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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5,701 | Test for bimodal distribution | As mentioned in comments, the Wikipedia page on 'Bimodal distribution' lists eight tests for multimodality against unimodality and supplies references for seven of them.
There are at least some in R. For example:
The package diptest implements Hartigan's dip test.
The stamp data in the bootstrap package was used in ... | Test for bimodal distribution | As mentioned in comments, the Wikipedia page on 'Bimodal distribution' lists eight tests for multimodality against unimodality and supplies references for seven of them.
There are at least some in R. | Test for bimodal distribution
As mentioned in comments, the Wikipedia page on 'Bimodal distribution' lists eight tests for multimodality against unimodality and supplies references for seven of them.
There are at least some in R. For example:
The package diptest implements Hartigan's dip test.
The stamp data in the b... | Test for bimodal distribution
As mentioned in comments, the Wikipedia page on 'Bimodal distribution' lists eight tests for multimodality against unimodality and supplies references for seven of them.
There are at least some in R. |
5,702 | Test for bimodal distribution | You should look at the multimode package, which has also a Journal of Statistical Software companion paper: multimode: An R Package for Mode Assessment
The function modetest provides many tests with the argument method=...
Bandwidth test: original test from Silverman (1981) method=SI and improved p-values by Hall and ... | Test for bimodal distribution | You should look at the multimode package, which has also a Journal of Statistical Software companion paper: multimode: An R Package for Mode Assessment
The function modetest provides many tests with t | Test for bimodal distribution
You should look at the multimode package, which has also a Journal of Statistical Software companion paper: multimode: An R Package for Mode Assessment
The function modetest provides many tests with the argument method=...
Bandwidth test: original test from Silverman (1981) method=SI and ... | Test for bimodal distribution
You should look at the multimode package, which has also a Journal of Statistical Software companion paper: multimode: An R Package for Mode Assessment
The function modetest provides many tests with t |
5,703 | Differences between Bhattacharyya distance and KL divergence | The Bhattacharyya coefficient is defined as $$D_B(p,q) = \int \sqrt{p(x)q(x)}\,\text{d}x$$ and can be turned into a distance $d_H(p,q)$ as $$d_H(p,q)=\{1-D_B(p,q)\}^{1/2}$$ which is called the Hellinger distance. A connection between this Hellinger distance and the Kullback-Leibler divergence is
$$d_{KL}(p\|q) \geq 2 d... | Differences between Bhattacharyya distance and KL divergence | The Bhattacharyya coefficient is defined as $$D_B(p,q) = \int \sqrt{p(x)q(x)}\,\text{d}x$$ and can be turned into a distance $d_H(p,q)$ as $$d_H(p,q)=\{1-D_B(p,q)\}^{1/2}$$ which is called the Helling | Differences between Bhattacharyya distance and KL divergence
The Bhattacharyya coefficient is defined as $$D_B(p,q) = \int \sqrt{p(x)q(x)}\,\text{d}x$$ and can be turned into a distance $d_H(p,q)$ as $$d_H(p,q)=\{1-D_B(p,q)\}^{1/2}$$ which is called the Hellinger distance. A connection between this Hellinger distance a... | Differences between Bhattacharyya distance and KL divergence
The Bhattacharyya coefficient is defined as $$D_B(p,q) = \int \sqrt{p(x)q(x)}\,\text{d}x$$ and can be turned into a distance $d_H(p,q)$ as $$d_H(p,q)=\{1-D_B(p,q)\}^{1/2}$$ which is called the Helling |
5,704 | Differences between Bhattacharyya distance and KL divergence | I don't know of any explicit relation between the two, but decided to have a quick poke at them to see what I could find. So this isn't much of an answer, but more of a point of interest.
For simplicity, let's work over discrete distributions. We can write the BC distance as
$$d_\text{BC}(p,q) = - \ln \sum_x (p(x)q(x)... | Differences between Bhattacharyya distance and KL divergence | I don't know of any explicit relation between the two, but decided to have a quick poke at them to see what I could find. So this isn't much of an answer, but more of a point of interest.
For simplici | Differences between Bhattacharyya distance and KL divergence
I don't know of any explicit relation between the two, but decided to have a quick poke at them to see what I could find. So this isn't much of an answer, but more of a point of interest.
For simplicity, let's work over discrete distributions. We can write th... | Differences between Bhattacharyya distance and KL divergence
I don't know of any explicit relation between the two, but decided to have a quick poke at them to see what I could find. So this isn't much of an answer, but more of a point of interest.
For simplici |
5,705 | How is softmax_cross_entropy_with_logits different from softmax_cross_entropy_with_logits_v2? | You have every reason to be confused, because in supervised learning one doesn't need to backpropagate to labels. They are considered fixed ground truth and only the weights need to be adjusted to match them.
But in some cases, the labels themselves may come from a differentiable source, another network. One example mi... | How is softmax_cross_entropy_with_logits different from softmax_cross_entropy_with_logits_v2? | You have every reason to be confused, because in supervised learning one doesn't need to backpropagate to labels. They are considered fixed ground truth and only the weights need to be adjusted to mat | How is softmax_cross_entropy_with_logits different from softmax_cross_entropy_with_logits_v2?
You have every reason to be confused, because in supervised learning one doesn't need to backpropagate to labels. They are considered fixed ground truth and only the weights need to be adjusted to match them.
But in some cases... | How is softmax_cross_entropy_with_logits different from softmax_cross_entropy_with_logits_v2?
You have every reason to be confused, because in supervised learning one doesn't need to backpropagate to labels. They are considered fixed ground truth and only the weights need to be adjusted to mat |
5,706 | Mixed Effects Model with Nesting | I think this is correct.
(1|Tree/Organ/Sample) expands to/is equivalent to (1|Tree)+(1|Tree:Organ)+(1|Tree:Organ:Sample) (where : denotes an interaction).
The fixed factors Treatment, Organ and Tissue automatically get handled at the correct level.
You should probably include Site as a fixed effect (conceptually ... | Mixed Effects Model with Nesting | I think this is correct.
(1|Tree/Organ/Sample) expands to/is equivalent to (1|Tree)+(1|Tree:Organ)+(1|Tree:Organ:Sample) (where : denotes an interaction).
The fixed factors Treatment, Organ and Ti | Mixed Effects Model with Nesting
I think this is correct.
(1|Tree/Organ/Sample) expands to/is equivalent to (1|Tree)+(1|Tree:Organ)+(1|Tree:Organ:Sample) (where : denotes an interaction).
The fixed factors Treatment, Organ and Tissue automatically get handled at the correct level.
You should probably include Site... | Mixed Effects Model with Nesting
I think this is correct.
(1|Tree/Organ/Sample) expands to/is equivalent to (1|Tree)+(1|Tree:Organ)+(1|Tree:Organ:Sample) (where : denotes an interaction).
The fixed factors Treatment, Organ and Ti |
5,707 | Mixed Effects Model with Nesting | I read this question and Dr. Bolker's answer, and tried to replicate the data (not caring much, frankly, about what "length" represents in biological terms or units, and then fit the model as above. I'm posting the results here to share and seek feedback as to the probable presence of misunderstandings.
The code I used... | Mixed Effects Model with Nesting | I read this question and Dr. Bolker's answer, and tried to replicate the data (not caring much, frankly, about what "length" represents in biological terms or units, and then fit the model as above. I | Mixed Effects Model with Nesting
I read this question and Dr. Bolker's answer, and tried to replicate the data (not caring much, frankly, about what "length" represents in biological terms or units, and then fit the model as above. I'm posting the results here to share and seek feedback as to the probable presence of m... | Mixed Effects Model with Nesting
I read this question and Dr. Bolker's answer, and tried to replicate the data (not caring much, frankly, about what "length" represents in biological terms or units, and then fit the model as above. I |
5,708 | OpenBugs vs. JAGS | BUGS/OpenBugs has a peculiar build system which made compiling the code difficult to impossible on some systems — such as Linux (and IIRC OS X) where people had to resort to Windows emulation etc.
Jags, on the other hand, is a completely new project written with standard GNU tools and hence portable to just about anywh... | OpenBugs vs. JAGS | BUGS/OpenBugs has a peculiar build system which made compiling the code difficult to impossible on some systems — such as Linux (and IIRC OS X) where people had to resort to Windows emulation etc.
Jag | OpenBugs vs. JAGS
BUGS/OpenBugs has a peculiar build system which made compiling the code difficult to impossible on some systems — such as Linux (and IIRC OS X) where people had to resort to Windows emulation etc.
Jags, on the other hand, is a completely new project written with standard GNU tools and hence portable t... | OpenBugs vs. JAGS
BUGS/OpenBugs has a peculiar build system which made compiling the code difficult to impossible on some systems — such as Linux (and IIRC OS X) where people had to resort to Windows emulation etc.
Jag |
5,709 | OpenBugs vs. JAGS | For those who find this question down the road: there's now also Stan. Stan may one day replace OpenBUGS and JAGS, but it does not yet support all the analyses that these other packages do. | OpenBugs vs. JAGS | For those who find this question down the road: there's now also Stan. Stan may one day replace OpenBUGS and JAGS, but it does not yet support all the analyses that these other packages do. | OpenBugs vs. JAGS
For those who find this question down the road: there's now also Stan. Stan may one day replace OpenBUGS and JAGS, but it does not yet support all the analyses that these other packages do. | OpenBugs vs. JAGS
For those who find this question down the road: there's now also Stan. Stan may one day replace OpenBUGS and JAGS, but it does not yet support all the analyses that these other packages do. |
5,710 | OpenBugs vs. JAGS | I recommend you jags over openbugs for speed reasons. I've tried both on a Linux system, and jags is way faster. | OpenBugs vs. JAGS | I recommend you jags over openbugs for speed reasons. I've tried both on a Linux system, and jags is way faster. | OpenBugs vs. JAGS
I recommend you jags over openbugs for speed reasons. I've tried both on a Linux system, and jags is way faster. | OpenBugs vs. JAGS
I recommend you jags over openbugs for speed reasons. I've tried both on a Linux system, and jags is way faster. |
5,711 | OpenBugs vs. JAGS | I find jags works more smoothly in Linux, and is easier to setup, but it does not presently support the spatial analyses that GeoBUGS supports. So, I use OpenBUGS. | OpenBugs vs. JAGS | I find jags works more smoothly in Linux, and is easier to setup, but it does not presently support the spatial analyses that GeoBUGS supports. So, I use OpenBUGS. | OpenBugs vs. JAGS
I find jags works more smoothly in Linux, and is easier to setup, but it does not presently support the spatial analyses that GeoBUGS supports. So, I use OpenBUGS. | OpenBugs vs. JAGS
I find jags works more smoothly in Linux, and is easier to setup, but it does not presently support the spatial analyses that GeoBUGS supports. So, I use OpenBUGS. |
5,712 | Statistics published in academic papers | After all, if a paper has taken years to write and has gone through rigorous peer review, then surely the statistics are going to be rock solid?
My experience of reading papers that attempt to apply statistics across a wide variety of areas (political science, economics, psychology, medicine, biology, finance, actuari... | Statistics published in academic papers | After all, if a paper has taken years to write and has gone through rigorous peer review, then surely the statistics are going to be rock solid?
My experience of reading papers that attempt to apply | Statistics published in academic papers
After all, if a paper has taken years to write and has gone through rigorous peer review, then surely the statistics are going to be rock solid?
My experience of reading papers that attempt to apply statistics across a wide variety of areas (political science, economics, psychol... | Statistics published in academic papers
After all, if a paper has taken years to write and has gone through rigorous peer review, then surely the statistics are going to be rock solid?
