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 |
|---|---|---|---|---|---|---|
901 | Does Julia have any hope of sticking in the statistical community? | The following probably does not deserve to be an answer, but it is too important to be buried as a comment to someone else's response...
I have not heard much said about memory consumption, just speed. R's entire semantics being pass-by-value can be painful, and this has been one criticism of the language (which is a s... | Does Julia have any hope of sticking in the statistical community? | The following probably does not deserve to be an answer, but it is too important to be buried as a comment to someone else's response...
I have not heard much said about memory consumption, just speed | Does Julia have any hope of sticking in the statistical community?
The following probably does not deserve to be an answer, but it is too important to be buried as a comment to someone else's response...
I have not heard much said about memory consumption, just speed. R's entire semantics being pass-by-value can be pai... | Does Julia have any hope of sticking in the statistical community?
The following probably does not deserve to be an answer, but it is too important to be buried as a comment to someone else's response...
I have not heard much said about memory consumption, just speed |
902 | Does Julia have any hope of sticking in the statistical community? | I think it's unlikely that Julia will ever replace R, for a lot of the reasons previously mentioned. Julia is a Matlab replacement, not a R replacement; they have different goals. Even after Julia has a fully-fleshed out statistics library, no one would ever teach an Intro to Statistics class in it.
However, an area ... | Does Julia have any hope of sticking in the statistical community? | I think it's unlikely that Julia will ever replace R, for a lot of the reasons previously mentioned. Julia is a Matlab replacement, not a R replacement; they have different goals. Even after Julia h | Does Julia have any hope of sticking in the statistical community?
I think it's unlikely that Julia will ever replace R, for a lot of the reasons previously mentioned. Julia is a Matlab replacement, not a R replacement; they have different goals. Even after Julia has a fully-fleshed out statistics library, no one wou... | Does Julia have any hope of sticking in the statistical community?
I think it's unlikely that Julia will ever replace R, for a lot of the reasons previously mentioned. Julia is a Matlab replacement, not a R replacement; they have different goals. Even after Julia h |
903 | Does Julia have any hope of sticking in the statistical community? | I am a Julia newbie, and am R competent. The reasons I find Julia interesting so far are performance and compatibility oriented.
GPU tools. I'd like to use CUSPARSE for a statistical application. CRAN results indicate there's not much out there. Julia has bindings available which seem to work smoothly so far.
using CUS... | Does Julia have any hope of sticking in the statistical community? | I am a Julia newbie, and am R competent. The reasons I find Julia interesting so far are performance and compatibility oriented.
GPU tools. I'd like to use CUSPARSE for a statistical application. CRAN | Does Julia have any hope of sticking in the statistical community?
I am a Julia newbie, and am R competent. The reasons I find Julia interesting so far are performance and compatibility oriented.
GPU tools. I'd like to use CUSPARSE for a statistical application. CRAN results indicate there's not much out there. Julia h... | Does Julia have any hope of sticking in the statistical community?
I am a Julia newbie, and am R competent. The reasons I find Julia interesting so far are performance and compatibility oriented.
GPU tools. I'd like to use CUSPARSE for a statistical application. CRAN |
904 | Does Julia have any hope of sticking in the statistical community? | Julia 1.0 has just come out with a very usable IDE (Juno). It came out a bit late to the party as Python has already dominated Machine Learning, while R continues to dominate every other kind of statistical analysis. That being said, Julia is already rising to prominence in the area of finance and trading algorithms as... | Does Julia have any hope of sticking in the statistical community? | Julia 1.0 has just come out with a very usable IDE (Juno). It came out a bit late to the party as Python has already dominated Machine Learning, while R continues to dominate every other kind of stati | Does Julia have any hope of sticking in the statistical community?
Julia 1.0 has just come out with a very usable IDE (Juno). It came out a bit late to the party as Python has already dominated Machine Learning, while R continues to dominate every other kind of statistical analysis. That being said, Julia is already ri... | Does Julia have any hope of sticking in the statistical community?
Julia 1.0 has just come out with a very usable IDE (Juno). It came out a bit late to the party as Python has already dominated Machine Learning, while R continues to dominate every other kind of stati |
905 | Does Julia have any hope of sticking in the statistical community? | I am interested by the promise of better speed and easy parallelisation using different architectures. For that reason I will certainly watch Julia development but I am unlikely to use it until it can handle generalised linear mixed models, the has a good generic bootstrap package, a simple model language for building ... | Does Julia have any hope of sticking in the statistical community? | I am interested by the promise of better speed and easy parallelisation using different architectures. For that reason I will certainly watch Julia development but I am unlikely to use it until it can | Does Julia have any hope of sticking in the statistical community?
I am interested by the promise of better speed and easy parallelisation using different architectures. For that reason I will certainly watch Julia development but I am unlikely to use it until it can handle generalised linear mixed models, the has a go... | Does Julia have any hope of sticking in the statistical community?
I am interested by the promise of better speed and easy parallelisation using different architectures. For that reason I will certainly watch Julia development but I am unlikely to use it until it can |
906 | Does Julia have any hope of sticking in the statistical community? | The luxury of NA's in R does not come without performance penalties. If Julia supports NA's with a smaller performance penalty then it becomes interesting to a segment of the stats community, but NA's also impose considerable extra work when using compiled code with R.
Many of the packages in R rely on routines writ... | Does Julia have any hope of sticking in the statistical community? | The luxury of NA's in R does not come without performance penalties. If Julia supports NA's with a smaller performance penalty then it becomes interesting to a segment of the stats community, but NA' | Does Julia have any hope of sticking in the statistical community?
The luxury of NA's in R does not come without performance penalties. If Julia supports NA's with a smaller performance penalty then it becomes interesting to a segment of the stats community, but NA's also impose considerable extra work when using comp... | Does Julia have any hope of sticking in the statistical community?
The luxury of NA's in R does not come without performance penalties. If Julia supports NA's with a smaller performance penalty then it becomes interesting to a segment of the stats community, but NA' |
907 | Does Julia have any hope of sticking in the statistical community? | I will be up front, I have no experience with R, but I work with plenty of people that think it is an excellent tool for statistical analysis. My background is in data warehousing, and due to Julia's easily distributed, but more standard programming model, I think it could be a very interesting substitute for the tran... | Does Julia have any hope of sticking in the statistical community? | I will be up front, I have no experience with R, but I work with plenty of people that think it is an excellent tool for statistical analysis. My background is in data warehousing, and due to Julia's | Does Julia have any hope of sticking in the statistical community?
I will be up front, I have no experience with R, but I work with plenty of people that think it is an excellent tool for statistical analysis. My background is in data warehousing, and due to Julia's easily distributed, but more standard programming mo... | Does Julia have any hope of sticking in the statistical community?
I will be up front, I have no experience with R, but I work with plenty of people that think it is an excellent tool for statistical analysis. My background is in data warehousing, and due to Julia's |
908 | Does Julia have any hope of sticking in the statistical community? | You can also use Julia and R together. There is Julia-to-R interface. With this packages you can play with Julia while calling R whenever it has a library that would be needed. | Does Julia have any hope of sticking in the statistical community? | You can also use Julia and R together. There is Julia-to-R interface. With this packages you can play with Julia while calling R whenever it has a library that would be needed. | Does Julia have any hope of sticking in the statistical community?
You can also use Julia and R together. There is Julia-to-R interface. With this packages you can play with Julia while calling R whenever it has a library that would be needed. | Does Julia have any hope of sticking in the statistical community?
You can also use Julia and R together. There is Julia-to-R interface. With this packages you can play with Julia while calling R whenever it has a library that would be needed. |
909 | Does Julia have any hope of sticking in the statistical community? | Julia has without doubt every chance of becoming a statistics power-users dream come true, take SAS for example, it's power lies in the numerous procs written in C - what Julia can do is give you the procs with the source code, with matrices as a built in data type dispensing with SAS/iml. I have no doubt that statisti... | Does Julia have any hope of sticking in the statistical community? | Julia has without doubt every chance of becoming a statistics power-users dream come true, take SAS for example, it's power lies in the numerous procs written in C - what Julia can do is give you the | Does Julia have any hope of sticking in the statistical community?
Julia has without doubt every chance of becoming a statistics power-users dream come true, take SAS for example, it's power lies in the numerous procs written in C - what Julia can do is give you the procs with the source code, with matrices as a built ... | Does Julia have any hope of sticking in the statistical community?
Julia has without doubt every chance of becoming a statistics power-users dream come true, take SAS for example, it's power lies in the numerous procs written in C - what Julia can do is give you the |
910 | Does Julia have any hope of sticking in the statistical community? | Oh yes, Julia will overtake R quite quickly. And the primary reasons will be "macros", 95% of the language is implemented in Julia, and its noise free, parsimonious syntax. If you don't have experience with lisp type of languages you might not understand it as yet, but you will see pretty quickly how R formula interfac... | Does Julia have any hope of sticking in the statistical community? | Oh yes, Julia will overtake R quite quickly. And the primary reasons will be "macros", 95% of the language is implemented in Julia, and its noise free, parsimonious syntax. If you don't have experienc | Does Julia have any hope of sticking in the statistical community?
Oh yes, Julia will overtake R quite quickly. And the primary reasons will be "macros", 95% of the language is implemented in Julia, and its noise free, parsimonious syntax. If you don't have experience with lisp type of languages you might not understan... | Does Julia have any hope of sticking in the statistical community?
Oh yes, Julia will overtake R quite quickly. And the primary reasons will be "macros", 95% of the language is implemented in Julia, and its noise free, parsimonious syntax. If you don't have experienc |
911 | Does Julia have any hope of sticking in the statistical community? | Julia's first target use cases are numerical problems. Basically, you can break these analysis and computational science fields into data science (data driven) and simulation science (model driven). Julia is dealing with the simulation science use cases first. They are also dealing with the data science cases, but more... | Does Julia have any hope of sticking in the statistical community? | Julia's first target use cases are numerical problems. Basically, you can break these analysis and computational science fields into data science (data driven) and simulation science (model driven). J | Does Julia have any hope of sticking in the statistical community?
Julia's first target use cases are numerical problems. Basically, you can break these analysis and computational science fields into data science (data driven) and simulation science (model driven). Julia is dealing with the simulation science use cases... | Does Julia have any hope of sticking in the statistical community?
Julia's first target use cases are numerical problems. Basically, you can break these analysis and computational science fields into data science (data driven) and simulation science (model driven). J |
912 | Does Julia have any hope of sticking in the statistical community? | It needs to be able to apply any function to large datasets that don't fit on memory transparently for the user.
That includes at least running mixed effects models, survival models or MCMC on datasets that fit on the disk but not on memory. And if possible on datasets distributed on several computers. | Does Julia have any hope of sticking in the statistical community? | It needs to be able to apply any function to large datasets that don't fit on memory transparently for the user.
That includes at least running mixed effects models, survival models or MCMC on dataset | Does Julia have any hope of sticking in the statistical community?
It needs to be able to apply any function to large datasets that don't fit on memory transparently for the user.
That includes at least running mixed effects models, survival models or MCMC on datasets that fit on the disk but not on memory. And if pos... | Does Julia have any hope of sticking in the statistical community?
It needs to be able to apply any function to large datasets that don't fit on memory transparently for the user.
