idx int64 1 56k | question stringlengths 15 155 | answer stringlengths 2 29.2k ⌀ | question_cut stringlengths 15 100 | answer_cut stringlengths 2 200 ⌀ | conversation stringlengths 47 29.3k | conversation_cut stringlengths 47 301 |
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5,601 | How to plot trends properly | One more version: ratios (mean death rate from 1927 to current year)/(death rate 1927)
Done with Mathematica code
data = {
{year, de, fr, be, nl, den, ch, aut, cz, pl},
{1927, 10.9, 16.5, 13.0, 10.2, 11.6, 12.4, 15.0, 16.0, 17.3},
{1928, 11.2, 16.4, 12.8, 9.6, 11.0, 12.0, 14.5, 15.1, 16.4},
{1929... | How to plot trends properly | One more version: ratios (mean death rate from 1927 to current year)/(death rate 1927)
Done with Mathematica code
data = {
{year, de, fr, be, nl, den, ch, aut, cz, pl},
{1927, 10.9 | How to plot trends properly
One more version: ratios (mean death rate from 1927 to current year)/(death rate 1927)
Done with Mathematica code
data = {
{year, de, fr, be, nl, den, ch, aut, cz, pl},
{1927, 10.9, 16.5, 13.0, 10.2, 11.6, 12.4, 15.0, 16.0, 17.3},
{1928, 11.2, 16.4, 12.8, 9.6, 11.0, 12.... | How to plot trends properly
One more version: ratios (mean death rate from 1927 to current year)/(death rate 1927)
Done with Mathematica code
data = {
{year, de, fr, be, nl, den, ch, aut, cz, pl},
{1927, 10.9 |
5,602 | What exactly is the alpha in the Dirichlet distribution? | The Dirichlet distribution is a multivariate probability distribution that describes $k\ge2$ variables $X_1,\dots,X_k$, such that each $x_i \in (0,1)$ and $\sum_{i=1}^N x_i = 1$, that is parametrized by a vector of positive-valued parameters $\boldsymbol{\alpha} = (\alpha_1,\dots,\alpha_k)$. The parameters do not have ... | What exactly is the alpha in the Dirichlet distribution? | The Dirichlet distribution is a multivariate probability distribution that describes $k\ge2$ variables $X_1,\dots,X_k$, such that each $x_i \in (0,1)$ and $\sum_{i=1}^N x_i = 1$, that is parametrized | What exactly is the alpha in the Dirichlet distribution?
The Dirichlet distribution is a multivariate probability distribution that describes $k\ge2$ variables $X_1,\dots,X_k$, such that each $x_i \in (0,1)$ and $\sum_{i=1}^N x_i = 1$, that is parametrized by a vector of positive-valued parameters $\boldsymbol{\alpha} ... | What exactly is the alpha in the Dirichlet distribution?
The Dirichlet distribution is a multivariate probability distribution that describes $k\ge2$ variables $X_1,\dots,X_k$, such that each $x_i \in (0,1)$ and $\sum_{i=1}^N x_i = 1$, that is parametrized |
5,603 | What exactly is the alpha in the Dirichlet distribution? | Disclaimer: I have never worked with this distribution before. This answer is based on this wikipedia article and my interpretation of it.
The Dirichlet distribution is a multivariate probability distribution with similar properties to the Beta distribution.
The PDF is defined as follows:
$$\{x_1, \dots, x_K\} \sim\fr... | What exactly is the alpha in the Dirichlet distribution? | Disclaimer: I have never worked with this distribution before. This answer is based on this wikipedia article and my interpretation of it.
The Dirichlet distribution is a multivariate probability dis | What exactly is the alpha in the Dirichlet distribution?
Disclaimer: I have never worked with this distribution before. This answer is based on this wikipedia article and my interpretation of it.
The Dirichlet distribution is a multivariate probability distribution with similar properties to the Beta distribution.
The... | What exactly is the alpha in the Dirichlet distribution?
Disclaimer: I have never worked with this distribution before. This answer is based on this wikipedia article and my interpretation of it.
The Dirichlet distribution is a multivariate probability dis |
5,604 | When to use simulations? | A quantitative model emulates some behavior of the world by (a) representing objects by some of their numerical properties and (b) combining those numbers in a definite way to produce numerical outputs that also represent properties of interest.
In this schematic, three numerical inputs on the left are combined to pro... | When to use simulations? | A quantitative model emulates some behavior of the world by (a) representing objects by some of their numerical properties and (b) combining those numbers in a definite way to produce numerical output | When to use simulations?
A quantitative model emulates some behavior of the world by (a) representing objects by some of their numerical properties and (b) combining those numbers in a definite way to produce numerical outputs that also represent properties of interest.