My experience of reading papers that attempt to apply |
5,713 | Statistics published in academic papers | I respect @Glen_b's stance on the right way to answer here (and certainly don't intend to detract from it), but I can't quite resist pointing to a particularly entertaining example that's close to my home. At the risk of politicizing things and doing this question's purpose a disservice, I recommend Wagenmakers, Wetzel... | Statistics published in academic papers | I respect @Glen_b's stance on the right way to answer here (and certainly don't intend to detract from it), but I can't quite resist pointing to a particularly entertaining example that's close to my | Statistics published in academic papers
I respect @Glen_b's stance on the right way to answer here (and certainly don't intend to detract from it), but I can't quite resist pointing to a particularly entertaining example that's close to my home. At the risk of politicizing things and doing this question's purpose a dis... | Statistics published in academic papers
I respect @Glen_b's stance on the right way to answer here (and certainly don't intend to detract from it), but I can't quite resist pointing to a particularly entertaining example that's close to my |
5,714 | Statistics published in academic papers | I recall at University being ask by a few final year social science students on different occasions (one of them got a 1st) how to work out an average for their project that had had a handful of data points. (So they were not having problem with using software, just with the concept of how to do the maths with a calc... | Statistics published in academic papers | I recall at University being ask by a few final year social science students on different occasions (one of them got a 1st) how to work out an average for their project that had had a handful of data | Statistics published in academic papers
I recall at University being ask by a few final year social science students on different occasions (one of them got a 1st) how to work out an average for their project that had had a handful of data points. (So they were not having problem with using software, just with the co... | Statistics published in academic papers
I recall at University being ask by a few final year social science students on different occasions (one of them got a 1st) how to work out an average for their project that had had a handful of data |
5,715 | Statistics published in academic papers | As a woefully incomplete list, I find statistics most frequently correct in 1) physics papers followed by 2) statistical papers and most miserable in 3) medical papers. The reasons for this are straightforward and have to do with the completeness of the requirements imposed upon the prototypical model in each field.
... | Statistics published in academic papers | As a woefully incomplete list, I find statistics most frequently correct in 1) physics papers followed by 2) statistical papers and most miserable in 3) medical papers. The reasons for this are straig | Statistics published in academic papers
As a woefully incomplete list, I find statistics most frequently correct in 1) physics papers followed by 2) statistical papers and most miserable in 3) medical papers. The reasons for this are straightforward and have to do with the completeness of the requirements imposed upon... | Statistics published in academic papers
As a woefully incomplete list, I find statistics most frequently correct in 1) physics papers followed by 2) statistical papers and most miserable in 3) medical papers. The reasons for this are straig |
5,716 | Statistics published in academic papers | Any paper that disproves the nil null hypothesis is using worthless statistics (the vast majority of what I have seen). This process can provide no information not already provided by the effect size. Further it tells us nothing about whether a significant result is actually due to the cause theorized by the researcher... | Statistics published in academic papers | Any paper that disproves the nil null hypothesis is using worthless statistics (the vast majority of what I have seen). This process can provide no information not already provided by the effect size. | Statistics published in academic papers
Any paper that disproves the nil null hypothesis is using worthless statistics (the vast majority of what I have seen). This process can provide no information not already provided by the effect size. Further it tells us nothing about whether a significant result is actually due ... | Statistics published in academic papers
Any paper that disproves the nil null hypothesis is using worthless statistics (the vast majority of what I have seen). This process can provide no information not already provided by the effect size. |
5,717 | Why is the sampling distribution of variance a chi-squared distribution? | [I'll assume from the discussion in your question that you're happy to accept as fact that if $Z_i, i=1,2,\ldots,k$ are independent identically distributed $N(0,1)$ random variables then $\sum_{i=1}^{k}Z_i^2\sim \chi^2_k$.]
Formally, the result you need follows from Cochran's theorem.
(Though it can be shown in other ... | Why is the sampling distribution of variance a chi-squared distribution? | [I'll assume from the discussion in your question that you're happy to accept as fact that if $Z_i, i=1,2,\ldots,k$ are independent identically distributed $N(0,1)$ random variables then $\sum_{i=1}^{ | Why is the sampling distribution of variance a chi-squared distribution?
[I'll assume from the discussion in your question that you're happy to accept as fact that if $Z_i, i=1,2,\ldots,k$ are independent identically distributed $N(0,1)$ random variables then $\sum_{i=1}^{k}Z_i^2\sim \chi^2_k$.]
Formally, the result yo... | Why is the sampling distribution of variance a chi-squared distribution?
[I'll assume from the discussion in your question that you're happy to accept as fact that if $Z_i, i=1,2,\ldots,k$ are independent identically distributed $N(0,1)$ random variables then $\sum_{i=1}^{ |
5,718 | Empirical relationship between mean, median and mode | Denote $\mu$ the mean ($\neq$ average), $m$ the median, $\sigma$ the standard deviation and $M$ the mode. Finally, let $X$ be the sample, a realization of a continuous unimodal distribution $F$ for which the first two moments exist.
It's well known that
$$|\mu-m|\leq\sigma\label{d}\tag{1}$$
This is a frequent textbook... | Empirical relationship between mean, median and mode | Denote $\mu$ the mean ($\neq$ average), $m$ the median, $\sigma$ the standard deviation and $M$ the mode. Finally, let $X$ be the sample, a realization of a continuous unimodal distribution $F$ for wh | Empirical relationship between mean, median and mode
Denote $\mu$ the mean ($\neq$ average), $m$ the median, $\sigma$ the standard deviation and $M$ the mode. Finally, let $X$ be the sample, a realization of a continuous unimodal distribution $F$ for which the first two moments exist.
It's well known that
$$|\mu-m|\le... | Empirical relationship between mean, median and mode
Denote $\mu$ the mean ($\neq$ average), $m$ the median, $\sigma$ the standard deviation and $M$ the mode. Finally, let $X$ be the sample, a realization of a continuous unimodal distribution $F$ for wh |
5,719 | Empirical relationship between mean, median and mode | The paper chl points to gives some important information -- showing that it's not close to a general rule (even for continuous, smooth, "nicely behaved" variables, like the Weibull). So while it may often be approximately true, it's frequently not.
So where is Pearson coming from? How did he arrive at this approximatio... | Empirical relationship between mean, median and mode | The paper chl points to gives some important information -- showing that it's not close to a general rule (even for continuous, smooth, "nicely behaved" variables, like the Weibull). So while it may o | Empirical relationship between mean, median and mode
The paper chl points to gives some important information -- showing that it's not close to a general rule (even for continuous, smooth, "nicely behaved" variables, like the Weibull). So while it may often be approximately true, it's frequently not.
So where is Pearso... | Empirical relationship between mean, median and mode
The paper chl points to gives some important information -- showing that it's not close to a general rule (even for continuous, smooth, "nicely behaved" variables, like the Weibull). So while it may o |
5,720 | Empirical relationship between mean, median and mode | This relationship was not derived. It was noticed to approximately hold on near symmetric distributions empirically. See Yule's exposition in The Introduction to the theory of statistics, (1922), p.121, Chapter VII Section 20. He presents the empirical example. | Empirical relationship between mean, median and mode | This relationship was not derived. It was noticed to approximately hold on near symmetric distributions empirically. See Yule's exposition in The Introduction to the theory of statistics, (1922), p.12 | Empirical relationship between mean, median and mode
This relationship was not derived. It was noticed to approximately hold on near symmetric distributions empirically. See Yule's exposition in The Introduction to the theory of statistics, (1922), p.121, Chapter VII Section 20. He presents the empirical example. | Empirical relationship between mean, median and mode
This relationship was not derived. It was noticed to approximately hold on near symmetric distributions empirically. See Yule's exposition in The Introduction to the theory of statistics, (1922), p.12 |
5,721 | Using R online - without installing it [closed] | Yes, there are some Rweb interface, like this one (dead as of September 2020), RDDR online REPL, or Repl.it.
Note: Installation of the R software is pretty straightforward and quick, on any platform. | Using R online - without installing it [closed] | Yes, there are some Rweb interface, like this one (dead as of September 2020), RDDR online REPL, or Repl.it.
Note: Installation of the R software is pretty straightforward and quick, on any platform. | Using R online - without installing it [closed]
Yes, there are some Rweb interface, like this one (dead as of September 2020), RDDR online REPL, or Repl.it.
Note: Installation of the R software is pretty straightforward and quick, on any platform. | Using R online - without installing it [closed]
Yes, there are some Rweb interface, like this one (dead as of September 2020), RDDR online REPL, or Repl.it.
Note: Installation of the R software is pretty straightforward and quick, on any platform. |
5,722 | Using R online - without installing it [closed] | Also, if you want to provide a solution to other users, you can set up a webserver with RApache. | Using R online - without installing it [closed] | Also, if you want to provide a solution to other users, you can set up a webserver with RApache. | Using R online - without installing it [closed]
Also, if you want to provide a solution to other users, you can set up a webserver with RApache. | Using R online - without installing it [closed]
Also, if you want to provide a solution to other users, you can set up a webserver with RApache. |
5,723 | Using R online - without installing it [closed] | Sage also has R included with a Python interface. The Sage system is available. Since a couple of years, the prefered way to run SageMath is via CoCalc. It also allows you to run R directly, e.g. in a Jupyter notebook using the R kernel.
Example:
r.data("faithful")
r.lm("eruptions ~ waiting", data=r.faithful)
Output:
... | Using R online - without installing it [closed] | Sage also has R included with a Python interface. The Sage system is available. Since a couple of years, the prefered way to run SageMath is via CoCalc. It also allows you to run R directly, e.g. in a | Using R online - without installing it [closed]
Sage also has R included with a Python interface. The Sage system is available. Since a couple of years, the prefered way to run SageMath is via CoCalc. It also allows you to run R directly, e.g. in a Jupyter notebook using the R kernel.
Example:
r.data("faithful")
r.lm("... | Using R online - without installing it [closed]
Sage also has R included with a Python interface. The Sage system is available. Since a couple of years, the prefered way to run SageMath is via CoCalc. It also allows you to run R directly, e.g. in a |
5,724 | Using R online - without installing it [closed] | Some of the pastebin services will allow you to enter R code. For example, ideone. Here is a very silly hello world in R. I believe ideone limits you to 15 seconds compute time per run, and no fancy IDE, despite the name. | Using R online - without installing it [closed] | Some of the pastebin services will allow you to enter R code. For example, ideone. Here is a very silly hello world in R. I believe ideone limits you to 15 seconds compute time per run, and no fancy I | Using R online - without installing it [closed]
Some of the pastebin services will allow you to enter R code. For example, ideone. Here is a very silly hello world in R. I believe ideone limits you to 15 seconds compute time per run, and no fancy IDE, despite the name. | Using R online - without installing it [closed]
Some of the pastebin services will allow you to enter R code. For example, ideone. Here is a very silly hello world in R. I believe ideone limits you to 15 seconds compute time per run, and no fancy I |
5,725 | Using R online - without installing it [closed] | Have a look at RStudio This has a desktop and web version. I have used the desktop version and it is pretty cool. | Using R online - without installing it [closed] | Have a look at RStudio This has a desktop and web version. I have used the desktop version and it is pretty cool. | Using R online - without installing it [closed]
Have a look at RStudio This has a desktop and web version. I have used the desktop version and it is pretty cool. | Using R online - without installing it [closed]
Have a look at RStudio This has a desktop and web version. I have used the desktop version and it is pretty cool. |
5,726 | What is the difference between conditional and unconditional quantile regression? | Set-up
Suppose you have a simple regression of the form
$$\ln y_i = \alpha + \beta S_i + \epsilon_i $$
where the outcome are the log earnings of person $i$, $S_i$ is the number of years of schooling, and $\epsilon_i$ is an error term. Instead of only looking at the average effect of education on earnings, which you wou... | What is the difference between conditional and unconditional quantile regression? | Set-up
Suppose you have a simple regression of the form
$$\ln y_i = \alpha + \beta S_i + \epsilon_i $$
where the outcome are the log earnings of person $i$, $S_i$ is the number of years of schooling, | What is the difference between conditional and unconditional quantile regression?