That includes at least running mixed effects models, survival models or MCMC on dataset |
913 | Gradient Boosting Tree vs Random Forest | $\text{error = bias + variance}$
Boosting is based on weak learners (high bias, low variance). In
terms of decision trees, weak learners are shallow trees, sometimes
even as small as decision stumps (trees with two leaves). Boosting
reduces error mainly by reducing bias (and also to some extent variance,
by aggregati... | Gradient Boosting Tree vs Random Forest | $\text{error = bias + variance}$
Boosting is based on weak learners (high bias, low variance). In
terms of decision trees, weak learners are shallow trees, sometimes
even as small as decision stumps | Gradient Boosting Tree vs Random Forest
$\text{error = bias + variance}$
Boosting is based on weak learners (high bias, low variance). In
terms of decision trees, weak learners are shallow trees, sometimes
even as small as decision stumps (trees with two leaves). Boosting
reduces error mainly by reducing bias (and als... | Gradient Boosting Tree vs Random Forest
$\text{error = bias + variance}$
Boosting is based on weak learners (high bias, low variance). In
terms of decision trees, weak learners are shallow trees, sometimes
even as small as decision stumps |
914 | Gradient Boosting Tree vs Random Forest | This question is addressed in this very nice post. Please take a look at it and the references therein. http://fastml.com/what-is-better-gradient-boosted-trees-or-random-forest/
Notice in the article that the speaks about calibration, and links to another (nice) blog post about it. Still, I find that the paper Obtainin... | Gradient Boosting Tree vs Random Forest | This question is addressed in this very nice post. Please take a look at it and the references therein. http://fastml.com/what-is-better-gradient-boosted-trees-or-random-forest/
Notice in the article | Gradient Boosting Tree vs Random Forest
This question is addressed in this very nice post. Please take a look at it and the references therein. http://fastml.com/what-is-better-gradient-boosted-trees-or-random-forest/
Notice in the article that the speaks about calibration, and links to another (nice) blog post about i... | Gradient Boosting Tree vs Random Forest
This question is addressed in this very nice post. Please take a look at it and the references therein. http://fastml.com/what-is-better-gradient-boosted-trees-or-random-forest/
Notice in the article |
915 | Gradient Boosting Tree vs Random Forest | Although the above answers are really great, I would like to explain the difference in a very simple language.
Bagging technique that is Bootstrap Aggregation where we build
separate decision trees using bootstrapped set of samples and average
the resulting predictions. Each individual decision tree are grown
deep wit... | Gradient Boosting Tree vs Random Forest | Although the above answers are really great, I would like to explain the difference in a very simple language.
Bagging technique that is Bootstrap Aggregation where we build
separate decision trees u | Gradient Boosting Tree vs Random Forest
Although the above answers are really great, I would like to explain the difference in a very simple language.
Bagging technique that is Bootstrap Aggregation where we build
separate decision trees using bootstrapped set of samples and average
the resulting predictions. Each ind... | Gradient Boosting Tree vs Random Forest
Although the above answers are really great, I would like to explain the difference in a very simple language.
Bagging technique that is Bootstrap Aggregation where we build
separate decision trees u |
916 | How to reverse PCA and reconstruct original variables from several principal components? | PCA computes eigenvectors of the covariance matrix ("principal axes") and sorts them by their eigenvalues (amount of explained variance). The centered data can then be projected onto these principal axes to yield principal components ("scores"). For the purposes of dimensionality reduction, one can keep only a subset o... | How to reverse PCA and reconstruct original variables from several principal components? | PCA computes eigenvectors of the covariance matrix ("principal axes") and sorts them by their eigenvalues (amount of explained variance). The centered data can then be projected onto these principal a | How to reverse PCA and reconstruct original variables from several principal components?
PCA computes eigenvectors of the covariance matrix ("principal axes") and sorts them by their eigenvalues (amount of explained variance). The centered data can then be projected onto these principal axes to yield principal componen... | How to reverse PCA and reconstruct original variables from several principal components?
PCA computes eigenvectors of the covariance matrix ("principal axes") and sorts them by their eigenvalues (amount of explained variance). The centered data can then be projected onto these principal a |
917 | How are the standard errors of coefficients calculated in a regression? | The linear model is written as
$$
\left|
\begin{array}{l}
\mathbf{y} = \mathbf{X} \mathbf{\beta} + \mathbf{\epsilon} \\
\mathbf{\epsilon} \sim N(0, \sigma^2 \mathbf{I}),
\end{array}
\right.$$
where $\mathbf{y}$ denotes the vector of responses, $\mathbf{\beta}$ is the vector of fixed effects parameters, $\mathbf{X}$ is... | How are the standard errors of coefficients calculated in a regression? | The linear model is written as
$$
\left|
\begin{array}{l}
\mathbf{y} = \mathbf{X} \mathbf{\beta} + \mathbf{\epsilon} \\
\mathbf{\epsilon} \sim N(0, \sigma^2 \mathbf{I}),
\end{array}
\right.$$
where $ | How are the standard errors of coefficients calculated in a regression?
The linear model is written as
$$
\left|
\begin{array}{l}
\mathbf{y} = \mathbf{X} \mathbf{\beta} + \mathbf{\epsilon} \\
\mathbf{\epsilon} \sim N(0, \sigma^2 \mathbf{I}),
\end{array}
\right.$$
where $\mathbf{y}$ denotes the vector of responses, $\m... | How are the standard errors of coefficients calculated in a regression?
The linear model is written as
$$
\left|
\begin{array}{l}
\mathbf{y} = \mathbf{X} \mathbf{\beta} + \mathbf{\epsilon} \\
\mathbf{\epsilon} \sim N(0, \sigma^2 \mathbf{I}),
\end{array}
\right.$$
where $ |
918 | How are the standard errors of coefficients calculated in a regression? | The formulae for these can be found in any intermediate text on statistics, in particular, you can find them in Sheather (2009, Chapter 5), from where the following exercise is also taken (page 138).
The following R code computes the coefficient estimates and their standard errors manually
dfData <- as.data.frame(
re... | How are the standard errors of coefficients calculated in a regression? | The formulae for these can be found in any intermediate text on statistics, in particular, you can find them in Sheather (2009, Chapter 5), from where the following exercise is also taken (page 138).
| How are the standard errors of coefficients calculated in a regression?
The formulae for these can be found in any intermediate text on statistics, in particular, you can find them in Sheather (2009, Chapter 5), from where the following exercise is also taken (page 138).
The following R code computes the coefficient es... | How are the standard errors of coefficients calculated in a regression?
The formulae for these can be found in any intermediate text on statistics, in particular, you can find them in Sheather (2009, Chapter 5), from where the following exercise is also taken (page 138).
|
919 | How are the standard errors of coefficients calculated in a regression? | Part of Ocram's answer is wrong.
Actually:
$\hat{\mathbf{\beta}} = (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{y} - (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{\epsilon}.$
$E(\hat{\mathbf{\beta}}) = (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{y}.$
And th... | How are the standard errors of coefficients calculated in a regression? | Part of Ocram's answer is wrong.
Actually:
$\hat{\mathbf{\beta}} = (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{y} - (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mat | How are the standard errors of coefficients calculated in a regression?
Part of Ocram's answer is wrong.
Actually:
$\hat{\mathbf{\beta}} = (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{y} - (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{\epsilon}.$
$E(\hat{\mathbf{\beta}}) = (\mat... | How are the standard errors of coefficients calculated in a regression?
Part of Ocram's answer is wrong.
Actually:
$\hat{\mathbf{\beta}} = (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mathbf{y} - (\mathbf{X}^{\prime} \mathbf{X})^{-1} \mathbf{X}^{\prime} \mat |
920 | When is R squared negative? [duplicate] | $R^2$ compares the fit of the chosen model with that of a horizontal straight line (the null hypothesis). If the chosen model fits worse than a horizontal line, then $R^2$ is negative. Note that $R^2$ is not always the square of anything, so it can have a negative value without violating any rules of math. $R^2$ is neg... | When is R squared negative? [duplicate] | $R^2$ compares the fit of the chosen model with that of a horizontal straight line (the null hypothesis). If the chosen model fits worse than a horizontal line, then $R^2$ is negative. Note that $R^2$ | When is R squared negative? [duplicate]
$R^2$ compares the fit of the chosen model with that of a horizontal straight line (the null hypothesis). If the chosen model fits worse than a horizontal line, then $R^2$ is negative. Note that $R^2$ is not always the square of anything, so it can have a negative value without v... | When is R squared negative? [duplicate]
$R^2$ compares the fit of the chosen model with that of a horizontal straight line (the null hypothesis). If the chosen model fits worse than a horizontal line, then $R^2$ is negative. Note that $R^2$ |
921 | When is R squared negative? [duplicate] | Have you forgotten to include an intercept in your regression? I'm not familiar with SPSS code, but on page 21 of Hayashi's Econometrics:
If the regressors do not include a constant but (as some regression
software packages do) you nevertheless calculate $R^2$ by the formula
$R^2=1-\frac{\sum_{i=1}^{n}e_i^2}{\sum_{i... | When is R squared negative? [duplicate] | Have you forgotten to include an intercept in your regression? I'm not familiar with SPSS code, but on page 21 of Hayashi's Econometrics:
If the regressors do not include a constant but (as some regr | When is R squared negative? [duplicate]
Have you forgotten to include an intercept in your regression? I'm not familiar with SPSS code, but on page 21 of Hayashi's Econometrics:
If the regressors do not include a constant but (as some regression
software packages do) you nevertheless calculate $R^2$ by the formula
$... | When is R squared negative? [duplicate]
Have you forgotten to include an intercept in your regression? I'm not familiar with SPSS code, but on page 21 of Hayashi's Econometrics:
If the regressors do not include a constant but (as some regr |
922 | When is R squared negative? [duplicate] | This can happen if you have a time series that is N.i.i.d. and you construct an inappropriate ARIMA model of the form(0,1,0) which is a first difference random walk model with no drift then the variance (sum of squares - SSE ) of the residuals will be larger than the variance (sum of squares SSO) of the original series... | When is R squared negative? [duplicate] | This can happen if you have a time series that is N.i.i.d. and you construct an inappropriate ARIMA model of the form(0,1,0) which is a first difference random walk model with no drift then the varian | When is R squared negative? [duplicate]
This can happen if you have a time series that is N.i.i.d. and you construct an inappropriate ARIMA model of the form(0,1,0) which is a first difference random walk model with no drift then the variance (sum of squares - SSE ) of the residuals will be larger than the variance (su... | When is R squared negative? [duplicate]
This can happen if you have a time series that is N.i.i.d. and you construct an inappropriate ARIMA model of the form(0,1,0) which is a first difference random walk model with no drift then the varian |
923 | When is R squared negative? [duplicate] | 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.
Here's an explanation for those from the ML field: a n... | When is R squared negative? [duplicate] | 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.
| When is R squared negative? [duplicate]
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.
Here's an expl... | When is R squared negative? [duplicate]
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.
|
924 | The Sleeping Beauty Paradox | Strategy
I would like to apply rational decision theory to the analysis, because that is one well-established way to attain rigor in solving a statistical decision problem. In trying to do so, one difficulty emerges as special: the alteration of SB’s consciousness.
Rational decision theory has no mechanism to handle ... | The Sleeping Beauty Paradox | Strategy
I would like to apply rational decision theory to the analysis, because that is one well-established way to attain rigor in solving a statistical decision problem. In trying to do so, one di | The Sleeping Beauty Paradox
Strategy
I would like to apply rational decision theory to the analysis, because that is one well-established way to attain rigor in solving a statistical decision problem. In trying to do so, one difficulty emerges as special: the alteration of SB’s consciousness.
Rational decision theory... | The Sleeping Beauty Paradox
Strategy
I would like to apply rational decision theory to the analysis, because that is one well-established way to attain rigor in solving a statistical decision problem. In trying to do so, one di |
925 | The Sleeping Beauty Paradox | Thanks for this brilliant post (+1) and solution (+1). This paradox already gives me a headache.
I just thought of the following situation which does not require fairies, miracles nor magic potions. Flip a fair coin on Monday noon. Upon 'Tails' send a mail to Alice and Bob (in a way that they don't know that the other ... | The Sleeping Beauty Paradox | Thanks for this brilliant post (+1) and solution (+1). This paradox already gives me a headache.
I just thought of the following situation which does not require fairies, miracles nor magic potions. F | The Sleeping Beauty Paradox
Thanks for this brilliant post (+1) and solution (+1). This paradox already gives me a headache.
I just thought of the following situation which does not require fairies, miracles nor magic potions. Flip a fair coin on Monday noon. Upon 'Tails' send a mail to Alice and Bob (in a way that the... | The Sleeping Beauty Paradox
Thanks for this brilliant post (+1) and solution (+1). This paradox already gives me a headache.
