order of explanatory variables matter when calculating their regression coefficients?
Why not try it and compare? Fit a set of regression coefficients, then change the order and fit them again and see if they differ (other than possible round-off error).
As @mpiktas points out it is n |
8,898 | Mean squared error vs. mean squared prediction error | The difference is not the mathematical expression, but rather what you are measuring.
Mean squared error measures the expected squared distance between an estimator and the true underlying parameter:
$$\text{MSE}(\hat{\theta}) = E\left[(\hat{\theta} - \theta)^2\right].$$
It is thus a measurement of the quality of an es... | Mean squared error vs. mean squared prediction error | The difference is not the mathematical expression, but rather what you are measuring.
Mean squared error measures the expected squared distance between an estimator and the true underlying parameter:
| Mean squared error vs. mean squared prediction error
The difference is not the mathematical expression, but rather what you are measuring.
Mean squared error measures the expected squared distance between an estimator and the true underlying parameter:
$$\text{MSE}(\hat{\theta}) = E\left[(\hat{\theta} - \theta)^2\right... | Mean squared error vs. mean squared prediction error
The difference is not the mathematical expression, but rather what you are measuring.
Mean squared error measures the expected squared distance between an estimator and the true underlying parameter:
|
8,899 | Mean squared error vs. mean squared prediction error | There is a correction to the second equation about:
$MSPE(L)=\mathbb{E}\Big[\Big(g(X))-\widehat{g}(X)\Big)^{2}\Big]$;
where $X$ is a random variable.
It is important to remember that when we are working with MSPE or MSEP (I usually use the last expression) we are dealing with random variables. We want to predict an un... | Mean squared error vs. mean squared prediction error | There is a correction to the second equation about:
$MSPE(L)=\mathbb{E}\Big[\Big(g(X))-\widehat{g}(X)\Big)^{2}\Big]$;
where $X$ is a random variable.
It is important to remember that when we are work | Mean squared error vs. mean squared prediction error
There is a correction to the second equation about:
$MSPE(L)=\mathbb{E}\Big[\Big(g(X))-\widehat{g}(X)\Big)^{2}\Big]$;
where $X$ is a random variable.
It is important to remember that when we are working with MSPE or MSEP (I usually use the last expression) we are de... | Mean squared error vs. mean squared prediction error
There is a correction to the second equation about:
$MSPE(L)=\mathbb{E}\Big[\Big(g(X))-\widehat{g}(X)\Big)^{2}\Big]$;
where $X$ is a random variable.
It is important to remember that when we are work |
8,900 | Mean squared error vs. mean squared prediction error | Typically, MSE involves only training data. The error here refers to how far the observed training response data is from the fitted response data (based on a model fit on the training data itself).
On the other hand, MSPE typically involves a testing set that was not part of the model training. The error here refers to... | Mean squared error vs. mean squared prediction error | Typically, MSE involves only training data. The error here refers to how far the observed training response data is from the fitted response data (based on a model fit on the training data itself).
On | Mean squared error vs. mean squared prediction error
Typically, MSE involves only training data. The error here refers to how far the observed training response data is from the fitted response data (based on a model fit on the training data itself).
On the other hand, MSPE typically involves a testing set that was not... | Mean squared error vs. mean squared prediction error
Typically, MSE involves only training data. The error here refers to how far the observed training response data is from the fitted response data (based on a model fit on the training data itself).
On |
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