Set-up
Suppose you have a simple regression of the form
$$\ln y_i = \alpha + \beta S_i + \epsilon_i $$
where the outcome are the log earnings of person $i$, $S_i$ is the number of years of schooling, and $\epsilon_i$ is an error term. Ins... | What is the difference between conditional and unconditional quantile regression?
Set-up
Suppose you have a simple regression of the form
$$\ln y_i = \alpha + \beta S_i + \epsilon_i $$
where the outcome are the log earnings of person $i$, $S_i$ is the number of years of schooling, |
5,727 | How do you use the 'test' dataset after cross-validation? | This is similar to another question I answered regarding cross-validation and test sets. The key concept to understand here is independent datasets. Consider just two scenarios:
If you have lot's of resources you would ideally collect one dataset and train your model via cross-validation. Then you would collect anot... | How do you use the 'test' dataset after cross-validation? | This is similar to another question I answered regarding cross-validation and test sets. The key concept to understand here is independent datasets. Consider just two scenarios:
If you have lot's o | How do you use the 'test' dataset after cross-validation?
This is similar to another question I answered regarding cross-validation and test sets. The key concept to understand here is independent datasets. Consider just two scenarios:
If you have lot's of resources you would ideally collect one dataset and train yo... | How do you use the 'test' dataset after cross-validation?
This is similar to another question I answered regarding cross-validation and test sets. The key concept to understand here is independent datasets. Consider just two scenarios:
If you have lot's o |
5,728 | How do you use the 'test' dataset after cross-validation? | If all you are going to do is train a model with default settings on the raw or minimally preprocessed dataset (e.g. one-hot encoding and/or removing NAs), you don't need a separate test set, you can simply train on your train set and test on your validation set, or even better, train on the entire set using cross-vali... | How do you use the 'test' dataset after cross-validation? | If all you are going to do is train a model with default settings on the raw or minimally preprocessed dataset (e.g. one-hot encoding and/or removing NAs), you don't need a separate test set, you can | How do you use the 'test' dataset after cross-validation?
If all you are going to do is train a model with default settings on the raw or minimally preprocessed dataset (e.g. one-hot encoding and/or removing NAs), you don't need a separate test set, you can simply train on your train set and test on your validation set... | How do you use the 'test' dataset after cross-validation?
If all you are going to do is train a model with default settings on the raw or minimally preprocessed dataset (e.g. one-hot encoding and/or removing NAs), you don't need a separate test set, you can |
5,729 | How do you use the 'test' dataset after cross-validation? | I'm assuming that you're doing classification.
Take your data and split it 70/30 into trainingData/ testData subsets. Take the trainingData subset and split it 70/30 again into trainingData/ validateData subsets. Now you have 3 subsets of your original data - trainingData(.7*.7), validateData(.7*.3), and testData(.3).
... | How do you use the 'test' dataset after cross-validation? | I'm assuming that you're doing classification.
Take your data and split it 70/30 into trainingData/ testData subsets. Take the trainingData subset and split it 70/30 again into trainingData/ validateD | How do you use the 'test' dataset after cross-validation?
I'm assuming that you're doing classification.
Take your data and split it 70/30 into trainingData/ testData subsets. Take the trainingData subset and split it 70/30 again into trainingData/ validateData subsets. Now you have 3 subsets of your original data - tr... | How do you use the 'test' dataset after cross-validation?
I'm assuming that you're doing classification.
Take your data and split it 70/30 into trainingData/ testData subsets. Take the trainingData subset and split it 70/30 again into trainingData/ validateD |
5,730 | How do you use the 'test' dataset after cross-validation? | Let us look at it the following way
Common practice
a) Training data - used for choosing model parameters.
i) E.g., finding intercept and slope parameters for an ordinary linear
regression model.
ii) The noise in the training data-set is used in some extent
in over-fitting model parameters.
b) Validat... | How do you use the 'test' dataset after cross-validation? | Let us look at it the following way
Common practice
a) Training data - used for choosing model parameters.
i) E.g., finding intercept and slope parameters for an ordinary linear
regression mode | How do you use the 'test' dataset after cross-validation?
Let us look at it the following way
Common practice
a) Training data - used for choosing model parameters.
i) E.g., finding intercept and slope parameters for an ordinary linear
regression model.
ii) The noise in the training data-set is used in some e... | How do you use the 'test' dataset after cross-validation?
Let us look at it the following way
Common practice
a) Training data - used for choosing model parameters.
i) E.g., finding intercept and slope parameters for an ordinary linear
regression mode |
5,731 | Does down-sampling change logistic regression coefficients? | Down-sampling is equivalent to case–control designs in medical statistics—you're fixing the counts of responses & observing the covariate patterns (predictors). Perhaps the key reference is Prentice & Pyke (1979), "Logistic Disease Incidence Models and Case–Control Studies", Biometrika, 66, 3.
They used Bayes' Theorem ... | Does down-sampling change logistic regression coefficients? | Down-sampling is equivalent to case–control designs in medical statistics—you're fixing the counts of responses & observing the covariate patterns (predictors). Perhaps the key reference is Prentice & | Does down-sampling change logistic regression coefficients?
Down-sampling is equivalent to case–control designs in medical statistics—you're fixing the counts of responses & observing the covariate patterns (predictors). Perhaps the key reference is Prentice & Pyke (1979), "Logistic Disease Incidence Models and Case–Co... | Does down-sampling change logistic regression coefficients?
Down-sampling is equivalent to case–control designs in medical statistics—you're fixing the counts of responses & observing the covariate patterns (predictors). Perhaps the key reference is Prentice & |
5,732 | what does the numbers in the classification report of sklearn mean? | The f1-score gives you the harmonic mean of precision and recall. The scores corresponding to every class will tell you the accuracy of the classifier in classifying the data points in that particular class compared to all other classes.
The support is the number of samples of the true response that lie in that class.... | what does the numbers in the classification report of sklearn mean? | The f1-score gives you the harmonic mean of precision and recall. The scores corresponding to every class will tell you the accuracy of the classifier in classifying the data points in that particular | what does the numbers in the classification report of sklearn mean?
The f1-score gives you the harmonic mean of precision and recall. The scores corresponding to every class will tell you the accuracy of the classifier in classifying the data points in that particular class compared to all other classes.
The support i... | what does the numbers in the classification report of sklearn mean?
The f1-score gives you the harmonic mean of precision and recall. The scores corresponding to every class will tell you the accuracy of the classifier in classifying the data points in that particular |
5,733 | Can somebody explain to me NUTS in english? | The no U-turn bit is how proposals are generated. HMC generates a hypothetical physical system: imagine a ball with a certain kinetic energy rolling around a landscape with valleys and hills (the analogy breaks down with more than 2 dimensions) defined by the posterior you want to sample from. Every time you want to t... | Can somebody explain to me NUTS in english? | The no U-turn bit is how proposals are generated. HMC generates a hypothetical physical system: imagine a ball with a certain kinetic energy rolling around a landscape with valleys and hills (the ana | Can somebody explain to me NUTS in english?
The no U-turn bit is how proposals are generated. HMC generates a hypothetical physical system: imagine a ball with a certain kinetic energy rolling around a landscape with valleys and hills (the analogy breaks down with more than 2 dimensions) defined by the posterior you w... | Can somebody explain to me NUTS in english?
The no U-turn bit is how proposals are generated. HMC generates a hypothetical physical system: imagine a ball with a certain kinetic energy rolling around a landscape with valleys and hills (the ana |
5,734 | Can somebody explain to me NUTS in english? | You're incorrect that HMC is not a Markov Chain method. Per Wikipedia:
In mathematics and physics, the hybrid Monte Carlo algorithm, also known as Hamiltonian Monte Carlo, is a Markov chain Monte Carlo method for obtaining a sequence of random samples from a probability distribution for which direct sampling is diffic... | Can somebody explain to me NUTS in english? | You're incorrect that HMC is not a Markov Chain method. Per Wikipedia:
In mathematics and physics, the hybrid Monte Carlo algorithm, also known as Hamiltonian Monte Carlo, is a Markov chain Monte Car | Can somebody explain to me NUTS in english?
You're incorrect that HMC is not a Markov Chain method. Per Wikipedia:
In mathematics and physics, the hybrid Monte Carlo algorithm, also known as Hamiltonian Monte Carlo, is a Markov chain Monte Carlo method for obtaining a sequence of random samples from a probability dist... | Can somebody explain to me NUTS in english?
You're incorrect that HMC is not a Markov Chain method. Per Wikipedia:
In mathematics and physics, the hybrid Monte Carlo algorithm, also known as Hamiltonian Monte Carlo, is a Markov chain Monte Car |
5,735 | Is it OK to remove outliers from data? | One option is to exclude outliers, but IMHO that is something you should only do if you can argue (with almost certainty) why such points are invalid (e.g. measurement equipment broke down, measurement method was unreliable for some reason, ...).
E.g. in frequency domain measurements, DC is often discarded since many d... | Is it OK to remove outliers from data? | One option is to exclude outliers, but IMHO that is something you should only do if you can argue (with almost certainty) why such points are invalid (e.g. measurement equipment broke down, measuremen | Is it OK to remove outliers from data?
One option is to exclude outliers, but IMHO that is something you should only do if you can argue (with almost certainty) why such points are invalid (e.g. measurement equipment broke down, measurement method was unreliable for some reason, ...).
E.g. in frequency domain measureme... | Is it OK to remove outliers from data?
One option is to exclude outliers, but IMHO that is something you should only do if you can argue (with almost certainty) why such points are invalid (e.g. measurement equipment broke down, measuremen |
5,736 | Is it OK to remove outliers from data? | I do not recommend excluding any outlier in the main analysis (unless you are really positive they are mistaken). You can do it in a sensitivity analysis, though, and compare the results of the two analyses. In science, often you discover new stuff precisely when focusing on such outliers.
To further elaborate, just th... | Is it OK to remove outliers from data? | I do not recommend excluding any outlier in the main analysis (unless you are really positive they are mistaken). You can do it in a sensitivity analysis, though, and compare the results of the two an | Is it OK to remove outliers from data?
I do not recommend excluding any outlier in the main analysis (unless you are really positive they are mistaken). You can do it in a sensitivity analysis, though, and compare the results of the two analyses. In science, often you discover new stuff precisely when focusing on such ... | Is it OK to remove outliers from data?
I do not recommend excluding any outlier in the main analysis (unless you are really positive they are mistaken). You can do it in a sensitivity analysis, though, and compare the results of the two an |
5,737 | Is it OK to remove outliers from data? | Thought I'd add a cautionary tale about removing outliers:
Remember the problem with the hole in the polar ozone layer? There was a satellite that was put in orbit over the pole specifically to measure ozone concentration. For a few years the post-processed data from the satellite reported that the polar ozone was pr... | Is it OK to remove outliers from data? | Thought I'd add a cautionary tale about removing outliers:
Remember the problem with the hole in the polar ozone layer? There was a satellite that was put in orbit over the pole specifically to measu | Is it OK to remove outliers from data?
Thought I'd add a cautionary tale about removing outliers:
Remember the problem with the hole in the polar ozone layer? There was a satellite that was put in orbit over the pole specifically to measure ozone concentration. For a few years the post-processed data from the satelli... | Is it OK to remove outliers from data?
Thought I'd add a cautionary tale about removing outliers:
Remember the problem with the hole in the polar ozone layer? There was a satellite that was put in orbit over the pole specifically to measu |
5,738 | Is it OK to remove outliers from data? | 'Outlier' is a convenient term for collecting data together that doesn't fit what you expect your process to look like, in order to remove from the analysis.