I just thought of the following situation which does not require fairies, miracles nor magic potions. F |
926 | The Sleeping Beauty Paradox | The paradox lies in the perspective change between a single experiment and its limit point. If # of experiments is taken into account, you can understand this even more precisely than the "either/or" of halvers and thirders:
Single Experiment: Halvers are right
If there is a single experiment, there are three outcome... | The Sleeping Beauty Paradox | The paradox lies in the perspective change between a single experiment and its limit point. If # of experiments is taken into account, you can understand this even more precisely than the "either/or" | The Sleeping Beauty Paradox
The paradox lies in the perspective change between a single experiment and its limit point. If # of experiments is taken into account, you can understand this even more precisely than the "either/or" of halvers and thirders:
Single Experiment: Halvers are right
If there is a single experim... | The Sleeping Beauty Paradox
The paradox lies in the perspective change between a single experiment and its limit point. If # of experiments is taken into account, you can understand this even more precisely than the "either/or" |
927 | The Sleeping Beauty Paradox | Let's vary the problem.
If the coin comes up Heads, then SB is never awakened.
If Tails, then SB is awakened once.
Now the camps are Halfers and Zeroers. And clearly the Zeroers are correct.
Or: Heads -> woken once; Tails -> woken a million times. Clearly, given she's awake, it's most likely tails.
(P.S. On the subject... | The Sleeping Beauty Paradox | Let's vary the problem.
If the coin comes up Heads, then SB is never awakened.
If Tails, then SB is awakened once.
Now the camps are Halfers and Zeroers. And clearly the Zeroers are correct.
Or: Heads | The Sleeping Beauty Paradox
Let's vary the problem.
If the coin comes up Heads, then SB is never awakened.
If Tails, then SB is awakened once.
Now the camps are Halfers and Zeroers. And clearly the Zeroers are correct.
Or: Heads -> woken once; Tails -> woken a million times. Clearly, given she's awake, it's most likely... | The Sleeping Beauty Paradox
Let's vary the problem.
If the coin comes up Heads, then SB is never awakened.
If Tails, then SB is awakened once.
Now the camps are Halfers and Zeroers. And clearly the Zeroers are correct.
Or: Heads |
928 | The Sleeping Beauty Paradox | "Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night." This is wrong, as wrong as saying "Either I win the lottery or I don't, so the probability is $50\%$." She has learned that she has woken up. This is information. Now she should believe each possible awakening is equally likely, no... | The Sleeping Beauty Paradox | "Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night." This is wrong, as wrong as saying "Either I win the lottery or I don't, so the probability is $50\%$." She has | The Sleeping Beauty Paradox
"Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night." This is wrong, as wrong as saying "Either I win the lottery or I don't, so the probability is $50\%$." She has learned that she has woken up. This is information. Now she should believe each possible awa... | The Sleeping Beauty Paradox
"Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night." This is wrong, as wrong as saying "Either I win the lottery or I don't, so the probability is $50\%$." She has |
929 | The Sleeping Beauty Paradox | When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
What do you mean by "should"? What are the consequences of my beliefs? In such an experiment I wouldn't believe anything. This question is tagged as decision-theory, but, the way this experiment is conceived, I have n... | The Sleeping Beauty Paradox | When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
What do you mean by "should"? What are the consequences of my beliefs? In such an experiment I wo | The Sleeping Beauty Paradox
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
What do you mean by "should"? What are the consequences of my beliefs? In such an experiment I wouldn't believe anything. This question is tagged as decision-theory, but, the way this exper... | The Sleeping Beauty Paradox
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
What do you mean by "should"? What are the consequences of my beliefs? In such an experiment I wo |
930 | The Sleeping Beauty Paradox | The question is ambiguous and so there only appears to be a paradox. The question is posed this way:
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
Which is confused with this question:
When you are awakened, to what degree should you believe Heads was the reas... | The Sleeping Beauty Paradox | The question is ambiguous and so there only appears to be a paradox. The question is posed this way:
When you are awakened, to what degree should you believe that the outcome of the coin toss was He | The Sleeping Beauty Paradox
The question is ambiguous and so there only appears to be a paradox. The question is posed this way:
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
Which is confused with this question:
When you are awakened, to what degree should yo... | The Sleeping Beauty Paradox
The question is ambiguous and so there only appears to be a paradox. The question is posed this way:
When you are awakened, to what degree should you believe that the outcome of the coin toss was He |
931 | The Sleeping Beauty Paradox | "Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night."
This isn't correct, which is the error in the halfer argument. One thing that makes it hard to argue with,tho, is that the halfer argument which is based on this statement is seldom expressed with any more rigor than what I quoted.... | The Sleeping Beauty Paradox | "Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night."
This isn't correct, which is the error in the halfer argument. One thing that makes it hard to argue with,tho, | The Sleeping Beauty Paradox
"Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night."
This isn't correct, which is the error in the halfer argument. One thing that makes it hard to argue with,tho, is that the halfer argument which is based on this statement is seldom expressed with any mo... | The Sleeping Beauty Paradox
"Whenever SB awakens, she has learned absolutely nothing she did not know Sunday night."
This isn't correct, which is the error in the halfer argument. One thing that makes it hard to argue with,tho, |
932 | The Sleeping Beauty Paradox | I just re-tripped across this. I've refined some of my thoughts since that last post, and thought I might find a receptive audience for them here.
First off, on the philosophy of how to address such a controversy: Say arguments A and B exist. Each has a premise, a sequence of deductions, and a result; and the results d... | The Sleeping Beauty Paradox | I just re-tripped across this. I've refined some of my thoughts since that last post, and thought I might find a receptive audience for them here.
First off, on the philosophy of how to address such a | The Sleeping Beauty Paradox
I just re-tripped across this. I've refined some of my thoughts since that last post, and thought I might find a receptive audience for them here.
First off, on the philosophy of how to address such a controversy: Say arguments A and B exist. Each has a premise, a sequence of deductions, and... | The Sleeping Beauty Paradox
I just re-tripped across this. I've refined some of my thoughts since that last post, and thought I might find a receptive audience for them here.
First off, on the philosophy of how to address such a |
933 | The Sleeping Beauty Paradox | Since sleeping beauty can't remember how many times she has woken up before, we are not looking at the probability of Heads given that she has woken up just this once, but the probability of Heads given that she has woken up at least once:
So we have: $P(Heads\mid x\geq1) = 1/2$ and not $P(Heads\mid x=1) = 1/3$
Thus th... | The Sleeping Beauty Paradox | Since sleeping beauty can't remember how many times she has woken up before, we are not looking at the probability of Heads given that she has woken up just this once, but the probability of Heads giv | The Sleeping Beauty Paradox
Since sleeping beauty can't remember how many times she has woken up before, we are not looking at the probability of Heads given that she has woken up just this once, but the probability of Heads given that she has woken up at least once:
So we have: $P(Heads\mid x\geq1) = 1/2$ and not $P(H... | The Sleeping Beauty Paradox
Since sleeping beauty can't remember how many times she has woken up before, we are not looking at the probability of Heads given that she has woken up just this once, but the probability of Heads giv |
934 | The Sleeping Beauty Paradox | A simple explanation for this would be that there are 3 ways in which sleeping beauty can wake up two of which are from a Tails toss. So the probability has to be 1/3 for a heads every time she wakes up. I've outlined it in a blog post
The main argument against the "halfer" point of view is the following: In a bayesian... | The Sleeping Beauty Paradox | A simple explanation for this would be that there are 3 ways in which sleeping beauty can wake up two of which are from a Tails toss. So the probability has to be 1/3 for a heads every time she wakes | The Sleeping Beauty Paradox
A simple explanation for this would be that there are 3 ways in which sleeping beauty can wake up two of which are from a Tails toss. So the probability has to be 1/3 for a heads every time she wakes up. I've outlined it in a blog post
The main argument against the "halfer" point of view is ... | The Sleeping Beauty Paradox
A simple explanation for this would be that there are 3 ways in which sleeping beauty can wake up two of which are from a Tails toss. So the probability has to be 1/3 for a heads every time she wakes |
935 | The Sleeping Beauty Paradox | One third of possible wakings are Heads wakings, and two thirds of possible wakings are Tails wakings. However, one half of princesses (or whatever) are Heads princesses, and one half are Tails princesses. The Tails princesses, individually and in aggregate, experience twice as many wakings as the Heads princesses. ... | The Sleeping Beauty Paradox | One third of possible wakings are Heads wakings, and two thirds of possible wakings are Tails wakings. However, one half of princesses (or whatever) are Heads princesses, and one half are Tails prin | The Sleeping Beauty Paradox
One third of possible wakings are Heads wakings, and two thirds of possible wakings are Tails wakings. However, one half of princesses (or whatever) are Heads princesses, and one half are Tails princesses. The Tails princesses, individually and in aggregate, experience twice as many wakin... | The Sleeping Beauty Paradox
One third of possible wakings are Heads wakings, and two thirds of possible wakings are Tails wakings. However, one half of princesses (or whatever) are Heads princesses, and one half are Tails prin |
936 | The Sleeping Beauty Paradox | Non-statistially
In all her congenial geniousness, Sleeping Beauty can perform the hypothetical experiment in her sleep, which will shape her believes:
import numpy as np
# Take clones of our Sleeping Beauties.
# One type of clones is persistently heads guessing,
# the other persistently guesses tails.
# Keeping ... | The Sleeping Beauty Paradox | Non-statistially
In all her congenial geniousness, Sleeping Beauty can perform the hypothetical experiment in her sleep, which will shape her believes:
import numpy as np
# Take clones of our Sle | The Sleeping Beauty Paradox
Non-statistially
In all her congenial geniousness, Sleeping Beauty can perform the hypothetical experiment in her sleep, which will shape her believes:
import numpy as np
# Take clones of our Sleeping Beauties.
# One type of clones is persistently heads guessing,
# the other persistentl... | The Sleeping Beauty Paradox
Non-statistially
In all her congenial geniousness, Sleeping Beauty can perform the hypothetical experiment in her sleep, which will shape her believes:
import numpy as np
# Take clones of our Sle |
937 | The Sleeping Beauty Paradox | I really like this example but I would argue that there is one point to make confounded with a couple of nuisance distractions.
To avoid nuisance distractions, one arguable should try to discern an abstract diagrammatic representation of the problem that is clearly beyond reasonable doubt (as an adequate representatio... | The Sleeping Beauty Paradox | I really like this example but I would argue that there is one point to make confounded with a couple of nuisance distractions.
To avoid nuisance distractions, one arguable should try to discern an a | The Sleeping Beauty Paradox
I really like this example but I would argue that there is one point to make confounded with a couple of nuisance distractions.
To avoid nuisance distractions, one arguable should try to discern an abstract diagrammatic representation of the problem that is clearly beyond reasonable doubt (... | The Sleeping Beauty Paradox
I really like this example but I would argue that there is one point to make confounded with a couple of nuisance distractions.
To avoid nuisance distractions, one arguable should try to discern an a |
938 | The Sleeping Beauty Paradox | I'm going to solve this problem for the generic case where SB is waken '$m$' times after 'Heads' and '$n$' times after 'Tails' with $m≤n$.
Specifically, if coin is 'Heads', she will be awakened on...
day 1
day 2
$\cdots$
$\cdots$
day $m$
...and if coin is 'Tails', she will be awakened on...
day 1
day 2
$\cdots$
$\cdots... | The Sleeping Beauty Paradox | I'm going to solve this problem for the generic case where SB is waken '$m$' times after 'Heads' and '$n$' times after 'Tails' with $m≤n$.
Specifically, if coin is 'Heads', she will be awakened on...
| The Sleeping Beauty Paradox
I'm going to solve this problem for the generic case where SB is waken '$m$' times after 'Heads' and '$n$' times after 'Tails' with $m≤n$.
Specifically, if coin is 'Heads', she will be awakened on...
day 1
day 2
$\cdots$
$\cdots$
day $m$
...and if coin is 'Tails', she will be awakened on...
... | The Sleeping Beauty Paradox
I'm going to solve this problem for the generic case where SB is waken '$m$' times after 'Heads' and '$n$' times after 'Tails' with $m≤n$.
Specifically, if coin is 'Heads', she will be awakened on...
|
939 | The Sleeping Beauty Paradox | Just another approach to frame this paradox with slightly different rules.
Sleeping Beauty is set to sleep. The scientists and Sleeping Beauty agree that the scientists will play the lottery (with winning chance one in a Million). If they win, they will wake up Sleeping Beauty 10 Million times. If they don't win, they... | The Sleeping Beauty Paradox | Just another approach to frame this paradox with slightly different rules.
Sleeping Beauty is set to sleep. The scientists and Sleeping Beauty agree that the scientists will play the lottery (with wi | The Sleeping Beauty Paradox
Just another approach to frame this paradox with slightly different rules.
Sleeping Beauty is set to sleep. The scientists and Sleeping Beauty agree that the scientists will play the lottery (with winning chance one in a Million). If they win, they will wake up Sleeping Beauty 10 Million ti... | The Sleeping Beauty Paradox
Just another approach to frame this paradox with slightly different rules.
Sleeping Beauty is set to sleep. The scientists and Sleeping Beauty agree that the scientists will play the lottery (with wi |
940 | The Sleeping Beauty Paradox | I just thought of a new way to explain my point, and what is wrong with the 1/2 answer. Run two versions of the experiment at the same time, using the same coin flip. One version is just like the original. In the other, three (or four - it doesn’t matter) volunteers are needed; each is assigned a different combination ... | The Sleeping Beauty Paradox | I just thought of a new way to explain my point, and what is wrong with the 1/2 answer. Run two versions of the experiment at the same time, using the same coin flip. One version is just like the orig | The Sleeping Beauty Paradox
I just thought of a new way to explain my point, and what is wrong with the 1/2 answer. Run two versions of the experiment at the same time, using the same coin flip. One version is just like the original. In the other, three (or four - it doesn’t matter) volunteers are needed; each is assig... | The Sleeping Beauty Paradox
I just thought of a new way to explain my point, and what is wrong with the 1/2 answer. Run two versions of the experiment at the same time, using the same coin flip. One version is just like the orig |
941 | The Sleeping Beauty Paradox | As many questions, it depends of the exact meaning of the question:
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
If you are interpret it as "what are the odds that a tossed coin is Heads", obviously the answer is "half the odds".
But what you are asking is not ... | The Sleeping Beauty Paradox | As many questions, it depends of the exact meaning of the question:
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
If you are interpret it as " | The Sleeping Beauty Paradox
As many questions, it depends of the exact meaning of the question:
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
If you are interpret it as "what are the odds that a tossed coin is Heads", obviously the answer is "half the odds".
But... | The Sleeping Beauty Paradox
As many questions, it depends of the exact meaning of the question:
When you are awakened, to what degree should you believe that the outcome of the coin toss was Heads?
If you are interpret it as " |
942 | The Sleeping Beauty Paradox | This is a very interesting question. I will give my answer as if I were to be sleeping beauty. I feel a key point to understand is that we 100% trust the experimenter.
1) On Sunday night, if you ask me what the probability the coin is heads, I will tell you $\frac{1}{2}$.
2) Whenever you wake me up and ask me, I will t... | The Sleeping Beauty Paradox | This is a very interesting question. I will give my answer as if I were to be sleeping beauty. I feel a key point to understand is that we 100% trust the experimenter.
1) On Sunday night, if you ask m | The Sleeping Beauty Paradox
This is a very interesting question. I will give my answer as if I were to be sleeping beauty. I feel a key point to understand is that we 100% trust the experimenter.
1) On Sunday night, if you ask me what the probability the coin is heads, I will tell you $\frac{1}{2}$.
2) Whenever you wak... | The Sleeping Beauty Paradox
This is a very interesting question. I will give my answer as if I were to be sleeping beauty. I feel a key point to understand is that we 100% trust the experimenter.
1) On Sunday night, if you ask m |
943 | The Sleeping Beauty Paradox | Rather than giving a statistically rigorous answer, I'd like to modify the question slightly in a way that might convince people whose intuition leads them to be halfers.
Some researchers want to put you to sleep. Depending on the secret toss of a fair coin, they will awaken you either once (Heads) or nine-hundred and... | The Sleeping Beauty Paradox | Rather than giving a statistically rigorous answer, I'd like to modify the question slightly in a way that might convince people whose intuition leads them to be halfers.
Some researchers want to put | The Sleeping Beauty Paradox
Rather than giving a statistically rigorous answer, I'd like to modify the question slightly in a way that might convince people whose intuition leads them to be halfers.
Some researchers want to put you to sleep. Depending on the secret toss of a fair coin, they will awaken you either once... | The Sleeping Beauty Paradox
Rather than giving a statistically rigorous answer, I'd like to modify the question slightly in a way that might convince people whose intuition leads them to be halfers.
Some researchers want to put |
944 | The Sleeping Beauty Paradox | I think the error is from the "thirders" and my reason for this is that the "awakenings" are not equally likely - if you are woken up then it is more likely to be "the first time" you were woken up - a 75% chance in fact.
This means you cannot count the "3 outcomes" (heads1, tails1, tails2) equally.
I think this also a... | The Sleeping Beauty Paradox | I think the error is from the "thirders" and my reason for this is that the "awakenings" are not equally likely - if you are woken up then it is more likely to be "the first time" you were woken up - | The Sleeping Beauty Paradox
I think the error is from the "thirders" and my reason for this is that the "awakenings" are not equally likely - if you are woken up then it is more likely to be "the first time" you were woken up - a 75% chance in fact.
This means you cannot count the "3 outcomes" (heads1, tails1, tails2) ... | The Sleeping Beauty Paradox
I think the error is from the "thirders" and my reason for this is that the "awakenings" are not equally likely - if you are woken up then it is more likely to be "the first time" you were woken up - |
945 | The Sleeping Beauty Paradox | The perception that there is a paradox here stems from the conflation of two different questions:
What is the probability of heads? (1/2)
What is the probability of observing a heads upon waking from the sleeper's perspective? (1/3)
However, these are both valid and different questions and so there is no paradox to r... | The Sleeping Beauty Paradox | The perception that there is a paradox here stems from the conflation of two different questions:
What is the probability of heads? (1/2)
What is the probability of observing a heads upon waking from | The Sleeping Beauty Paradox
The perception that there is a paradox here stems from the conflation of two different questions:
What is the probability of heads? (1/2)
What is the probability of observing a heads upon waking from the sleeper's perspective? (1/3)
However, these are both valid and different questions and... | The Sleeping Beauty Paradox
The perception that there is a paradox here stems from the conflation of two different questions:
What is the probability of heads? (1/2)
What is the probability of observing a heads upon waking from |
946 | The Sleeping Beauty Paradox | Beauty learns no new information, yet her credence for heads is 1/3.
The 1/3 answer comes from two applications of the law of total probability (show below), and the fact that B's credence for her belief in the current day being Monday, given she's told the coin landed tails, is 1/2. The decision quadruple defined belo... | The Sleeping Beauty Paradox | Beauty learns no new information, yet her credence for heads is 1/3.
The 1/3 answer comes from two applications of the law of total probability (show below), and the fact that B's credence for her bel | The Sleeping Beauty Paradox
Beauty learns no new information, yet her credence for heads is 1/3.
The 1/3 answer comes from two applications of the law of total probability (show below), and the fact that B's credence for her belief in the current day being Monday, given she's told the coin landed tails, is 1/2. The dec... | The Sleeping Beauty Paradox
Beauty learns no new information, yet her credence for heads is 1/3.
The 1/3 answer comes from two applications of the law of total probability (show below), and the fact that B's credence for her bel |
947 | The Sleeping Beauty Paradox | Ignore all the complex theory and just calculate the odds.
There are 3 possible events: awake-from-heads, awake-from-tails, awake-from-tails. Heads has one event, while tails has two events. The odds are 1:2 against heads. Since flipping heads and tails are equally likely, we can just count the events from heads divide... | The Sleeping Beauty Paradox | Ignore all the complex theory and just calculate the odds.
There are 3 possible events: awake-from-heads, awake-from-tails, awake-from-tails. Heads has one event, while tails has two events. The odds | The Sleeping Beauty Paradox
Ignore all the complex theory and just calculate the odds.
There are 3 possible events: awake-from-heads, awake-from-tails, awake-from-tails. Heads has one event, while tails has two events. The odds are 1:2 against heads. Since flipping heads and tails are equally likely, we can just count ... | The Sleeping Beauty Paradox
Ignore all the complex theory and just calculate the odds.
There are 3 possible events: awake-from-heads, awake-from-tails, awake-from-tails. Heads has one event, while tails has two events. The odds |
948 | The Sleeping Beauty Paradox | If sleeping beauty had to say either heads or tails - she would minimise her expected 0-1 loss function (evaluated each day) by picking tails. If, however, the 0-1 loss function was only evaluated each trial then either heads or tails would be equally good. | The Sleeping Beauty Paradox | If sleeping beauty had to say either heads or tails - she would minimise her expected 0-1 loss function (evaluated each day) by picking tails. If, however, the 0-1 loss function was only evaluated eac | The Sleeping Beauty Paradox
If sleeping beauty had to say either heads or tails - she would minimise her expected 0-1 loss function (evaluated each day) by picking tails. If, however, the 0-1 loss function was only evaluated each trial then either heads or tails would be equally good. | The Sleeping Beauty Paradox
If sleeping beauty had to say either heads or tails - she would minimise her expected 0-1 loss function (evaluated each day) by picking tails. If, however, the 0-1 loss function was only evaluated eac |
949 | The Sleeping Beauty Paradox | The thirders win
Instead of a coin, lets a assume a fair dice:
on friday, the sleeping beauty will sleep:
if the dice == 1 , they will awake her on saturday;
if the dice == 2 , they will awake her on saturday and sunday;
if the dice == 3 , they will awake her on saturday, sunday and monday;
if the dice == 4 , they will... | The Sleeping Beauty Paradox | The thirders win
Instead of a coin, lets a assume a fair dice:
on friday, the sleeping beauty will sleep:
if the dice == 1 , they will awake her on saturday;
if the dice == 2 , they will awake her on | The Sleeping Beauty Paradox
The thirders win
Instead of a coin, lets a assume a fair dice:
on friday, the sleeping beauty will sleep:
if the dice == 1 , they will awake her on saturday;
if the dice == 2 , they will awake her on saturday and sunday;
if the dice == 3 , they will awake her on saturday, sunday and monday;
... | The Sleeping Beauty Paradox
The thirders win
Instead of a coin, lets a assume a fair dice:
on friday, the sleeping beauty will sleep:
if the dice == 1 , they will awake her on saturday;
if the dice == 2 , they will awake her on |
950 | The Sleeping Beauty Paradox | The apparent paradox derives from the false premise that probabilities are absolute. In fact, probabilities are relative to the definition of the events being counted.
This is an important point to understand for machine learning. We may wish to calculate the probability of something (eg, a transcription being correct ... | The Sleeping Beauty Paradox | The apparent paradox derives from the false premise that probabilities are absolute. In fact, probabilities are relative to the definition of the events being counted.
This is an important point to un | The Sleeping Beauty Paradox
The apparent paradox derives from the false premise that probabilities are absolute. In fact, probabilities are relative to the definition of the events being counted.
This is an important point to understand for machine learning. We may wish to calculate the probability of something (eg, a ... | The Sleeping Beauty Paradox
The apparent paradox derives from the false premise that probabilities are absolute. In fact, probabilities are relative to the definition of the events being counted.
This is an important point to un |
951 | The Sleeping Beauty Paradox | Late to the party, I know.
This question is very similar to the Monty Hall problem, where you are asked to guess behind which of 3 doors the prize is. Say you choose Door No.1. Then the presenter (who knows where the prize is) removes Door No.3 from the game, and asks if you'd like to switch your guess from Door No1 to... | The Sleeping Beauty Paradox | Late to the party, I know.
This question is very similar to the Monty Hall problem, where you are asked to guess behind which of 3 doors the prize is. Say you choose Door No.1. Then the presenter (who | The Sleeping Beauty Paradox
Late to the party, I know.
This question is very similar to the Monty Hall problem, where you are asked to guess behind which of 3 doors the prize is. Say you choose Door No.1. Then the presenter (who knows where the prize is) removes Door No.3 from the game, and asks if you'd like to switch... | The Sleeping Beauty Paradox
Late to the party, I know.
This question is very similar to the Monty Hall problem, where you are asked to guess behind which of 3 doors the prize is. Say you choose Door No.1. Then the presenter (who |
952 | The Sleeping Beauty Paradox | When Sleeping Beauty is awoken, she knows:
A fair coin was tossed to give result $r$; if $r = \mathrm{H}$ then this is the sole subsequent awakening; and if $r = \mathrm{T}$ then this is one of two subsequent awakenings.