I would suggest never (caveat later) removing outliers. My background is statistical process control, so often deal with large volumes of automatically generated... | Is it OK to remove outliers from data? | 'Outlier' is a convenient term for collecting data together that doesn't fit what you expect your process to look like, in order to remove from the analysis.
I would suggest never (caveat later) remo | Is it OK to remove outliers from data?
'Outlier' is a convenient term for collecting data together that doesn't fit what you expect your process to look like, in order to remove from the analysis.
I would suggest never (caveat later) removing outliers. My background is statistical process control, so often deal with l... | Is it OK to remove outliers from data?
'Outlier' is a convenient term for collecting data together that doesn't fit what you expect your process to look like, in order to remove from the analysis.
I would suggest never (caveat later) remo |
5,739 | Is it OK to remove outliers from data? | If you are removing outliers the, in most situations you need to document that you're doing so and why. If this is for a scientific paper, or for regulatory purposes, this could result in having your final statistics discounted and/or rejected.
The better solution is to identify when you think you're getting bad data ... | Is it OK to remove outliers from data? | If you are removing outliers the, in most situations you need to document that you're doing so and why. If this is for a scientific paper, or for regulatory purposes, this could result in having your | Is it OK to remove outliers from data?
If you are removing outliers the, in most situations you need to document that you're doing so and why. If this is for a scientific paper, or for regulatory purposes, this could result in having your final statistics discounted and/or rejected.
The better solution is to identify ... | Is it OK to remove outliers from data?
If you are removing outliers the, in most situations you need to document that you're doing so and why. If this is for a scientific paper, or for regulatory purposes, this could result in having your |
5,740 | Is it OK to remove outliers from data? | It's a moral dilemma for sure. On one hand, why should you let a few suspicious data points ruin your model's fit to the bulk of the data? On the other hand, deleting observations that don't agree with your model's concept of reality is a censorship of sorts. To @Egon's point, those outliers could be trying to tell you... | Is it OK to remove outliers from data? | It's a moral dilemma for sure. On one hand, why should you let a few suspicious data points ruin your model's fit to the bulk of the data? On the other hand, deleting observations that don't agree wit | Is it OK to remove outliers from data?
It's a moral dilemma for sure. On one hand, why should you let a few suspicious data points ruin your model's fit to the bulk of the data? On the other hand, deleting observations that don't agree with your model's concept of reality is a censorship of sorts. To @Egon's point, tho... | Is it OK to remove outliers from data?
It's a moral dilemma for sure. On one hand, why should you let a few suspicious data points ruin your model's fit to the bulk of the data? On the other hand, deleting observations that don't agree wit |
5,741 | Is it OK to remove outliers from data? | My answer aligns with the majority: Do not remove outliers unless you are certain they are erroneous. What I add is:
A brief overview of published papers on this topic (those that I am aware of and primarily those published in psychology. There are many more).
Based on that, an answer to the question: What method can ... | Is it OK to remove outliers from data? | My answer aligns with the majority: Do not remove outliers unless you are certain they are erroneous. What I add is:
A brief overview of published papers on this topic (those that I am aware of and p | Is it OK to remove outliers from data?
My answer aligns with the majority: Do not remove outliers unless you are certain they are erroneous. What I add is:
A brief overview of published papers on this topic (those that I am aware of and primarily those published in psychology. There are many more).
Based on that, an a... | Is it OK to remove outliers from data?
My answer aligns with the majority: Do not remove outliers unless you are certain they are erroneous. What I add is:
A brief overview of published papers on this topic (those that I am aware of and p |
5,742 | Is it OK to remove outliers from data? | If I conduct a random sample of 100 people, and one of those people happens to be Bill Gates, then as far as I can tell, Bill Gates is representative of 1/100th of the population.
A trimmed mean tells me the average lottery earnings is $0. | Is it OK to remove outliers from data? | If I conduct a random sample of 100 people, and one of those people happens to be Bill Gates, then as far as I can tell, Bill Gates is representative of 1/100th of the population.
A trimmed mean tell | Is it OK to remove outliers from data?
If I conduct a random sample of 100 people, and one of those people happens to be Bill Gates, then as far as I can tell, Bill Gates is representative of 1/100th of the population.
A trimmed mean tells me the average lottery earnings is $0. | Is it OK to remove outliers from data?
If I conduct a random sample of 100 people, and one of those people happens to be Bill Gates, then as far as I can tell, Bill Gates is representative of 1/100th of the population.
A trimmed mean tell |
5,743 | Is it OK to remove outliers from data? | Of course you should remove the outliers, as by definition they do not follow the distribution under scrutiny and are a parasitic phenomenon.
The real question is "how can I reliably detect the outliers" ! | Is it OK to remove outliers from data? | Of course you should remove the outliers, as by definition they do not follow the distribution under scrutiny and are a parasitic phenomenon.
The real question is "how can I reliably detect the outlie | Is it OK to remove outliers from data?
Of course you should remove the outliers, as by definition they do not follow the distribution under scrutiny and are a parasitic phenomenon.
The real question is "how can I reliably detect the outliers" ! | Is it OK to remove outliers from data?
Of course you should remove the outliers, as by definition they do not follow the distribution under scrutiny and are a parasitic phenomenon.
The real question is "how can I reliably detect the outlie |
5,744 | What exactly is Big Data? | I had the pleasure of attending a lecture given by Dr. Hadley Wickham, of RStudio fame. He defined it such that
Big Data: Can't fit in memory on one computer: > 1 TB
Medium Data: Fits in memory on a server: 10 GB - 1 TB
Small Data: Fits in memory on a laptop: < 10 GB
Hadley also believes that most data can at least b... | What exactly is Big Data? | I had the pleasure of attending a lecture given by Dr. Hadley Wickham, of RStudio fame. He defined it such that
Big Data: Can't fit in memory on one computer: > 1 TB
Medium Data: Fits in memory on a | What exactly is Big Data?
I had the pleasure of attending a lecture given by Dr. Hadley Wickham, of RStudio fame. He defined it such that
Big Data: Can't fit in memory on one computer: > 1 TB
Medium Data: Fits in memory on a server: 10 GB - 1 TB
Small Data: Fits in memory on a laptop: < 10 GB
Hadley also believes tha... | What exactly is Big Data?
I had the pleasure of attending a lecture given by Dr. Hadley Wickham, of RStudio fame. He defined it such that
Big Data: Can't fit in memory on one computer: > 1 TB
Medium Data: Fits in memory on a |
5,745 | What exactly is Big Data? | A data set/stream is called Big Data, if it satisfies all the four V's
Volume
Velocity
Veracity
Variety
Unless and until it isn't satisfied, the data set can't be termed as Big Data.
A similar answer of mine, for reference.
Having said that, as a data scientist; I find the Map-Reduce framework really nice. Splitting... | What exactly is Big Data? | A data set/stream is called Big Data, if it satisfies all the four V's
Volume
Velocity
Veracity
Variety
Unless and until it isn't satisfied, the data set can't be termed as Big Data.
A similar answe | What exactly is Big Data?
A data set/stream is called Big Data, if it satisfies all the four V's
Volume
Velocity
Veracity
Variety
Unless and until it isn't satisfied, the data set can't be termed as Big Data.
A similar answer of mine, for reference.
Having said that, as a data scientist; I find the Map-Reduce framew... | What exactly is Big Data?
A data set/stream is called Big Data, if it satisfies all the four V's
Volume
Velocity
Veracity
Variety
Unless and until it isn't satisfied, the data set can't be termed as Big Data.
A similar answe |
5,746 | What exactly is Big Data? | I think the only useful definition of big data is data which catalogs all information about a particular phenomenon. What I mean by that is that rather than sampling from some population of interest and collecting some measurements on those units, big data collects measurements on the whole population of interest. Supp... | What exactly is Big Data? | I think the only useful definition of big data is data which catalogs all information about a particular phenomenon. What I mean by that is that rather than sampling from some population of interest a | What exactly is Big Data?
I think the only useful definition of big data is data which catalogs all information about a particular phenomenon. What I mean by that is that rather than sampling from some population of interest and collecting some measurements on those units, big data collects measurements on the whole po... | What exactly is Big Data?
I think the only useful definition of big data is data which catalogs all information about a particular phenomenon. What I mean by that is that rather than sampling from some population of interest a |
5,747 | What exactly is Big Data? | Crosschecking the huge literature on Big Data, I have collected up to 14 "V" terms, 13 of them along about 11 dimensions:
Validity,
Value,
Variability/Variance,
Variety,
Velocity,
Veracity/Veraciousness,
Viability,
Virtuality,
Visualization,
Volatility,
Volume.
The 14th term is Vacuity. According to recent a provo... | What exactly is Big Data? | Crosschecking the huge literature on Big Data, I have collected up to 14 "V" terms, 13 of them along about 11 dimensions:
Validity,
Value,
Variability/Variance,
Variety,
Velocity,
Veracity/Veraciousn | What exactly is Big Data?
Crosschecking the huge literature on Big Data, I have collected up to 14 "V" terms, 13 of them along about 11 dimensions:
Validity,
Value,
Variability/Variance,
Variety,
Velocity,
Veracity/Veraciousness,
Viability,
Virtuality,
Visualization,
Volatility,
Volume.
The 14th term is Vacuity. A... | What exactly is Big Data?
Crosschecking the huge literature on Big Data, I have collected up to 14 "V" terms, 13 of them along about 11 dimensions:
Validity,
Value,
Variability/Variance,
Variety,
Velocity,
Veracity/Veraciousn |
5,748 | What exactly is Big Data? | People seem to fixate on a big qualifier in Big Data. However, the size is only one of the components of this term (domain). It's not enough that your data set was big to call your problem (domain) a big data, you also need it be difficult to understand and analyze and even process. Some call this feature unstructured,... | What exactly is Big Data? | People seem to fixate on a big qualifier in Big Data. However, the size is only one of the components of this term (domain). It's not enough that your data set was big to call your problem (domain) a | What exactly is Big Data?
People seem to fixate on a big qualifier in Big Data. However, the size is only one of the components of this term (domain). It's not enough that your data set was big to call your problem (domain) a big data, you also need it be difficult to understand and analyze and even process. Some call ... | What exactly is Big Data?
People seem to fixate on a big qualifier in Big Data. However, the size is only one of the components of this term (domain). It's not enough that your data set was big to call your problem (domain) a |
5,749 | What exactly is Big Data? | I think the reason why people get confused of what is Big Data is that they doesn't see its benefits. The value of Big Data (technique) is not only on the amount of data that you can collect, but also on the Predictive Modeling, which is eventually more important:
Predictive Modeling changed completely the way we do s... | What exactly is Big Data? | I think the reason why people get confused of what is Big Data is that they doesn't see its benefits. The value of Big Data (technique) is not only on the amount of data that you can collect, but also | What exactly is Big Data?
I think the reason why people get confused of what is Big Data is that they doesn't see its benefits. The value of Big Data (technique) is not only on the amount of data that you can collect, but also on the Predictive Modeling, which is eventually more important:
Predictive Modeling changed ... | What exactly is Big Data?
I think the reason why people get confused of what is Big Data is that they doesn't see its benefits. The value of Big Data (technique) is not only on the amount of data that you can collect, but also |
5,750 | What exactly is Big Data? | The tricky thing about Big Data vs. its antonym (presumably Small Data?) is that it is a continuum. The big data people have gone to one side of the spectrum, the small data people have gone to the other, but there's no clear line in the sand that everyone can agree upon.
I would look at behavioral differences between... | What exactly is Big Data? | The tricky thing about Big Data vs. its antonym (presumably Small Data?) is that it is a continuum. The big data people have gone to one side of the spectrum, the small data people have gone to the o | What exactly is Big Data?