Call this information $\mathcal{I}$. Nothing else is relevant to her question, which is:
What is... | The Sleeping Beauty Paradox | When Sleeping Beauty is awoken, she knows:
A fair coin was tossed to give result $r$; if $r = \mathrm{H}$ then this is the sole subsequent awakening; and if $r = \mathrm{T}$ then this is one of two s | The Sleeping Beauty Paradox
When Sleeping Beauty is awoken, she knows:
A fair coin was tossed to give result $r$; if $r = \mathrm{H}$ then this is the sole subsequent awakening; and if $r = \mathrm{T}$ then this is one of two subsequent awakenings.
Call this information $\mathcal{I}$. Nothing else is relevant to her ... | The Sleeping Beauty Paradox
When Sleeping Beauty is awoken, she knows:
A fair coin was tossed to give result $r$; if $r = \mathrm{H}$ then this is the sole subsequent awakening; and if $r = \mathrm{T}$ then this is one of two s |
953 | The Sleeping Beauty Paradox | Here's an argument that being a halfer can lead Sleeping Beauty astray.
When halfer Sleeping Beauty wakes up she believes $\mathbb{P}(heads) = \frac12$. Suppose she suddenly decides she can't take the uncertainty, overpowers the experimenter, and forces him to tell her whether this is the first or second time she has b... | The Sleeping Beauty Paradox | Here's an argument that being a halfer can lead Sleeping Beauty astray.
When halfer Sleeping Beauty wakes up she believes $\mathbb{P}(heads) = \frac12$. Suppose she suddenly decides she can't take the | The Sleeping Beauty Paradox
Here's an argument that being a halfer can lead Sleeping Beauty astray.
When halfer Sleeping Beauty wakes up she believes $\mathbb{P}(heads) = \frac12$. Suppose she suddenly decides she can't take the uncertainty, overpowers the experimenter, and forces him to tell her whether this is the fi... | The Sleeping Beauty Paradox
Here's an argument that being a halfer can lead Sleeping Beauty astray.
When halfer Sleeping Beauty wakes up she believes $\mathbb{P}(heads) = \frac12$. Suppose she suddenly decides she can't take the |
954 | Objective function, cost function, loss function: are they the same thing? | These are not very strict terms and they are highly related. However:
Loss function is usually a function defined on a data point, prediction and label, and measures the penalty. For example:
Square loss: $l(f(x_i|\theta),y_i) = \left (f(x_i|\theta)-y_i \right )^2$, used in linear regression
Hinge loss: $l(f(x_i|\the... | Objective function, cost function, loss function: are they the same thing? | These are not very strict terms and they are highly related. However:
Loss function is usually a function defined on a data point, prediction and label, and measures the penalty. For example:
Square | Objective function, cost function, loss function: are they the same thing?
These are not very strict terms and they are highly related. However:
Loss function is usually a function defined on a data point, prediction and label, and measures the penalty. For example:
Square loss: $l(f(x_i|\theta),y_i) = \left (f(x_i|\... | Objective function, cost function, loss function: are they the same thing?
These are not very strict terms and they are highly related. However:
Loss function is usually a function defined on a data point, prediction and label, and measures the penalty. For example:
Square |
955 | Objective function, cost function, loss function: are they the same thing? | Quoting from section 4.3 in "Deep Learning" book by Ian Goodfellow, Yoshua Bengio, Aaron Courville (emphasis in the original):
The function we want to minimize or maximize is called the objective function, or criterion. When we are minimizing it, we may also call it the cost function, loss function, or error function.... | Objective function, cost function, loss function: are they the same thing? | Quoting from section 4.3 in "Deep Learning" book by Ian Goodfellow, Yoshua Bengio, Aaron Courville (emphasis in the original):
The function we want to minimize or maximize is called the objective fun | Objective function, cost function, loss function: are they the same thing?
Quoting from section 4.3 in "Deep Learning" book by Ian Goodfellow, Yoshua Bengio, Aaron Courville (emphasis in the original):
The function we want to minimize or maximize is called the objective function, or criterion. When we are minimizing i... | Objective function, cost function, loss function: are they the same thing?
Quoting from section 4.3 in "Deep Learning" book by Ian Goodfellow, Yoshua Bengio, Aaron Courville (emphasis in the original):
The function we want to minimize or maximize is called the objective fun |
956 | Objective function, cost function, loss function: are they the same thing? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
In Andrew NG's words-
"Finally, the loss function was defined with respect to a single
training example. It... | Objective function, cost function, loss function: are they the same thing? | Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
| Objective function, cost function, loss function: are they the same thing?
Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
In Andrew NG's words-
"Finally, th... | Objective function, cost function, loss function: are they the same thing?
Want to improve this post? Add citations from reputable sources by editing the post. Posts with unsourced content may be edited or deleted.
|
957 | Objective function, cost function, loss function: are they the same thing? | According to Prof. Andrew Ng (see slides on page 11),
Function h(X) represents your hypothesis. For fixed fitting parameters theta, it is a function of features X. I'd say this can also be called the Objective Function.
The Cost function J is a function of the fitting parameters theta. J = J(theta).
According to the Ha... | Objective function, cost function, loss function: are they the same thing? | According to Prof. Andrew Ng (see slides on page 11),
Function h(X) represents your hypothesis. For fixed fitting parameters theta, it is a function of features X. I'd say this can also be called the | Objective function, cost function, loss function: are they the same thing?
According to Prof. Andrew Ng (see slides on page 11),
Function h(X) represents your hypothesis. For fixed fitting parameters theta, it is a function of features X. I'd say this can also be called the Objective Function.
The Cost function J is a ... | Objective function, cost function, loss function: are they the same thing?
According to Prof. Andrew Ng (see slides on page 11),
Function h(X) represents your hypothesis. For fixed fitting parameters theta, it is a function of features X. I'd say this can also be called the |
958 | Objective function, cost function, loss function: are they the same thing? | The loss function computes the error for a single training example, while the cost function is the average of the loss functions of the entire training set. | Objective function, cost function, loss function: are they the same thing? | The loss function computes the error for a single training example, while the cost function is the average of the loss functions of the entire training set. | Objective function, cost function, loss function: are they the same thing?
The loss function computes the error for a single training example, while the cost function is the average of the loss functions of the entire training set. | Objective function, cost function, loss function: are they the same thing?
The loss function computes the error for a single training example, while the cost function is the average of the loss functions of the entire training set. |
959 | Objective function, cost function, loss function: are they the same thing? | Actually to be simple
If you have m training data like this (x(1),y(1)),(x(2),y(2)), . . . (x(m),y(m))
We use loss function L(ycap,y) to find loss between ycap and y of a single training set
If we want to find loss between ycap and y of a whole training set we use cost function.
Note:- ycap means output from our model
... | Objective function, cost function, loss function: are they the same thing? | Actually to be simple
If you have m training data like this (x(1),y(1)),(x(2),y(2)), . . . (x(m),y(m))
We use loss function L(ycap,y) to find loss between ycap and y of a single training set
If we wan | Objective function, cost function, loss function: are they the same thing?
Actually to be simple
If you have m training data like this (x(1),y(1)),(x(2),y(2)), . . . (x(m),y(m))
We use loss function L(ycap,y) to find loss between ycap and y of a single training set
If we want to find loss between ycap and y of a whole ... | Objective function, cost function, loss function: are they the same thing?
Actually to be simple
If you have m training data like this (x(1),y(1)),(x(2),y(2)), . . . (x(m),y(m))
We use loss function L(ycap,y) to find loss between ycap and y of a single training set
If we wan |
960 | Objective function, cost function, loss function: are they the same thing? | The terms cost and loss functions are synonymous. Some people also call them the error function. The more general scenario is to define an objective function first that we want to optimize. This objective function could be to:
maximize the posterior probabilities (e.g., naive Bayes)
maximize a fitness function (geneti... | Objective function, cost function, loss function: are they the same thing? | The terms cost and loss functions are synonymous. Some people also call them the error function. The more general scenario is to define an objective function first that we want to optimize. This objec | Objective function, cost function, loss function: are they the same thing?
The terms cost and loss functions are synonymous. Some people also call them the error function. The more general scenario is to define an objective function first that we want to optimize. This objective function could be to:
maximize the post... | Objective function, cost function, loss function: are they the same thing?
The terms cost and loss functions are synonymous. Some people also call them the error function. The more general scenario is to define an objective function first that we want to optimize. This objec |
961 | Objective function, cost function, loss function: are they the same thing? | To give you a short answer, according to me they are synonymous. However, the cost function is used more in optimization problem and loss function is used in parameter estimation. | Objective function, cost function, loss function: are they the same thing? | To give you a short answer, according to me they are synonymous. However, the cost function is used more in optimization problem and loss function is used in parameter estimation. | Objective function, cost function, loss function: are they the same thing?
To give you a short answer, according to me they are synonymous. However, the cost function is used more in optimization problem and loss function is used in parameter estimation. | Objective function, cost function, loss function: are they the same thing?
To give you a short answer, according to me they are synonymous. However, the cost function is used more in optimization problem and loss function is used in parameter estimation. |
962 | Objective function, cost function, loss function: are they the same thing? | How about Score function?
Not related directly to the question, but I wanted to add this here, to have a completed reference to all these computational terminologies.
In statistics, the score (or informant[1]) is the gradient of the
log-likelihood function with respect to the parameter vector.
This term is used speci... | Objective function, cost function, loss function: are they the same thing? | How about Score function?
Not related directly to the question, but I wanted to add this here, to have a completed reference to all these computational terminologies.
In statistics, the score (or inf | Objective function, cost function, loss function: are they the same thing?
How about Score function?
Not related directly to the question, but I wanted to add this here, to have a completed reference to all these computational terminologies.
In statistics, the score (or informant[1]) is the gradient of the
log-likelih... | Objective function, cost function, loss function: are they the same thing?
How about Score function?
Not related directly to the question, but I wanted to add this here, to have a completed reference to all these computational terminologies.
In statistics, the score (or inf |
963 | What's the difference between principal component analysis and multidimensional scaling? | Classic Torgerson's metric MDS is actually done by transforming distances into similarities and performing PCA (eigen-decomposition or singular-value-decomposition) on those. [The other name of this procedure (distances between objects -> similarities between them -> PCA, whereby loadings are the sought-for coordinates... | What's the difference between principal component analysis and multidimensional scaling? | Classic Torgerson's metric MDS is actually done by transforming distances into similarities and performing PCA (eigen-decomposition or singular-value-decomposition) on those. [The other name of this p | What's the difference between principal component analysis and multidimensional scaling?
Classic Torgerson's metric MDS is actually done by transforming distances into similarities and performing PCA (eigen-decomposition or singular-value-decomposition) on those. [The other name of this procedure (distances between obj... | What's the difference between principal component analysis and multidimensional scaling?
Classic Torgerson's metric MDS is actually done by transforming distances into similarities and performing PCA (eigen-decomposition or singular-value-decomposition) on those. [The other name of this p |
964 | What's the difference between principal component analysis and multidimensional scaling? | Two types of metric MDS
The task of metric multidimensional scaling (MDS) can be abstractly formulated as follows: given a $n\times n$ matrix $\mathbf D$ of pairwise distances between $n$ points, find a low-dimensional embedding of data points in $\mathbb R^k$ such that Euclidean distances between them approximate the... | What's the difference between principal component analysis and multidimensional scaling? | Two types of metric MDS
The task of metric multidimensional scaling (MDS) can be abstractly formulated as follows: given a $n\times n$ matrix $\mathbf D$ of pairwise distances between $n$ points, fin | What's the difference between principal component analysis and multidimensional scaling?
Two types of metric MDS
The task of metric multidimensional scaling (MDS) can be abstractly formulated as follows: given a $n\times n$ matrix $\mathbf D$ of pairwise distances between $n$ points, find a low-dimensional embedding o... | What's the difference between principal component analysis and multidimensional scaling?
Two types of metric MDS
The task of metric multidimensional scaling (MDS) can be abstractly formulated as follows: given a $n\times n$ matrix $\mathbf D$ of pairwise distances between $n$ points, fin |
965 | What's the difference between principal component analysis and multidimensional scaling? | Uhm... quite different. In PCA, you are given the multivariate continuous data (a multivariate vector for each subject), and you are trying to figure out if you don't need that many dimensions to conceptualize them. In (metric) MDS, you are given the matrix of distances between the objects, and you are trying to figure... | What's the difference between principal component analysis and multidimensional scaling? | Uhm... quite different. In PCA, you are given the multivariate continuous data (a multivariate vector for each subject), and you are trying to figure out if you don't need that many dimensions to conc | What's the difference between principal component analysis and multidimensional scaling?
Uhm... quite different. In PCA, you are given the multivariate continuous data (a multivariate vector for each subject), and you are trying to figure out if you don't need that many dimensions to conceptualize them. In (metric) MDS... | What's the difference between principal component analysis and multidimensional scaling?
Uhm... quite different. In PCA, you are given the multivariate continuous data (a multivariate vector for each subject), and you are trying to figure out if you don't need that many dimensions to conc |
966 | What's the difference between principal component analysis and multidimensional scaling? | PCA yields the EXACT same results as classical MDS if Euclidean distance is used.
I'm quoting Cox & Cox (2001), p 43-44:
There is a duality between a principals components analysis and PCO [principal coordinates analysis, aka classical MDS] where dissimilarities are given by Euclidean distance.
The section in Cox & C... | What's the difference between principal component analysis and multidimensional scaling? | PCA yields the EXACT same results as classical MDS if Euclidean distance is used.
I'm quoting Cox & Cox (2001), p 43-44:
There is a duality between a principals components analysis and PCO [principal | What's the difference between principal component analysis and multidimensional scaling?
PCA yields the EXACT same results as classical MDS if Euclidean distance is used.
I'm quoting Cox & Cox (2001), p 43-44:
There is a duality between a principals components analysis and PCO [principal coordinates analysis, aka clas... | What's the difference between principal component analysis and multidimensional scaling?
PCA yields the EXACT same results as classical MDS if Euclidean distance is used.
I'm quoting Cox & Cox (2001), p 43-44:
There is a duality between a principals components analysis and PCO [principal |
967 | What's the difference between principal component analysis and multidimensional scaling? | Comparison: "Metric MDS gives the SAME result as PCA"- procedurally- when we look at the way SVD is used to obtain the optimum. But, the preserved high-dimensional criteria is different. PCA uses a centered covariance matrix while MDS uses a gram matrix obtained by double-centering distance matrices.
Will put the diffe... | What's the difference between principal component analysis and multidimensional scaling? | Comparison: "Metric MDS gives the SAME result as PCA"- procedurally- when we look at the way SVD is used to obtain the optimum. But, the preserved high-dimensional criteria is different. PCA uses a ce | What's the difference between principal component analysis and multidimensional scaling?
Comparison: "Metric MDS gives the SAME result as PCA"- procedurally- when we look at the way SVD is used to obtain the optimum. But, the preserved high-dimensional criteria is different. PCA uses a centered covariance matrix while ... | What's the difference between principal component analysis and multidimensional scaling?
Comparison: "Metric MDS gives the SAME result as PCA"- procedurally- when we look at the way SVD is used to obtain the optimum. But, the preserved high-dimensional criteria is different. PCA uses a ce |
968 | Why are p-values uniformly distributed under the null hypothesis? | To clarify a bit. The p-value is uniformly distributed when the null hypothesis is true and all other assumptions are met. The reason for this is really the definition of alpha as the probability of a type I error. We want the probability of rejecting a true null hypothesis to be alpha, we reject when the observed $... | Why are p-values uniformly distributed under the null hypothesis? | To clarify a bit. The p-value is uniformly distributed when the null hypothesis is true and all other assumptions are met. The reason for this is really the definition of alpha as the probability of | Why are p-values uniformly distributed under the null hypothesis?
To clarify a bit. The p-value is uniformly distributed when the null hypothesis is true and all other assumptions are met. The reason for this is really the definition of alpha as the probability of a type I error. We want the probability of rejecting... | Why are p-values uniformly distributed under the null hypothesis?
To clarify a bit. The p-value is uniformly distributed when the null hypothesis is true and all other assumptions are met. The reason for this is really the definition of alpha as the probability of |
969 | Why are p-values uniformly distributed under the null hypothesis? | Under the null hypothesis, your test statistic $T$ has the distribution $F(t)$ (e.g., standard normal). We show that the p-value $P=F(T)$ has a probability distribution
$$\begin{equation*} \Pr(P < p) = \Pr(F^{-1}(P) < F^{-1}(p)) = \Pr(T < t) \equiv p; \end{equation*}$$
in other words, $P$ is distributed uniformly. This... | Why are p-values uniformly distributed under the null hypothesis? | Under the null hypothesis, your test statistic $T$ has the distribution $F(t)$ (e.g., standard normal). We show that the p-value $P=F(T)$ has a probability distribution
$$\begin{equation*} \Pr(P < p) | Why are p-values uniformly distributed under the null hypothesis?
Under the null hypothesis, your test statistic $T$ has the distribution $F(t)$ (e.g., standard normal). We show that the p-value $P=F(T)$ has a probability distribution
$$\begin{equation*} \Pr(P < p) = \Pr(F^{-1}(P) < F^{-1}(p)) = \Pr(T < t) \equiv p; \e... | Why are p-values uniformly distributed under the null hypothesis?
Under the null hypothesis, your test statistic $T$ has the distribution $F(t)$ (e.g., standard normal). We show that the p-value $P=F(T)$ has a probability distribution
$$\begin{equation*} \Pr(P < p) |
970 | Why are p-values uniformly distributed under the null hypothesis? | Let $T$ denote the random variable with cumulative distribution function $F(t) \equiv \Pr(T<t)$ for all $t$. Assuming that $F$ is invertible we can derive distribution of the random p-value $P = F(T)$ as follows:
$$
\Pr(P<p) = \Pr(F(T) < p) = \Pr(T < F^{-1}(p)) = F(F^{-1}(p)) = p,
$$
from which we can conclude that the... | Why are p-values uniformly distributed under the null hypothesis? | Let $T$ denote the random variable with cumulative distribution function $F(t) \equiv \Pr(T<t)$ for all $t$. Assuming that $F$ is invertible we can derive distribution of the random p-value $P = F(T)$ | Why are p-values uniformly distributed under the null hypothesis?
Let $T$ denote the random variable with cumulative distribution function $F(t) \equiv \Pr(T<t)$ for all $t$. Assuming that $F$ is invertible we can derive distribution of the random p-value $P = F(T)$ as follows:
$$
\Pr(P<p) = \Pr(F(T) < p) = \Pr(T < F^{... | Why are p-values uniformly distributed under the null hypothesis?
Let $T$ denote the random variable with cumulative distribution function $F(t) \equiv \Pr(T<t)$ for all $t$. Assuming that $F$ is invertible we can derive distribution of the random p-value $P = F(T)$ |
971 | Why are p-values uniformly distributed under the null hypothesis? | I think the answer as to "Why are p-values uniformly distributed under the null hypothesis?" has been sufficiently discussed from a mathematical perspective. What I thought is missing is a visual explanation of this and the idea of thinking of p-values as areas to the left of a set of quantiles under a given continuous... | Why are p-values uniformly distributed under the null hypothesis? | I think the answer as to "Why are p-values uniformly distributed under the null hypothesis?" has been sufficiently discussed from a mathematical perspective. What I thought is missing is a visual expl | Why are p-values uniformly distributed under the null hypothesis?
I think the answer as to "Why are p-values uniformly distributed under the null hypothesis?" has been sufficiently discussed from a mathematical perspective. What I thought is missing is a visual explanation of this and the idea of thinking of p-values a... | Why are p-values uniformly distributed under the null hypothesis?
I think the answer as to "Why are p-values uniformly distributed under the null hypothesis?" has been sufficiently discussed from a mathematical perspective. What I thought is missing is a visual expl |
972 | Why are p-values uniformly distributed under the null hypothesis? | Simple simulation of distribution of p-values in case of linear regression between two independent variables :
# estimated model is: y = a0 + a1*x + e
obs<-100 # obs in each single regression
Nloops<-1000 # number of experiments
output<-numeric(Nloops) # vector holding p-values of estimated a... | Why are p-values uniformly distributed under the null hypothesis? | Simple simulation of distribution of p-values in case of linear regression between two independent variables :
# estimated model is: y = a0 + a1*x + e
obs<-100 # obs in each single reg | Why are p-values uniformly distributed under the null hypothesis?
Simple simulation of distribution of p-values in case of linear regression between two independent variables :
# estimated model is: y = a0 + a1*x + e
obs<-100 # obs in each single regression
Nloops<-1000 # number of experiment... | Why are p-values uniformly distributed under the null hypothesis?
Simple simulation of distribution of p-values in case of linear regression between two independent variables :
# estimated model is: y = a0 + a1*x + e
obs<-100 # obs in each single reg |
973 | Percentile vs quantile vs quartile | 0 quartile = 0 quantile = 0 percentile
1 quartile = 0.25 quantile = 25 percentile
2 quartile = .5 quantile = 50 percentile (median)
3 quartile = .75 quantile = 75 percentile
4 quartile = 1 quantile = 100 percentile | Percentile vs quantile vs quartile | 0 quartile = 0 quantile = 0 percentile
1 quartile = 0.25 quantile = 25 percentile
2 quartile = .5 quantile = 50 percentile (median)
3 quartile = .75 quantile = 75 percentile
4 quartile = 1 quantile = | Percentile vs quantile vs quartile
0 quartile = 0 quantile = 0 percentile
1 quartile = 0.25 quantile = 25 percentile
2 quartile = .5 quantile = 50 percentile (median)
3 quartile = .75 quantile = 75 percentile
4 quartile = 1 quantile = 100 percentile | Percentile vs quantile vs quartile
0 quartile = 0 quantile = 0 percentile
1 quartile = 0.25 quantile = 25 percentile
2 quartile = .5 quantile = 50 percentile (median)
3 quartile = .75 quantile = 75 percentile
4 quartile = 1 quantile = |
974 | Percentile vs quantile vs quartile | Percentiles go from $0$ to $100$.
Quartiles go from $1$ to $4$ (or $0$ to $4$).
Quantiles can go from anything to anything.
Percentiles and quartiles are examples of quantiles. | Percentile vs quantile vs quartile | Percentiles go from $0$ to $100$.
Quartiles go from $1$ to $4$ (or $0$ to $4$).
Quantiles can go from anything to anything.
Percentiles and quartiles are examples of quantiles. | Percentile vs quantile vs quartile
Percentiles go from $0$ to $100$.
Quartiles go from $1$ to $4$ (or $0$ to $4$).
Quantiles can go from anything to anything.
Percentiles and quartiles are examples of quantiles. | Percentile vs quantile vs quartile
Percentiles go from $0$ to $100$.
Quartiles go from $1$ to $4$ (or $0$ to $4$).
Quantiles can go from anything to anything.
Percentiles and quartiles are examples of quantiles. |
975 | Percentile vs quantile vs quartile | In order to define these terms rigorously,
it is helpful to first define the quantile function
which is also known as the inverse cumulative distribution function.
Recall that for a random variable $X$,
the cumulative distribution function $F_X$ is defined by the equation
$$
F_X(x) := \Pr(X \le x).
$$
The quantile func... | Percentile vs quantile vs quartile | In order to define these terms rigorously,
it is helpful to first define the quantile function
which is also known as the inverse cumulative distribution function.
Recall that for a random variable $X | Percentile vs quantile vs quartile
In order to define these terms rigorously,
it is helpful to first define the quantile function
which is also known as the inverse cumulative distribution function.
Recall that for a random variable $X$,
the cumulative distribution function $F_X$ is defined by the equation
$$
F_X(x) :=... | Percentile vs quantile vs quartile
In order to define these terms rigorously,
it is helpful to first define the quantile function
which is also known as the inverse cumulative distribution function.