The tricky thing about Big Data vs. its antonym (presumably Small Data?) is that it is a continuum. The big data people have gone to one side of the spectrum, the small data people have gone to the other, but there's no clear line in the sand that everyone can agree upon.
I would look at beha... | What exactly is Big Data?
The tricky thing about Big Data vs. its antonym (presumably Small Data?) is that it is a continuum. The big data people have gone to one side of the spectrum, the small data people have gone to the o |
5,751 | What exactly is Big Data? | I'd say there are three components that are essential in defining big data: the direction of analysis, the size of the data with respect to the population, and the size of the data with respect to computational problems.
The question itself posits that hypotheses are developed after data exists. I don't use "collected"... | What exactly is Big Data? | I'd say there are three components that are essential in defining big data: the direction of analysis, the size of the data with respect to the population, and the size of the data with respect to com | What exactly is Big Data?
I'd say there are three components that are essential in defining big data: the direction of analysis, the size of the data with respect to the population, and the size of the data with respect to computational problems.
The question itself posits that hypotheses are developed after data exist... | What exactly is Big Data?
I'd say there are three components that are essential in defining big data: the direction of analysis, the size of the data with respect to the population, and the size of the data with respect to com |
5,752 | What exactly is Big Data? | Wikipedia provides quite clear definition
Big data is a broad term for data sets so large or complex that
traditional data processing applications are inadequate. (source
https://en.wikipedia.org/wiki/Big_data)
other simple definition I know is
Data that does not fit computer memory.
Unfortunately I do not reme... | What exactly is Big Data? | Wikipedia provides quite clear definition
Big data is a broad term for data sets so large or complex that
traditional data processing applications are inadequate. (source
https://en.wikipedia.org | What exactly is Big Data?
Wikipedia provides quite clear definition
Big data is a broad term for data sets so large or complex that
traditional data processing applications are inadequate. (source
https://en.wikipedia.org/wiki/Big_data)
other simple definition I know is
Data that does not fit computer memory.
U... | What exactly is Big Data?
Wikipedia provides quite clear definition
Big data is a broad term for data sets so large or complex that
traditional data processing applications are inadequate. (source
https://en.wikipedia.org |
5,753 | What exactly is Big Data? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I would add that Big Data is a reference to either wor... | What exactly is Big Data? | Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
| What exactly is Big Data?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
I would add that Big Data is... | What exactly is Big Data?
Want to improve this post? Provide detailed answers to this question, including citations and an explanation of why your answer is correct. Answers without enough detail may be edited or deleted.
|
5,754 | Are there any examples of where the central limit theorem does not hold? | To understand this, you need to first state a version of the Central Limit Theorem. Here's the "typical" statement of the central limit theorem:
Lindeberg–Lévy CLT. Suppose ${X_1, X_2, \dots}$ is a sequence of i.i.d.
random variables with $E[X_i] = \mu$ and $Var[X_i] = \sigma^2 < \infty$.
Let $S_{n}:={\frac {X_{... | Are there any examples of where the central limit theorem does not hold? | To understand this, you need to first state a version of the Central Limit Theorem. Here's the "typical" statement of the central limit theorem:
Lindeberg–Lévy CLT. Suppose ${X_1, X_2, \dots}$ is a | Are there any examples of where the central limit theorem does not hold?
To understand this, you need to first state a version of the Central Limit Theorem. Here's the "typical" statement of the central limit theorem:
Lindeberg–Lévy CLT. Suppose ${X_1, X_2, \dots}$ is a sequence of i.i.d.
random variables with $E[X... | Are there any examples of where the central limit theorem does not hold?
To understand this, you need to first state a version of the Central Limit Theorem. Here's the "typical" statement of the central limit theorem:
Lindeberg–Lévy CLT. Suppose ${X_1, X_2, \dots}$ is a |
5,755 | Are there any examples of where the central limit theorem does not hold? | Although I'm pretty sure that it has been answered before, here's another one:
There are several versions of the central limit theorem, the most general being that given arbitrary probability density functions, the sum of the variables will be distributed normally with a mean value equal to the sum of mean values, as w... | Are there any examples of where the central limit theorem does not hold? | Although I'm pretty sure that it has been answered before, here's another one:
There are several versions of the central limit theorem, the most general being that given arbitrary probability density | Are there any examples of where the central limit theorem does not hold?
Although I'm pretty sure that it has been answered before, here's another one:
There are several versions of the central limit theorem, the most general being that given arbitrary probability density functions, the sum of the variables will be dis... | Are there any examples of where the central limit theorem does not hold?
Although I'm pretty sure that it has been answered before, here's another one:
There are several versions of the central limit theorem, the most general being that given arbitrary probability density |
5,756 | Are there any examples of where the central limit theorem does not hold? | No, CLT always holds when its assumptions hold. Qualifications such as "in most situations" are informal references to the conditions under which CLT should be applied.
For instance, a linear combination of independent variables from Cauchy distribution will not add up to Normal distributed variable. One of the reason... | Are there any examples of where the central limit theorem does not hold? | No, CLT always holds when its assumptions hold. Qualifications such as "in most situations" are informal references to the conditions under which CLT should be applied.
For instance, a linear combina | Are there any examples of where the central limit theorem does not hold?
No, CLT always holds when its assumptions hold. Qualifications such as "in most situations" are informal references to the conditions under which CLT should be applied.
For instance, a linear combination of independent variables from Cauchy distr... | Are there any examples of where the central limit theorem does not hold?
No, CLT always holds when its assumptions hold. Qualifications such as "in most situations" are informal references to the conditions under which CLT should be applied.
For instance, a linear combina |
5,757 | Are there any examples of where the central limit theorem does not hold? | Here is an illustration of cherub's answer, a histogram of 1e6 draws from scaled (by $\sqrt{n}$) and standardized (by the sample standard deviation) sample means of t-distributions with two degrees of freedom, such that the variance does not exist.
If the CLT did apply, the histogram for $n$ as large as $n=2000$ should... | Are there any examples of where the central limit theorem does not hold? | Here is an illustration of cherub's answer, a histogram of 1e6 draws from scaled (by $\sqrt{n}$) and standardized (by the sample standard deviation) sample means of t-distributions with two degrees of | Are there any examples of where the central limit theorem does not hold?
Here is an illustration of cherub's answer, a histogram of 1e6 draws from scaled (by $\sqrt{n}$) and standardized (by the sample standard deviation) sample means of t-distributions with two degrees of freedom, such that the variance does not exist... | Are there any examples of where the central limit theorem does not hold?
Here is an illustration of cherub's answer, a histogram of 1e6 draws from scaled (by $\sqrt{n}$) and standardized (by the sample standard deviation) sample means of t-distributions with two degrees of |
5,758 | Are there any examples of where the central limit theorem does not hold? | A simple case where the CLT cannot hold for very practical reasons, is when the sequence of random variables approaches its probability limit strictly from the one side. This is encountered for example in estimators that estimate something that lies on a boundary.
The standard example here perhaps is the estimation o... | Are there any examples of where the central limit theorem does not hold? | A simple case where the CLT cannot hold for very practical reasons, is when the sequence of random variables approaches its probability limit strictly from the one side. This is encountered for exampl | Are there any examples of where the central limit theorem does not hold?
A simple case where the CLT cannot hold for very practical reasons, is when the sequence of random variables approaches its probability limit strictly from the one side. This is encountered for example in estimators that estimate something that li... | Are there any examples of where the central limit theorem does not hold?
A simple case where the CLT cannot hold for very practical reasons, is when the sequence of random variables approaches its probability limit strictly from the one side. This is encountered for exampl |
5,759 | Are there any examples of where the central limit theorem does not hold? | You can find a quick solution here.
Exceptions to the central-limit theorem arise
When there are multiple maxima of the same height, and
Where the second derivative vanishes at the maximum.
There are certain other exceptions which are outlined in the answer of @cherub.
The same question has already been asked on ... | Are there any examples of where the central limit theorem does not hold? | You can find a quick solution here.
Exceptions to the central-limit theorem arise
When there are multiple maxima of the same height, and
Where the second derivative vanishes at the maximum.
There | Are there any examples of where the central limit theorem does not hold?
You can find a quick solution here.
Exceptions to the central-limit theorem arise
When there are multiple maxima of the same height, and
Where the second derivative vanishes at the maximum.
There are certain other exceptions which are outline... | Are there any examples of where the central limit theorem does not hold?
You can find a quick solution here.
Exceptions to the central-limit theorem arise
When there are multiple maxima of the same height, and
Where the second derivative vanishes at the maximum.
There |
5,760 | Are there any examples of where the central limit theorem does not hold? | The (usual) central limit theorem applies only if the random variables involved are mutually independent with the same distribution and finite mean and variance. If the variables are merely pairwise independent (meaning any two of them are independent of each other, but more than two are not necessarily independent), t... | Are there any examples of where the central limit theorem does not hold? | The (usual) central limit theorem applies only if the random variables involved are mutually independent with the same distribution and finite mean and variance. If the variables are merely pairwise i | Are there any examples of where the central limit theorem does not hold?
The (usual) central limit theorem applies only if the random variables involved are mutually independent with the same distribution and finite mean and variance. If the variables are merely pairwise independent (meaning any two of them are indepen... | Are there any examples of where the central limit theorem does not hold?
The (usual) central limit theorem applies only if the random variables involved are mutually independent with the same distribution and finite mean and variance. If the variables are merely pairwise i |
5,761 | What best practices should I follow when preparing plots? | The Tufte principles are very good practices when preparing plots. See also his book Beautiful Evidence
The principles include:
Keep a high data-ink ratio
Remove chart junk
Give graphical element multiple functions
Keep in mind the data density
The term to search for is Information Visualization | What best practices should I follow when preparing plots? | The Tufte principles are very good practices when preparing plots. See also his book Beautiful Evidence
The principles include:
Keep a high data-ink ratio
Remove chart junk
Give graphical element mul | What best practices should I follow when preparing plots?
The Tufte principles are very good practices when preparing plots. See also his book Beautiful Evidence
The principles include:
Keep a high data-ink ratio
Remove chart junk
Give graphical element multiple functions
Keep in mind the data density
The term to sea... | What best practices should I follow when preparing plots?
The Tufte principles are very good practices when preparing plots. See also his book Beautiful Evidence
The principles include:
Keep a high data-ink ratio
Remove chart junk
Give graphical element mul |
5,762 | What best practices should I follow when preparing plots? | We could stay here all day denoting best practices, but you should start by reading Tufte. My primary recommendation:
Keep it simple.
Often people try to load up their charts with information. But you should really just have one main idea that you're trying to convey and if someone doesn't get your message almost imm... | What best practices should I follow when preparing plots? | We could stay here all day denoting best practices, but you should start by reading Tufte. My primary recommendation:
Keep it simple.
Often people try to load up their charts with information. But y | What best practices should I follow when preparing plots?
We could stay here all day denoting best practices, but you should start by reading Tufte. My primary recommendation:
Keep it simple.
Often people try to load up their charts with information. But you should really just have one main idea that you're trying to... | What best practices should I follow when preparing plots?
We could stay here all day denoting best practices, but you should start by reading Tufte. My primary recommendation:
Keep it simple.
Often people try to load up their charts with information. But y |
5,763 | What best practices should I follow when preparing plots? | One rule of thumb that I don't always follow but which is on occasion useful is to take into account that it is likely that your plot will at some point in its future be
sent by fax,
photocopied, and/or
reproduced in black-and-white.
You need to try and make your plots clear enough that even if they are imprecisely r... | What best practices should I follow when preparing plots? | One rule of thumb that I don't always follow but which is on occasion useful is to take into account that it is likely that your plot will at some point in its future be
sent by fax,
photocopied, and | What best practices should I follow when preparing plots?
One rule of thumb that I don't always follow but which is on occasion useful is to take into account that it is likely that your plot will at some point in its future be
sent by fax,
photocopied, and/or
reproduced in black-and-white.
You need to try and make y... | What best practices should I follow when preparing plots?
One rule of thumb that I don't always follow but which is on occasion useful is to take into account that it is likely that your plot will at some point in its future be
sent by fax,
photocopied, and |
5,764 | What best practices should I follow when preparing plots? | In the physics field there is a rule that the whole paper/report should be understandable only from quick look at the plots. So I would mainly advise that they should be self-explanatory.
This also implies that you must always check whether your audience is familiar with some kind of plot -- I had once made a big mista... | What best practices should I follow when preparing plots? | In the physics field there is a rule that the whole paper/report should be understandable only from quick look at the plots. So I would mainly advise that they should be self-explanatory.
This also im | What best practices should I follow when preparing plots?
In the physics field there is a rule that the whole paper/report should be understandable only from quick look at the plots. So I would mainly advise that they should be self-explanatory.
This also implies that you must always check whether your audience is fami... | What best practices should I follow when preparing plots?
In the physics field there is a rule that the whole paper/report should be understandable only from quick look at the plots. So I would mainly advise that they should be self-explanatory.
This also im |
5,765 | What best practices should I follow when preparing plots? | In addition to conveying a clear message I always try to remember the plotsmanship:
font sizes for labels and legends should be big enough, preferably the same font size and font used in the final publication.
linewidths should be big enough (1 pt lines tend to disappear if plots are shrunk only slightly). I try to go... | What best practices should I follow when preparing plots? | In addition to conveying a clear message I always try to remember the plotsmanship:
font sizes for labels and legends should be big enough, preferably the same font size and font used in the final pu | What best practices should I follow when preparing plots?
In addition to conveying a clear message I always try to remember the plotsmanship:
font sizes for labels and legends should be big enough, preferably the same font size and font used in the final publication.
linewidths should be big enough (1 pt lines tend to... | What best practices should I follow when preparing plots?
In addition to conveying a clear message I always try to remember the plotsmanship:
font sizes for labels and legends should be big enough, preferably the same font size and font used in the final pu |
5,766 | What best practices should I follow when preparing plots? | Take a look at the R graphics library, ggplot2. Details are at the web page http://had.co.nz/ggplot2/ This package generates very good default plots, that follow the Tufte principles, Cleveland's guidelines and Ihaka's color package. | What best practices should I follow when preparing plots? | Take a look at the R graphics library, ggplot2. Details are at the web page http://had.co.nz/ggplot2/ This package generates very good default plots, that follow the Tufte principles, Cleveland's guid | What best practices should I follow when preparing plots?
Take a look at the R graphics library, ggplot2. Details are at the web page http://had.co.nz/ggplot2/ This package generates very good default plots, that follow the Tufte principles, Cleveland's guidelines and Ihaka's color package. | What best practices should I follow when preparing plots?
Take a look at the R graphics library, ggplot2. Details are at the web page http://had.co.nz/ggplot2/ This package generates very good default plots, that follow the Tufte principles, Cleveland's guid |
5,767 | What best practices should I follow when preparing plots? | If plotting in color, consider that colorblind people may have trouble distinguishing elements by color alone. So:
Use line styles to distinguish lines.
Use extra weight in elements, make linewidth at least 2 pt, etc.
Use different markers as well as colors to distinguish points.
Use labels and annotations, referring ... | What best practices should I follow when preparing plots? | If plotting in color, consider that colorblind people may have trouble distinguishing elements by color alone. So:
Use line styles to distinguish lines.
Use extra weight in elements, make linewidth a | What best practices should I follow when preparing plots?
If plotting in color, consider that colorblind people may have trouble distinguishing elements by color alone. So:
Use line styles to distinguish lines.
Use extra weight in elements, make linewidth at least 2 pt, etc.
Use different markers as well as colors to ... | What best practices should I follow when preparing plots?
If plotting in color, consider that colorblind people may have trouble distinguishing elements by color alone. So:
Use line styles to distinguish lines.
Use extra weight in elements, make linewidth a |
5,768 | What best practices should I follow when preparing plots? | Here are my guidelines, based on the most common errors I see (in addition to all the other good points mentioned)
Use scatter graphs, not line plots, if element order is not relevant.
When preparing plots that are meant to be compared, use the same scale factor for all of them.
Even better - find a way to combine the... | What best practices should I follow when preparing plots? | Here are my guidelines, based on the most common errors I see (in addition to all the other good points mentioned)
Use scatter graphs, not line plots, if element order is not relevant.
When preparing | What best practices should I follow when preparing plots?
Here are my guidelines, based on the most common errors I see (in addition to all the other good points mentioned)
Use scatter graphs, not line plots, if element order is not relevant.
When preparing plots that are meant to be compared, use the same scale facto... | What best practices should I follow when preparing plots?
Here are my guidelines, based on the most common errors I see (in addition to all the other good points mentioned)
Use scatter graphs, not line plots, if element order is not relevant.
When preparing |
5,769 | What best practices should I follow when preparing plots? | These are wonderful suggestions. We have assembled a lot of materials here. A group of statisticians in the pharma industry, academia, and FDA have also creating a resource that are useful for clinical trials and related research here$^\dagger.$
My personal favorite graphics book is Elements of Graphing Data by Willi... | What best practices should I follow when preparing plots? | These are wonderful suggestions. We have assembled a lot of materials here. A group of statisticians in the pharma industry, academia, and FDA have also creating a resource that are useful for clini | What best practices should I follow when preparing plots?
These are wonderful suggestions. We have assembled a lot of materials here. A group of statisticians in the pharma industry, academia, and FDA have also creating a resource that are useful for clinical trials and related research here$^\dagger.$
My personal fa... | What best practices should I follow when preparing plots?
These are wonderful suggestions. We have assembled a lot of materials here. A group of statisticians in the pharma industry, academia, and FDA have also creating a resource that are useful for clini |
5,770 | What best practices should I follow when preparing plots? | It also depends on where you wan't to publish your plots. You'll save yourself a lot of trouble by consulting the guide for authors before making any plots for a journal.
Also save the plots in a format that is easy to modify or save the code you have used to create them. Chances are that you need to make corrections. | What best practices should I follow when preparing plots? | It also depends on where you wan't to publish your plots. You'll save yourself a lot of trouble by consulting the guide for authors before making any plots for a journal.
Also save the plots in a for | What best practices should I follow when preparing plots?
It also depends on where you wan't to publish your plots. You'll save yourself a lot of trouble by consulting the guide for authors before making any plots for a journal.
Also save the plots in a format that is easy to modify or save the code you have used to c... | What best practices should I follow when preparing plots?
It also depends on where you wan't to publish your plots. You'll save yourself a lot of trouble by consulting the guide for authors before making any plots for a journal.
Also save the plots in a for |
5,771 | What best practices should I follow when preparing plots? | Don't use dynamite plots:
http://pablomarin-garcia.blogspot.com/2010/02/why-dynamite-plots-are-bad.html, use violin plots or similar (boxplots family) | What best practices should I follow when preparing plots? | Don't use dynamite plots:
http://pablomarin-garcia.blogspot.com/2010/02/why-dynamite-plots-are-bad.html, use violin plots or similar (boxplots family) | What best practices should I follow when preparing plots?
Don't use dynamite plots:
http://pablomarin-garcia.blogspot.com/2010/02/why-dynamite-plots-are-bad.html, use violin plots or similar (boxplots family) | What best practices should I follow when preparing plots?
Don't use dynamite plots:
http://pablomarin-garcia.blogspot.com/2010/02/why-dynamite-plots-are-bad.html, use violin plots or similar (boxplots family) |
5,772 | What best practices should I follow when preparing plots? | One thing that I seem to remember Tufte mentioning, that isn't in the other answers is mapping - that is, make position, direction, size, etc. on your graph represent reality. What is up on the graph should be up in the real world. What is big should be big (keeping in mind that areas should represent areas, and volume... | What best practices should I follow when preparing plots? | One thing that I seem to remember Tufte mentioning, that isn't in the other answers is mapping - that is, make position, direction, size, etc. on your graph represent reality. What is up on the graph | What best practices should I follow when preparing plots?
One thing that I seem to remember Tufte mentioning, that isn't in the other answers is mapping - that is, make position, direction, size, etc. on your graph represent reality. What is up on the graph should be up in the real world. What is big should be big (kee... | What best practices should I follow when preparing plots?
One thing that I seem to remember Tufte mentioning, that isn't in the other answers is mapping - that is, make position, direction, size, etc. on your graph represent reality. What is up on the graph |
5,773 | What best practices should I follow when preparing plots? | I would add that the choice of plot should reflect the type of statistical test used to analyse the data. In other words, whatever characteristics of the data were used for analysis should be shown visually - so you would show means and standard errors if you used a t-test but boxplots if you used a Mann-Whitney test. | What best practices should I follow when preparing plots? | I would add that the choice of plot should reflect the type of statistical test used to analyse the data. In other words, whatever characteristics of the data were used for analysis should be shown v | What best practices should I follow when preparing plots?
I would add that the choice of plot should reflect the type of statistical test used to analyse the data. In other words, whatever characteristics of the data were used for analysis should be shown visually - so you would show means and standard errors if you u... | What best practices should I follow when preparing plots?
I would add that the choice of plot should reflect the type of statistical test used to analyse the data. In other words, whatever characteristics of the data were used for analysis should be shown v |
5,774 | What best practices should I follow when preparing plots? | The other answers are too formulaic to be convincing, so let me give a more general answer. I've struggled with this question for a while. I offer this process:
Know your message
Know your audience
Know your constraints
Tailor your message to your audience given your constraints
I am skeptical of blanket claims such ... | What best practices should I follow when preparing plots? | The other answers are too formulaic to be convincing, so let me give a more general answer. I've struggled with this question for a while. I offer this process:
Know your message
Know your audience
K | What best practices should I follow when preparing plots?
The other answers are too formulaic to be convincing, so let me give a more general answer. I've struggled with this question for a while. I offer this process:
Know your message
Know your audience
Know your constraints
Tailor your message to your audience give... | What best practices should I follow when preparing plots?
The other answers are too formulaic to be convincing, so let me give a more general answer. I've struggled with this question for a while. I offer this process:
Know your message
Know your audience
K |
5,775 | What best practices should I follow when preparing plots? | It depends on the way in which the plots will be discussed.
For instance, if I'm sending out plots for a group meeting that will be done with callers from different locations, I prefer putting them together in Powerpoint as opposed to Excel, so it's easier to flip around.
For one-on-one technical calls, I'll put some... | What best practices should I follow when preparing plots? | It depends on the way in which the plots will be discussed.
For instance, if I'm sending out plots for a group meeting that will be done with callers from different locations, I prefer putting them t | What best practices should I follow when preparing plots?
It depends on the way in which the plots will be discussed.
For instance, if I'm sending out plots for a group meeting that will be done with callers from different locations, I prefer putting them together in Powerpoint as opposed to Excel, so it's easier to f... | What best practices should I follow when preparing plots?
It depends on the way in which the plots will be discussed.
For instance, if I'm sending out plots for a group meeting that will be done with callers from different locations, I prefer putting them t |
5,776 | What best practices should I follow when preparing plots? | Here are my personal best practices (subjective):
Generally important:
Settle for a main message and try to most easily and effectively communicate it
Name your plot axes appropriately, e.g., „hours“, „dollars“, „dollars per hour“
If the axes titles do not already make it fully clear, indicate what unit the axis is ... | What best practices should I follow when preparing plots? | Here are my personal best practices (subjective):
Generally important:
Settle for a main message and try to most easily and effectively communicate it
Name your plot axes appropriately, e.g., „hours | What best practices should I follow when preparing plots?