Recall that for a random variable $X |
976 | Percentile vs quantile vs quartile | From wiki page: https://en.wikipedia.org/wiki/Quantile
Some q-quantiles have special names:
The only 2-quantile is called the median
The 3-quantiles are called tertiles or terciles → T
The 4-quantiles are called quartiles → Q
The 5-quantiles are called quintiles → QU
The 6-quantiles are called sextiles → S
The 8-quant... | Percentile vs quantile vs quartile | From wiki page: https://en.wikipedia.org/wiki/Quantile
Some q-quantiles have special names:
The only 2-quantile is called the median
The 3-quantiles are called tertiles or terciles → T
The 4-quantile | Percentile vs quantile vs quartile
From wiki page: https://en.wikipedia.org/wiki/Quantile
Some q-quantiles have special names:
The only 2-quantile is called the median
The 3-quantiles are called tertiles or terciles → T
The 4-quantiles are called quartiles → Q
The 5-quantiles are called quintiles → QU
The 6-quantiles ... | Percentile vs quantile vs quartile
From wiki page: https://en.wikipedia.org/wiki/Quantile
Some q-quantiles have special names:
The only 2-quantile is called the median
The 3-quantiles are called tertiles or terciles → T
The 4-quantile |
977 | How to choose between Pearson and Spearman correlation? | If you want to explore your data it is best to compute both, since the relation between the Spearman (S) and Pearson (P) correlations will give some information. Briefly, S is computed on ranks and so depicts monotonic relationships while P is on true values and depicts linear relationships.
As an example, if you set: ... | How to choose between Pearson and Spearman correlation? | If you want to explore your data it is best to compute both, since the relation between the Spearman (S) and Pearson (P) correlations will give some information. Briefly, S is computed on ranks and so | How to choose between Pearson and Spearman correlation?
If you want to explore your data it is best to compute both, since the relation between the Spearman (S) and Pearson (P) correlations will give some information. Briefly, S is computed on ranks and so depicts monotonic relationships while P is on true values and d... | How to choose between Pearson and Spearman correlation?
If you want to explore your data it is best to compute both, since the relation between the Spearman (S) and Pearson (P) correlations will give some information. Briefly, S is computed on ranks and so |
978 | How to choose between Pearson and Spearman correlation? | Shortest and mostly correct answer is:
Pearson benchmarks linear relationship, Spearman benchmarks monotonic relationship (few infinities more general case, but for some power tradeoff).
So if you assume/think that the relation is linear (or, as a special case, that those are a two measures of the same thing, so the re... | How to choose between Pearson and Spearman correlation? | Shortest and mostly correct answer is:
Pearson benchmarks linear relationship, Spearman benchmarks monotonic relationship (few infinities more general case, but for some power tradeoff).
So if you ass | How to choose between Pearson and Spearman correlation?
Shortest and mostly correct answer is:
Pearson benchmarks linear relationship, Spearman benchmarks monotonic relationship (few infinities more general case, but for some power tradeoff).
So if you assume/think that the relation is linear (or, as a special case, th... | How to choose between Pearson and Spearman correlation?
Shortest and mostly correct answer is:
Pearson benchmarks linear relationship, Spearman benchmarks monotonic relationship (few infinities more general case, but for some power tradeoff).
So if you ass |
979 | How to choose between Pearson and Spearman correlation? | This happens often in statistics: there are a variety of methods which could be applied in your situation, and you don't know which one to choose. You should base your decision the pros and cons of the methods under consideration and the specifics of your problem, but even then the decision is usually subjective with ... | How to choose between Pearson and Spearman correlation? | This happens often in statistics: there are a variety of methods which could be applied in your situation, and you don't know which one to choose. You should base your decision the pros and cons of t | How to choose between Pearson and Spearman correlation?
This happens often in statistics: there are a variety of methods which could be applied in your situation, and you don't know which one to choose. You should base your decision the pros and cons of the methods under consideration and the specifics of your problem... | How to choose between Pearson and Spearman correlation?
This happens often in statistics: there are a variety of methods which could be applied in your situation, and you don't know which one to choose. You should base your decision the pros and cons of t |
980 | How to choose between Pearson and Spearman correlation? | I ran into an interesting corner case today.
If we are looking at very small numbers of samples, the difference between Spearman and Pearson can be dramatic.
In case below, the two methods report an exactly opposite correlation.
Some quick rules of thumb to decide on Spearman vs. Pearson:
The assumptions of Pearson's... | How to choose between Pearson and Spearman correlation? | I ran into an interesting corner case today.
If we are looking at very small numbers of samples, the difference between Spearman and Pearson can be dramatic.
In case below, the two methods report an e | How to choose between Pearson and Spearman correlation?
I ran into an interesting corner case today.
If we are looking at very small numbers of samples, the difference between Spearman and Pearson can be dramatic.
In case below, the two methods report an exactly opposite correlation.
Some quick rules of thumb to decid... | How to choose between Pearson and Spearman correlation?
I ran into an interesting corner case today.
If we are looking at very small numbers of samples, the difference between Spearman and Pearson can be dramatic.
In case below, the two methods report an e |
981 | How to choose between Pearson and Spearman correlation? | While agreeing with Charles' answer, I would suggest (on a strictly practical level) that you compute both of the coefficients and look at the differences. In many cases, they will be exactly the same, so you don't need to worry.
If however, they are different then you need to look at whether or not you met the assumpt... | How to choose between Pearson and Spearman correlation? | While agreeing with Charles' answer, I would suggest (on a strictly practical level) that you compute both of the coefficients and look at the differences. In many cases, they will be exactly the same | How to choose between Pearson and Spearman correlation?
While agreeing with Charles' answer, I would suggest (on a strictly practical level) that you compute both of the coefficients and look at the differences. In many cases, they will be exactly the same, so you don't need to worry.
If however, they are different the... | How to choose between Pearson and Spearman correlation?
While agreeing with Charles' answer, I would suggest (on a strictly practical level) that you compute both of the coefficients and look at the differences. In many cases, they will be exactly the same |
982 | R vs SAS, why is SAS preferred by private companies? | I think there are several issues (in ascending order of possible validity):
Tradition / habit: people are used to SAS, and don't want to have to learn something new. (Making it more difficult, the way you think in SAS and R is different.) This can apply to anyone who might have to send you code, or read / use your... | R vs SAS, why is SAS preferred by private companies? | I think there are several issues (in ascending order of possible validity):
Tradition / habit: people are used to SAS, and don't want to have to learn something new. (Making it more difficult, the | R vs SAS, why is SAS preferred by private companies?
I think there are several issues (in ascending order of possible validity):
Tradition / habit: people are used to SAS, and don't want to have to learn something new. (Making it more difficult, the way you think in SAS and R is different.) This can apply to anyon... | R vs SAS, why is SAS preferred by private companies?
I think there are several issues (in ascending order of possible validity):
Tradition / habit: people are used to SAS, and don't want to have to learn something new. (Making it more difficult, the |
983 | R vs SAS, why is SAS preferred by private companies? | In addition to the good answers so far, I'd add the embarrassment factor. If you spend hundreds of thousands of dollars last year on SAS and SAS support, and you propose spending nothing for R, with extremely low support prices (Revolution, etc), someone up the chain's going to ask why. Was it a mistake to spend so muc... | R vs SAS, why is SAS preferred by private companies? | In addition to the good answers so far, I'd add the embarrassment factor. If you spend hundreds of thousands of dollars last year on SAS and SAS support, and you propose spending nothing for R, with e | R vs SAS, why is SAS preferred by private companies?
In addition to the good answers so far, I'd add the embarrassment factor. If you spend hundreds of thousands of dollars last year on SAS and SAS support, and you propose spending nothing for R, with extremely low support prices (Revolution, etc), someone up the chain... | R vs SAS, why is SAS preferred by private companies?
In addition to the good answers so far, I'd add the embarrassment factor. If you spend hundreds of thousands of dollars last year on SAS and SAS support, and you propose spending nothing for R, with e |
984 | R vs SAS, why is SAS preferred by private companies? | On top of what gung has correctly identified here, the biggest issue in the corporate world is legacy. And when you have a good quality production code that is known to do the job, you don't change it. SAS was out there since 1970s, and at the time it was the only effective, by then-standards, scripting statistical lan... | R vs SAS, why is SAS preferred by private companies? | On top of what gung has correctly identified here, the biggest issue in the corporate world is legacy. And when you have a good quality production code that is known to do the job, you don't change it | R vs SAS, why is SAS preferred by private companies?
On top of what gung has correctly identified here, the biggest issue in the corporate world is legacy. And when you have a good quality production code that is known to do the job, you don't change it. SAS was out there since 1970s, and at the time it was the only ef... | R vs SAS, why is SAS preferred by private companies?
On top of what gung has correctly identified here, the biggest issue in the corporate world is legacy. And when you have a good quality production code that is known to do the job, you don't change it |
985 | R vs SAS, why is SAS preferred by private companies? | I have worked as effectively a SAS programmer for the last seven years, next to me a co-worker has been programming SAS longer than I have been alive. As noted here, there is a massive amount of inertia/legacy behind SAS; but SAS just like R is a way to a means, not the means itself.
SAS is extremely efficient at se... | R vs SAS, why is SAS preferred by private companies? | I have worked as effectively a SAS programmer for the last seven years, next to me a co-worker has been programming SAS longer than I have been alive. As noted here, there is a massive amount of iner | R vs SAS, why is SAS preferred by private companies?
I have worked as effectively a SAS programmer for the last seven years, next to me a co-worker has been programming SAS longer than I have been alive. As noted here, there is a massive amount of inertia/legacy behind SAS; but SAS just like R is a way to a means, not... | R vs SAS, why is SAS preferred by private companies?
I have worked as effectively a SAS programmer for the last seven years, next to me a co-worker has been programming SAS longer than I have been alive. As noted here, there is a massive amount of iner |
986 | R vs SAS, why is SAS preferred by private companies? | So I use both R and SAS - admittedly in academia - but there are a couple reasons that I tend to head toward SAS at times:
Better documentation. R is getting better at this, but documentation, especially the official documentation, is often kind of terrible and opaque. Beyond that, SAS is supported by a massive infras... | R vs SAS, why is SAS preferred by private companies? | So I use both R and SAS - admittedly in academia - but there are a couple reasons that I tend to head toward SAS at times:
Better documentation. R is getting better at this, but documentation, especi | R vs SAS, why is SAS preferred by private companies?
So I use both R and SAS - admittedly in academia - but there are a couple reasons that I tend to head toward SAS at times:
Better documentation. R is getting better at this, but documentation, especially the official documentation, is often kind of terrible and opaq... | R vs SAS, why is SAS preferred by private companies?
So I use both R and SAS - admittedly in academia - but there are a couple reasons that I tend to head toward SAS at times:
Better documentation. R is getting better at this, but documentation, especi |
987 | R vs SAS, why is SAS preferred by private companies? | Nobody has suggested the reason it is preferred is plain idiocy. Here's two quotes I recently came across:
"Using open-source software such as R was out of the question – we
couldn't guarantee a perfectly repeatable outcome"
and
"We would be unable to provide any support for this as it is open
source software"
... | R vs SAS, why is SAS preferred by private companies? | Nobody has suggested the reason it is preferred is plain idiocy. Here's two quotes I recently came across:
"Using open-source software such as R was out of the question – we
couldn't guarantee a pe | R vs SAS, why is SAS preferred by private companies?
Nobody has suggested the reason it is preferred is plain idiocy. Here's two quotes I recently came across:
"Using open-source software such as R was out of the question – we
couldn't guarantee a perfectly repeatable outcome"
and
"We would be unable to provide an... | R vs SAS, why is SAS preferred by private companies?
Nobody has suggested the reason it is preferred is plain idiocy. Here's two quotes I recently came across:
"Using open-source software such as R was out of the question – we
couldn't guarantee a pe |
988 | R vs SAS, why is SAS preferred by private companies? | One issue does not seem to have been addressed explicitly: ass-covering. If you go with SAS and things blow up, the decision maker can always say that he bought state-of-the-art software, and how was he to know it would break? If he decided to go with R, this argument will be harder to make. Yes, this is related to the... | R vs SAS, why is SAS preferred by private companies? | One issue does not seem to have been addressed explicitly: ass-covering. If you go with SAS and things blow up, the decision maker can always say that he bought state-of-the-art software, and how was | R vs SAS, why is SAS preferred by private companies?