Here are my personal best practices (subjective):
Generally important:
Settle for a main message and try to most easily and effectively communicate it
Name your plot axes appropriately, e.g., „hours“, „dollars“, „dollars per hour“
If the axes titles do not al... | What best practices should I follow when preparing plots?
Here are my personal best practices (subjective):
Generally important:
Settle for a main message and try to most easily and effectively communicate it
Name your plot axes appropriately, e.g., „hours |
5,777 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | In the context of linear regression in the social sciences, Gelman and Hill write[1]:
We prefer natural logs (that is, logarithms base $e$) because, as
described above, coefficients on the natural-log scale are directly
interpretable as approximate proportional differences: with a
coefficient of 0.06, a differen... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | In the context of linear regression in the social sciences, Gelman and Hill write[1]:
We prefer natural logs (that is, logarithms base $e$) because, as
described above, coefficients on the natural- | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
In the context of linear regression in the social sciences, Gelman and Hill write[1]:
We prefer natural logs (that is, logarithms base $e$) because, as
described above, coefficients on the natural-... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
In the context of linear regression in the social sciences, Gelman and Hill write[1]:
We prefer natural logs (that is, logarithms base $e$) because, as
described above, coefficients on the natural- |
5,778 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | There is no very strong reason for preferring natural logarithms. Suppose we are estimating the model:
ln Y = a + b ln X
The relation between natural (ln) and base 10 (log) logarithms is ln X = 2.303 log X (source). Hence the model is equivalent to:
2.303 log Y = a + 2.303b log X
or, putting a / 2.303 = a*:
log Y =... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | There is no very strong reason for preferring natural logarithms. Suppose we are estimating the model:
ln Y = a + b ln X
The relation between natural (ln) and base 10 (log) logarithms is ln X = 2.30 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
There is no very strong reason for preferring natural logarithms. Suppose we are estimating the model:
ln Y = a + b ln X
The relation between natural (ln) and base 10 (log) logarithms is ln X = 2.30... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
There is no very strong reason for preferring natural logarithms. Suppose we are estimating the model:
ln Y = a + b ln X
The relation between natural (ln) and base 10 (log) logarithms is ln X = 2.30 |
5,779 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | I think that the natural logarithm is used because the exponential is often used when doing interest/growth calculation.
If you are in continuous time and that you are compounding interests, you will end up having a future value of a certain sum equal to $F(t)=N.e^{rt}$ (where r is the interest rate and N the nominal a... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | I think that the natural logarithm is used because the exponential is often used when doing interest/growth calculation.
If you are in continuous time and that you are compounding interests, you will | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
I think that the natural logarithm is used because the exponential is often used when doing interest/growth calculation.
If you are in continuous time and that you are compounding interests, you will ... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
I think that the natural logarithm is used because the exponential is often used when doing interest/growth calculation.
If you are in continuous time and that you are compounding interests, you will |
5,780 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | An additional reason why economists like to use regressions with logarithmic functional forms is an economic one: Coefficients can be understood as elasticities of a Cobb-Douglas function. This function is probably the most common one used among economists to analyze issues regarding microeconomic behaviour (consumers´... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | An additional reason why economists like to use regressions with logarithmic functional forms is an economic one: Coefficients can be understood as elasticities of a Cobb-Douglas function. This functi | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
An additional reason why economists like to use regressions with logarithmic functional forms is an economic one: Coefficients can be understood as elasticities of a Cobb-Douglas function. This functi... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
An additional reason why economists like to use regressions with logarithmic functional forms is an economic one: Coefficients can be understood as elasticities of a Cobb-Douglas function. This functi |
5,781 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | The only reason is that the Taylor expansion, gives an intuitive interpretation of the result.
Let's look at a typical variable used in econometrics a lot, the log difference of GDP:
$$\Delta \ln Y_t=\ln Y_t-\ln Y_{t-1}=\ln\frac{Y_{t}}{Y_{t-1}}=\ln\left(1+\frac{\Delta Y_t}{Y_{t-1}}\right)$$
, where $\frac{\Delta Y_t}{... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | The only reason is that the Taylor expansion, gives an intuitive interpretation of the result.
Let's look at a typical variable used in econometrics a lot, the log difference of GDP:
$$\Delta \ln Y_t | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
The only reason is that the Taylor expansion, gives an intuitive interpretation of the result.
Let's look at a typical variable used in econometrics a lot, the log difference of GDP:
$$\Delta \ln Y_t... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
The only reason is that the Taylor expansion, gives an intuitive interpretation of the result.
Let's look at a typical variable used in econometrics a lot, the log difference of GDP:
$$\Delta \ln Y_t |
5,782 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | Is this unique to economics? The standard normal distribution features an $e^{-{1\over2}x^2}$ in it, and the normal distribution is only one of the large family of exponential distributions that cover a huge swath of statistics. (See GLM's.) It seems like the natural log would be useful in these cases. | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | Is this unique to economics? The standard normal distribution features an $e^{-{1\over2}x^2}$ in it, and the normal distribution is only one of the large family of exponential distributions that cover | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
Is this unique to economics? The standard normal distribution features an $e^{-{1\over2}x^2}$ in it, and the normal distribution is only one of the large family of exponential distributions that cover... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
Is this unique to economics? The standard normal distribution features an $e^{-{1\over2}x^2}$ in it, and the normal distribution is only one of the large family of exponential distributions that cover |
5,783 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | There is a good reason to use the log transformation of the variable if you think that the inverse function of logarithm is the exponential function which is a continuous version of conpounding. The economic variable which is growing around 10% at a time can be transformed to the variable with its mean around 10 (plus ... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | There is a good reason to use the log transformation of the variable if you think that the inverse function of logarithm is the exponential function which is a continuous version of conpounding. The e | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
There is a good reason to use the log transformation of the variable if you think that the inverse function of logarithm is the exponential function which is a continuous version of conpounding. The e... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
There is a good reason to use the log transformation of the variable if you think that the inverse function of logarithm is the exponential function which is a continuous version of conpounding. The e |
5,784 | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics? | Not only in econometrics, using base $e$ is more "natural" in almost every domain, including computer science, where dominated by $0,1$ (where $\log_2$ may be natural).
I would like to use some experiments to show the base $e$ is very natural.
Consider following three functions $f_1(x)=2^x$, $f_{2}(x)=10^x$, $f_3(x)=e... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi | Not only in econometrics, using base $e$ is more "natural" in almost every domain, including computer science, where dominated by $0,1$ (where $\log_2$ may be natural).
I would like to use some experi | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying function in econometrics?
Not only in econometrics, using base $e$ is more "natural" in almost every domain, including computer science, where dominated by $0,1$ (where $\log_2$ may be natural).
I would like to use some experi... | What is the reason why we use natural logarithm (ln) rather than log to base 10 in specifying functi
Not only in econometrics, using base $e$ is more "natural" in almost every domain, including computer science, where dominated by $0,1$ (where $\log_2$ may be natural).
I would like to use some experi |
5,785 | How does cross-validation overcome the overfitting problem? | I can't think of a sufficiently clear explanation just at the moment, so I'll leave that to someone else; however cross-validation does not completely overcome the over-fitting problem in model selection, it just reduces it. The cross-validation error does not have a negligible variance, especially if the size of the ... | How does cross-validation overcome the overfitting problem? | I can't think of a sufficiently clear explanation just at the moment, so I'll leave that to someone else; however cross-validation does not completely overcome the over-fitting problem in model select | How does cross-validation overcome the overfitting problem?
I can't think of a sufficiently clear explanation just at the moment, so I'll leave that to someone else; however cross-validation does not completely overcome the over-fitting problem in model selection, it just reduces it. The cross-validation error does no... | How does cross-validation overcome the overfitting problem?
I can't think of a sufficiently clear explanation just at the moment, so I'll leave that to someone else; however cross-validation does not completely overcome the over-fitting problem in model select |
5,786 | How does cross-validation overcome the overfitting problem? | Not at all. However, cross validation helps you to assess by how much your method overfits.
For instance, if your training data R-squared of a regression is 0.50 and the crossvalidated R-squared is 0.48, you hardly have any overfitting and you feel good. On the other hand, if the crossvalidated R-squared is only 0.3 h... | How does cross-validation overcome the overfitting problem? | Not at all. However, cross validation helps you to assess by how much your method overfits.
For instance, if your training data R-squared of a regression is 0.50 and the crossvalidated R-squared is 0 | How does cross-validation overcome the overfitting problem?
Not at all. However, cross validation helps you to assess by how much your method overfits.
For instance, if your training data R-squared of a regression is 0.50 and the crossvalidated R-squared is 0.48, you hardly have any overfitting and you feel good. On t... | How does cross-validation overcome the overfitting problem?
Not at all. However, cross validation helps you to assess by how much your method overfits.
For instance, if your training data R-squared of a regression is 0.50 and the crossvalidated R-squared is 0 |
5,787 | How does cross-validation overcome the overfitting problem? | My answer is more intuitive than rigorous, but maybe it will help...
As I understand it, overfitting is the result of model selection based on training and testing using the same data, where you have a flexible fitting mechanism: you fit your sample of data so closely that you're fitting the noise, outliers, and all th... | How does cross-validation overcome the overfitting problem? | My answer is more intuitive than rigorous, but maybe it will help...
As I understand it, overfitting is the result of model selection based on training and testing using the same data, where you have | How does cross-validation overcome the overfitting problem?
My answer is more intuitive than rigorous, but maybe it will help...
As I understand it, overfitting is the result of model selection based on training and testing using the same data, where you have a flexible fitting mechanism: you fit your sample of data so... | How does cross-validation overcome the overfitting problem?
My answer is more intuitive than rigorous, but maybe it will help...
As I understand it, overfitting is the result of model selection based on training and testing using the same data, where you have |
5,788 | How does cross-validation overcome the overfitting problem? | Cross-Validation is a good, but not perfect, technique to minimize over-fitting.
Cross-Validation will not perform well to outside data if the data you do have is not representative of the data you'll be trying to predict!
Here are two concrete situations when cross-validation has flaws:
You are using the past to pr... | How does cross-validation overcome the overfitting problem? | Cross-Validation is a good, but not perfect, technique to minimize over-fitting.
Cross-Validation will not perform well to outside data if the data you do have is not representative of the data you'l | How does cross-validation overcome the overfitting problem?
Cross-Validation is a good, but not perfect, technique to minimize over-fitting.
Cross-Validation will not perform well to outside data if the data you do have is not representative of the data you'll be trying to predict!
Here are two concrete situations wh... | How does cross-validation overcome the overfitting problem?
Cross-Validation is a good, but not perfect, technique to minimize over-fitting.
Cross-Validation will not perform well to outside data if the data you do have is not representative of the data you'l |
5,789 | How does cross-validation overcome the overfitting problem? | From a Bayesian perspective, I'm not so sure that cross validation does anything that a "proper" Bayesian analysis doesn't do for comparing models. But I am not 100% certain that it does.
This is because if you are comparing models in a Bayesian way, then you are essentially already doing cross validation. This is be... | How does cross-validation overcome the overfitting problem? | From a Bayesian perspective, I'm not so sure that cross validation does anything that a "proper" Bayesian analysis doesn't do for comparing models. But I am not 100% certain that it does.
This is bec | How does cross-validation overcome the overfitting problem?
From a Bayesian perspective, I'm not so sure that cross validation does anything that a "proper" Bayesian analysis doesn't do for comparing models. But I am not 100% certain that it does.
This is because if you are comparing models in a Bayesian way, then you... | How does cross-validation overcome the overfitting problem?
From a Bayesian perspective, I'm not so sure that cross validation does anything that a "proper" Bayesian analysis doesn't do for comparing models. But I am not 100% certain that it does.
This is bec |
5,790 | How does cross-validation overcome the overfitting problem? | Also I can recomend these videos from the Stanford course in Statistical learning. These videos goes in quite depth regarding how to use cross-valudation effectively.
Cross-Validation and the Bootstrap (14:01)
K-fold Cross-Validation (13:33)
Cross-Validation: The Right and Wrong Ways (10:07) | How does cross-validation overcome the overfitting problem? | Also I can recomend these videos from the Stanford course in Statistical learning. These videos goes in quite depth regarding how to use cross-valudation effectively.
Cross-Validation and the Bootstra | How does cross-validation overcome the overfitting problem?
Also I can recomend these videos from the Stanford course in Statistical learning. These videos goes in quite depth regarding how to use cross-valudation effectively.
Cross-Validation and the Bootstrap (14:01)
K-fold Cross-Validation (13:33)
Cross-Validation: ... | How does cross-validation overcome the overfitting problem?
Also I can recomend these videos from the Stanford course in Statistical learning. These videos goes in quite depth regarding how to use cross-valudation effectively.
Cross-Validation and the Bootstra |
5,791 | Mean absolute percentage error (MAPE) in Scikit-learn [closed] | As noted (for example, in Wikipedia), MAPE can be problematic. Most pointedly, it can cause division-by-zero errors. My guess is that this is why it is not included in the sklearn metrics.
However, it is simple to implement.
from sklearn.utils import check_arrays
def mean_absolute_percentage_error(y_true, y_pred):
... | Mean absolute percentage error (MAPE) in Scikit-learn [closed] | As noted (for example, in Wikipedia), MAPE can be problematic. Most pointedly, it can cause division-by-zero errors. My guess is that this is why it is not included in the sklearn metrics.
However, i | Mean absolute percentage error (MAPE) in Scikit-learn [closed]
As noted (for example, in Wikipedia), MAPE can be problematic. Most pointedly, it can cause division-by-zero errors. My guess is that this is why it is not included in the sklearn metrics.
However, it is simple to implement.
from sklearn.utils import chec... | Mean absolute percentage error (MAPE) in Scikit-learn [closed]
As noted (for example, in Wikipedia), MAPE can be problematic. Most pointedly, it can cause division-by-zero errors. My guess is that this is why it is not included in the sklearn metrics.
However, i |
5,792 | Mean absolute percentage error (MAPE) in Scikit-learn [closed] | here is an updated version:
import numpy as np
def mean_absolute_percentage_error(y_true, y_pred):
y_true, y_pred = np.array(y_true), np.array(y_pred)
return np.mean(np.abs((y_true - y_pred) / y_true)) * 100 | Mean absolute percentage error (MAPE) in Scikit-learn [closed] | here is an updated version:
import numpy as np
def mean_absolute_percentage_error(y_true, y_pred):
y_true, y_pred = np.array(y_true), np.array(y_pred)
return np.mean(np.abs((y_true - y_pred) | Mean absolute percentage error (MAPE) in Scikit-learn [closed]
here is an updated version:
import numpy as np
def mean_absolute_percentage_error(y_true, y_pred):
y_true, y_pred = np.array(y_true), np.array(y_pred)
return np.mean(np.abs((y_true - y_pred) / y_true)) * 100 | Mean absolute percentage error (MAPE) in Scikit-learn [closed]
here is an updated version:
import numpy as np
def mean_absolute_percentage_error(y_true, y_pred):
y_true, y_pred = np.array(y_true), np.array(y_pred)
return np.mean(np.abs((y_true - y_pred) |
5,793 | Should covariates that are not statistically significant be 'kept in' when creating a model? | You have gotten several good answers already. There are reasons to keep covariates and reasons to drop covariates. Statistical significance should not be a key factor, in the vast majority of cases.
Covariates may be of such substantive importance that they have to be there.
The effect size of a covariate may be high... | Should covariates that are not statistically significant be 'kept in' when creating a model? | You have gotten several good answers already. There are reasons to keep covariates and reasons to drop covariates. Statistical significance should not be a key factor, in the vast majority of cases.
| Should covariates that are not statistically significant be 'kept in' when creating a model?
You have gotten several good answers already. There are reasons to keep covariates and reasons to drop covariates. Statistical significance should not be a key factor, in the vast majority of cases.
Covariates may be of such s... | Should covariates that are not statistically significant be 'kept in' when creating a model?
You have gotten several good answers already. There are reasons to keep covariates and reasons to drop covariates. Statistical significance should not be a key factor, in the vast majority of cases.
|
5,794 | Should covariates that are not statistically significant be 'kept in' when creating a model? | The long answer is "yes". There are few reasons to remove insignificant predictors and many reasons not to. As far as interpreting them you do so ignoring the $P$-value just as you might interpret other predictors: with confidence intervals for effects over interesting ranges of the predictor. | Should covariates that are not statistically significant be 'kept in' when creating a model? | The long answer is "yes". There are few reasons to remove insignificant predictors and many reasons not to. As far as interpreting them you do so ignoring the $P$-value just as you might interpret o | Should covariates that are not statistically significant be 'kept in' when creating a model?
The long answer is "yes". There are few reasons to remove insignificant predictors and many reasons not to. As far as interpreting them you do so ignoring the $P$-value just as you might interpret other predictors: with confi... | Should covariates that are not statistically significant be 'kept in' when creating a model?
The long answer is "yes". There are few reasons to remove insignificant predictors and many reasons not to. As far as interpreting them you do so ignoring the $P$-value just as you might interpret o |
5,795 | Should covariates that are not statistically significant be 'kept in' when creating a model? | One useful insight is that there is really nothing specific about a covariate statistically speaking, see e.g. Help writing covariates into regression formula. Incidentally, it might explain why there is no covariate tag. Consequently, material here and elsewhere about non-significant terms in a linear model are releva... | Should covariates that are not statistically significant be 'kept in' when creating a model? | One useful insight is that there is really nothing specific about a covariate statistically speaking, see e.g. Help writing covariates into regression formula. Incidentally, it might explain why there | Should covariates that are not statistically significant be 'kept in' when creating a model?
One useful insight is that there is really nothing specific about a covariate statistically speaking, see e.g. Help writing covariates into regression formula. Incidentally, it might explain why there is no covariate tag. Conse... | Should covariates that are not statistically significant be 'kept in' when creating a model?
One useful insight is that there is really nothing specific about a covariate statistically speaking, see e.g. Help writing covariates into regression formula. Incidentally, it might explain why there |
5,796 | Should covariates that are not statistically significant be 'kept in' when creating a model? | We really need more information about your goals to answer this question. Regressions are used for two main purposes:
Prediction
Inference
Prediction is when your goal is to be able to guess at values of the outcome variable for observations that are not in the sample (although usually they are within the range of th... | Should covariates that are not statistically significant be 'kept in' when creating a model? | We really need more information about your goals to answer this question. Regressions are used for two main purposes:
Prediction
Inference
Prediction is when your goal is to be able to guess at valu | Should covariates that are not statistically significant be 'kept in' when creating a model?
We really need more information about your goals to answer this question. Regressions are used for two main purposes:
Prediction
Inference
Prediction is when your goal is to be able to guess at values of the outcome variable ... | Should covariates that are not statistically significant be 'kept in' when creating a model?
We really need more information about your goals to answer this question. Regressions are used for two main purposes:
Prediction
Inference
Prediction is when your goal is to be able to guess at valu |
5,797 | Difference between LOESS and LOWESS | I think it is important to distinguish between methods and their implementations in software. The main difference with respect to the first is that lowess allows only one predictor, whereas loess can be used to smooth multivariate data into a kind of surface. It also gives you confidence intervals. In these senses, loe... | Difference between LOESS and LOWESS | I think it is important to distinguish between methods and their implementations in software. The main difference with respect to the first is that lowess allows only one predictor, whereas loess can | Difference between LOESS and LOWESS
I think it is important to distinguish between methods and their implementations in software. The main difference with respect to the first is that lowess allows only one predictor, whereas loess can be used to smooth multivariate data into a kind of surface. It also gives you confid... | Difference between LOESS and LOWESS
I think it is important to distinguish between methods and their implementations in software. The main difference with respect to the first is that lowess allows only one predictor, whereas loess can |
5,798 | Difference between LOESS and LOWESS | lowess and loess are algorithms and software programs created by William Cleveland.
lowess is for adding a smooth curve to a scatterplot, i.e., for univariate smoothing.
loess is for fitting a smooth surface to multivariate data.
Both algorithms use locally-weighted polynomial regression, usually with robustifying iter... | Difference between LOESS and LOWESS | lowess and loess are algorithms and software programs created by William Cleveland.
lowess is for adding a smooth curve to a scatterplot, i.e., for univariate smoothing.
loess is for fitting a smooth | Difference between LOESS and LOWESS
lowess and loess are algorithms and software programs created by William Cleveland.
lowess is for adding a smooth curve to a scatterplot, i.e., for univariate smoothing.
loess is for fitting a smooth surface to multivariate data.
Both algorithms use locally-weighted polynomial regres... | Difference between LOESS and LOWESS
lowess and loess are algorithms and software programs created by William Cleveland.
lowess is for adding a smooth curve to a scatterplot, i.e., for univariate smoothing.
loess is for fitting a smooth |
5,799 | Why is RSS distributed chi square times n-p? | I consider the following linear model: ${y} = X \beta + \epsilon$.
The vector of residuals is estimated by
$$\hat{\epsilon} = y - X \hat{\beta}
= (I - X (X'X)^{-1} X') y
= Q y
= Q (X \beta + \epsilon) = Q \epsilon$$
where $Q = I - X (X'X)^{-1} X'$.
Observe... | Why is RSS distributed chi square times n-p? | I consider the following linear model: ${y} = X \beta + \epsilon$.
The vector of residuals is estimated by
$$\hat{\epsilon} = y - X \hat{\beta}
= (I - X (X'X)^{-1} X') y
| Why is RSS distributed chi square times n-p?
I consider the following linear model: ${y} = X \beta + \epsilon$.
The vector of residuals is estimated by
$$\hat{\epsilon} = y - X \hat{\beta}
= (I - X (X'X)^{-1} X') y
= Q y
= Q (X \beta + \epsilon) = Q \epsil... | Why is RSS distributed chi square times n-p?
I consider the following linear model: ${y} = X \beta + \epsilon$.
The vector of residuals is estimated by
$$\hat{\epsilon} = y - X \hat{\beta}
= (I - X (X'X)^{-1} X') y
|
5,800 | Why is RSS distributed chi square times n-p? | IMHO, the matricial notation $Y=X\beta+\epsilon$ complicates things. Pure vector space language is cleaner. The model can be written $\boxed{Y=\mu + \sigma G}$ where $G$ has the standard normal distributon on $\mathbb{R}^n$ and $\mu$ is assumed to belong to a vector subspace $W \subset \mathbb{R}^n$.
Now the language o... | Why is RSS distributed chi square times n-p? | IMHO, the matricial notation $Y=X\beta+\epsilon$ complicates things. Pure vector space language is cleaner. The model can be written $\boxed{Y=\mu + \sigma G}$ where $G$ has the standard normal distri | Why is RSS distributed chi square times n-p?
IMHO, the matricial notation $Y=X\beta+\epsilon$ complicates things. Pure vector space language is cleaner. The model can be written $\boxed{Y=\mu + \sigma G}$ where $G$ has the standard normal distributon on $\mathbb{R}^n$ and $\mu$ is assumed to belong to a vector subspace... | Why is RSS distributed chi square times n-p?
IMHO, the matricial notation $Y=X\beta+\epsilon$ complicates things. Pure vector space language is cleaner. The model can be written $\boxed{Y=\mu + \sigma G}$ where $G$ has the standard normal distri |
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