One issue does not seem to have been addressed explicitly: ass-covering. If you go with SAS and things blow up, the decision maker can always say that he bought state-of-the-art software, and how was he to know it would break? If he decided to go with R, this argumen... | R vs SAS, why is SAS preferred by private companies?
One issue does not seem to have been addressed explicitly: ass-covering. If you go with SAS and things blow up, the decision maker can always say that he bought state-of-the-art software, and how was |
989 | R vs SAS, why is SAS preferred by private companies? | The times they are a changing
As of 2015, actuaries under the age of about 35 prefer using R - the text books use both R and SAS code. Older actuaries never learnt to use R and prefer SAS and do not use R. The proportion of actuaries actually coding in SAS will decline.
If you search Google scholar for papers referri... | R vs SAS, why is SAS preferred by private companies? | The times they are a changing
As of 2015, actuaries under the age of about 35 prefer using R - the text books use both R and SAS code. Older actuaries never learnt to use R and prefer SAS and do not | R vs SAS, why is SAS preferred by private companies?
The times they are a changing
As of 2015, actuaries under the age of about 35 prefer using R - the text books use both R and SAS code. Older actuaries never learnt to use R and prefer SAS and do not use R. The proportion of actuaries actually coding in SAS will dec... | R vs SAS, why is SAS preferred by private companies?
The times they are a changing
As of 2015, actuaries under the age of about 35 prefer using R - the text books use both R and SAS code. Older actuaries never learnt to use R and prefer SAS and do not |
990 | R vs SAS, why is SAS preferred by private companies? | As a user of both SAS and R, I would say the biggest reason we use SAS over R (when we do) is its ability for sequential processing. We only need machines with no more than 4GB RAM to process 15 years worth of data. I would need a much larger machine using stock R and I have not tried to migrate the SAS code to run w... | R vs SAS, why is SAS preferred by private companies? | As a user of both SAS and R, I would say the biggest reason we use SAS over R (when we do) is its ability for sequential processing. We only need machines with no more than 4GB RAM to process 15 year | R vs SAS, why is SAS preferred by private companies?
As a user of both SAS and R, I would say the biggest reason we use SAS over R (when we do) is its ability for sequential processing. We only need machines with no more than 4GB RAM to process 15 years worth of data. I would need a much larger machine using stock R ... | R vs SAS, why is SAS preferred by private companies?
As a user of both SAS and R, I would say the biggest reason we use SAS over R (when we do) is its ability for sequential processing. We only need machines with no more than 4GB RAM to process 15 year |
991 | R vs SAS, why is SAS preferred by private companies? | In the pharmaceutical industry SAS is used because it is what the FDA uses and likes. There are some serious reasons though. Results are traceable and the output has a time stamp. FDA statisticians can check what you get. It is very good for database management and it is reliable software. Of course many of the att... | R vs SAS, why is SAS preferred by private companies? | In the pharmaceutical industry SAS is used because it is what the FDA uses and likes. There are some serious reasons though. Results are traceable and the output has a time stamp. FDA statisticians | R vs SAS, why is SAS preferred by private companies?
In the pharmaceutical industry SAS is used because it is what the FDA uses and likes. There are some serious reasons though. Results are traceable and the output has a time stamp. FDA statisticians can check what you get. It is very good for database management an... | R vs SAS, why is SAS preferred by private companies?
In the pharmaceutical industry SAS is used because it is what the FDA uses and likes. There are some serious reasons though. Results are traceable and the output has a time stamp. FDA statisticians |
992 | R vs SAS, why is SAS preferred by private companies? | I think this quote from Anne H. Milley sums up the way a lot of people feel about R:
We have customers who build engines for aircraft. I am happy they are
not using freeware when I get on a jet.
Unfortunately, I think this misconception (free==inferior) is common in the general public. | R vs SAS, why is SAS preferred by private companies? | I think this quote from Anne H. Milley sums up the way a lot of people feel about R:
We have customers who build engines for aircraft. I am happy they are
not using freeware when I get on a jet.
U | R vs SAS, why is SAS preferred by private companies?
I think this quote from Anne H. Milley sums up the way a lot of people feel about R:
We have customers who build engines for aircraft. I am happy they are
not using freeware when I get on a jet.
Unfortunately, I think this misconception (free==inferior) is common... | R vs SAS, why is SAS preferred by private companies?
I think this quote from Anne H. Milley sums up the way a lot of people feel about R:
We have customers who build engines for aircraft. I am happy they are
not using freeware when I get on a jet.
U |
993 | R vs SAS, why is SAS preferred by private companies? | (slightly off topic): viewing it the other point round: some of the advantages R has in academia don't apply to industry.
E.g. in academia it is a clear advantage if you can tell the students to go and get the software and work at home. In industry, you're usually not supposed to take any data home with you...
Neither... | R vs SAS, why is SAS preferred by private companies? | (slightly off topic): viewing it the other point round: some of the advantages R has in academia don't apply to industry.
E.g. in academia it is a clear advantage if you can tell the students to go a | R vs SAS, why is SAS preferred by private companies?
(slightly off topic): viewing it the other point round: some of the advantages R has in academia don't apply to industry.
E.g. in academia it is a clear advantage if you can tell the students to go and get the software and work at home. In industry, you're usually n... | R vs SAS, why is SAS preferred by private companies?
(slightly off topic): viewing it the other point round: some of the advantages R has in academia don't apply to industry.
E.g. in academia it is a clear advantage if you can tell the students to go a |
994 | R vs SAS, why is SAS preferred by private companies? | Whilst its quite pessimistic, my answer would be that the kind of people who make sweeping decisions in corporations like 'we just use SAS' are also the kind of people who don't trust what they don't understand, and automatically think the value of something is directly proportional to the amount of money you spend on ... | R vs SAS, why is SAS preferred by private companies? | Whilst its quite pessimistic, my answer would be that the kind of people who make sweeping decisions in corporations like 'we just use SAS' are also the kind of people who don't trust what they don't | R vs SAS, why is SAS preferred by private companies?
Whilst its quite pessimistic, my answer would be that the kind of people who make sweeping decisions in corporations like 'we just use SAS' are also the kind of people who don't trust what they don't understand, and automatically think the value of something is direc... | R vs SAS, why is SAS preferred by private companies?
Whilst its quite pessimistic, my answer would be that the kind of people who make sweeping decisions in corporations like 'we just use SAS' are also the kind of people who don't trust what they don't |
995 | R vs SAS, why is SAS preferred by private companies? | Why would a major drug company even want to convert to R from SAS? SAS costs millions but it is nothing to a drug company. However, converting all the stable reporting systems from SAS to R would cost 50-100 times more.
SAS has phenomenal support system: every time I needed help they were able to provide it within few... | R vs SAS, why is SAS preferred by private companies? | Why would a major drug company even want to convert to R from SAS? SAS costs millions but it is nothing to a drug company. However, converting all the stable reporting systems from SAS to R would cost | R vs SAS, why is SAS preferred by private companies?
Why would a major drug company even want to convert to R from SAS? SAS costs millions but it is nothing to a drug company. However, converting all the stable reporting systems from SAS to R would cost 50-100 times more.
SAS has phenomenal support system: every time ... | R vs SAS, why is SAS preferred by private companies?
Why would a major drug company even want to convert to R from SAS? SAS costs millions but it is nothing to a drug company. However, converting all the stable reporting systems from SAS to R would cost |
996 | R vs SAS, why is SAS preferred by private companies? | There are several main advantages, in no particular order
SAS has a large installed base and a long track record
I'm purposefully avoiding use of pejorative terms like "legacy" or "habit" Many companies have been using SAS for 30 or 40 years, and they have millions of lines of working code. In addition, there are al... | R vs SAS, why is SAS preferred by private companies? | There are several main advantages, in no particular order
SAS has a large installed base and a long track record
I'm purposefully avoiding use of pejorative terms like "legacy" or "habit" Many comp | R vs SAS, why is SAS preferred by private companies?
There are several main advantages, in no particular order
SAS has a large installed base and a long track record
I'm purposefully avoiding use of pejorative terms like "legacy" or "habit" Many companies have been using SAS for 30 or 40 years, and they have million... | R vs SAS, why is SAS preferred by private companies?
There are several main advantages, in no particular order
SAS has a large installed base and a long track record
I'm purposefully avoiding use of pejorative terms like "legacy" or "habit" Many comp |
997 | R vs SAS, why is SAS preferred by private companies? | Customer support.
I once had a chat with a friend working in a company specializing in installing servers, and he then explained to me why big companies always opt for Microsoft products rather than go open source. The advantage Microsoft has over its open source competitors is the customer support. If something goes w... | R vs SAS, why is SAS preferred by private companies? | Customer support.
I once had a chat with a friend working in a company specializing in installing servers, and he then explained to me why big companies always opt for Microsoft products rather than g | R vs SAS, why is SAS preferred by private companies?
Customer support.
I once had a chat with a friend working in a company specializing in installing servers, and he then explained to me why big companies always opt for Microsoft products rather than go open source. The advantage Microsoft has over its open source com... | R vs SAS, why is SAS preferred by private companies?
Customer support.
I once had a chat with a friend working in a company specializing in installing servers, and he then explained to me why big companies always opt for Microsoft products rather than g |
998 | R vs SAS, why is SAS preferred by private companies? | I once worked for a consulting company that gave SAS assistance to a large chip manufacturer in the Silicon Valley. Our contact person at the company told us that he got an offer by another company to give them the exact same consulting, by using a different software which covers all areas covered by SAS and which wou... | R vs SAS, why is SAS preferred by private companies? | I once worked for a consulting company that gave SAS assistance to a large chip manufacturer in the Silicon Valley. Our contact person at the company told us that he got an offer by another company t | R vs SAS, why is SAS preferred by private companies?
I once worked for a consulting company that gave SAS assistance to a large chip manufacturer in the Silicon Valley. Our contact person at the company told us that he got an offer by another company to give them the exact same consulting, by using a different softwar... | R vs SAS, why is SAS preferred by private companies?
I once worked for a consulting company that gave SAS assistance to a large chip manufacturer in the Silicon Valley. Our contact person at the company told us that he got an offer by another company t |
999 | R vs SAS, why is SAS preferred by private companies? | What about Frontends? What is R's equivalent for the SAS Enterprise Guide, Web Report Studio or Enterprise Miner?
Edit:
These tools make it possible for a non-programming User to use a DATA WAREHOUSE, without knowledge about the underlying technology. They are not primarily tools for the use of SAS as such.
R GUI's are... | R vs SAS, why is SAS preferred by private companies? | What about Frontends? What is R's equivalent for the SAS Enterprise Guide, Web Report Studio or Enterprise Miner?
Edit:
These tools make it possible for a non-programming User to use a DATA WAREHOUSE, | R vs SAS, why is SAS preferred by private companies?
What about Frontends? What is R's equivalent for the SAS Enterprise Guide, Web Report Studio or Enterprise Miner?
Edit:
These tools make it possible for a non-programming User to use a DATA WAREHOUSE, without knowledge about the underlying technology. They are not pr... | R vs SAS, why is SAS preferred by private companies?
What about Frontends? What is R's equivalent for the SAS Enterprise Guide, Web Report Studio or Enterprise Miner?
Edit:
These tools make it possible for a non-programming User to use a DATA WAREHOUSE, |
1,000 | R vs SAS, why is SAS preferred by private companies? | I don't think application security has been mentioned. This question was raised in Stack Overflow but dropped since it was off topic.
I collaborate with the the Swedish National Board of Health and Welfare that use SAS. When I talked to their statisticians (that like R) they claim that their IT-folks prefer SAS since t... | R vs SAS, why is SAS preferred by private companies? | I don't think application security has been mentioned. This question was raised in Stack Overflow but dropped since it was off topic.
I collaborate with the the Swedish National Board of Health and We | R vs SAS, why is SAS preferred by private companies?
I don't think application security has been mentioned. This question was raised in Stack Overflow but dropped since it was off topic.
I collaborate with the the Swedish National Board of Health and Welfare that use SAS. When I talked to their statisticians (that like... | R vs SAS, why is SAS preferred by private companies?
I don't think application security has been mentioned. This question was raised in Stack Overflow but dropped since it was off topic.
I collaborate with the the Swedish National Board of Health and We |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.