In this schematic, three numerical inputs on the... | When to use simulations?
A quantitative model emulates some behavior of the world by (a) representing objects by some of their numerical properties and (b) combining those numbers in a definite way to produce numerical output |
5,605 | When to use simulations? | First, let me say that there is no single answer for your question. There is multiple examples of when you can (or have to) use simulation. I will try to give you few examples below. Second, notice that there are multiple ways you can define a "simulation", so the answer at least partly depends on the definition you ch... | When to use simulations? | First, let me say that there is no single answer for your question. There is multiple examples of when you can (or have to) use simulation. I will try to give you few examples below. Second, notice th | When to use simulations?
First, let me say that there is no single answer for your question. There is multiple examples of when you can (or have to) use simulation. I will try to give you few examples below. Second, notice that there are multiple ways you can define a "simulation", so the answer at least partly depends... | When to use simulations?
First, let me say that there is no single answer for your question. There is multiple examples of when you can (or have to) use simulation. I will try to give you few examples below. Second, notice th |
5,606 | When to use simulations? | I think that the discussion of TrynnaDoStat's answer illustrates the point well: we use simulations whenever the problem is impossible to solve analytically (e.g. the posterior distributions of parameters in a hierarchical model), or when we're simply too annoyed to put the time into working out the solution analytical... | When to use simulations? | I think that the discussion of TrynnaDoStat's answer illustrates the point well: we use simulations whenever the problem is impossible to solve analytically (e.g. the posterior distributions of parame | When to use simulations?
I think that the discussion of TrynnaDoStat's answer illustrates the point well: we use simulations whenever the problem is impossible to solve analytically (e.g. the posterior distributions of parameters in a hierarchical model), or when we're simply too annoyed to put the time into working ou... | When to use simulations?
I think that the discussion of TrynnaDoStat's answer illustrates the point well: we use simulations whenever the problem is impossible to solve analytically (e.g. the posterior distributions of parame |
5,607 | When to use simulations? | Simulations are often done when you can't get a closed form for something (such as a distribution) or you want a nitty-gritty and fast way to get that something.
For example, say I'm running a logistic regression using one variable $X$ to explain $Y$. I know that distribution of the coefficient $\beta$ for $X$ is asymp... | When to use simulations? | Simulations are often done when you can't get a closed form for something (such as a distribution) or you want a nitty-gritty and fast way to get that something.
For example, say I'm running a logisti | When to use simulations?
Simulations are often done when you can't get a closed form for something (such as a distribution) or you want a nitty-gritty and fast way to get that something.
For example, say I'm running a logistic regression using one variable $X$ to explain $Y$. I know that distribution of the coefficient... | When to use simulations?
Simulations are often done when you can't get a closed form for something (such as a distribution) or you want a nitty-gritty and fast way to get that something.
For example, say I'm running a logisti |
5,608 | When to use simulations? | Simulations are an excellent way to check whether you can obtain useful estimates from a model.
You would do this by generating/simulating fake data that follows the distribution implied by your model. Then go ahead and fit your model to that data. This is an ideal case: your model is, in fact, true. So if the fit is n... | When to use simulations? | Simulations are an excellent way to check whether you can obtain useful estimates from a model.
You would do this by generating/simulating fake data that follows the distribution implied by your model | When to use simulations?
Simulations are an excellent way to check whether you can obtain useful estimates from a model.
You would do this by generating/simulating fake data that follows the distribution implied by your model. Then go ahead and fit your model to that data. This is an ideal case: your model is, in fact,... | When to use simulations?
Simulations are an excellent way to check whether you can obtain useful estimates from a model.
You would do this by generating/simulating fake data that follows the distribution implied by your model |
5,609 | When to use simulations? | The simplest case for simulation. Let's say you have a forecasting model for the number of loan defaults, you also have a model for losses on defaulted loans. Now you need to forecast the total loss which the product of defaults and losses given the default. You can't simply multiply the defaults and losses on defaults... | When to use simulations? | The simplest case for simulation. Let's say you have a forecasting model for the number of loan defaults, you also have a model for losses on defaulted loans. Now you need to forecast the total loss w | When to use simulations?
The simplest case for simulation. Let's say you have a forecasting model for the number of loan defaults, you also have a model for losses on defaulted loans. Now you need to forecast the total loss which the product of defaults and losses given the default. You can't simply multiply the defaul... | When to use simulations?
The simplest case for simulation. Let's say you have a forecasting model for the number of loan defaults, you also have a model for losses on defaulted loans. Now you need to forecast the total loss w |
5,610 | Are there any good movies involving mathematics or probability? | Pi | Are there any good movies involving mathematics or probability? | Pi | Are there any good movies involving mathematics or probability?
Pi | Are there any good movies involving mathematics or probability?
Pi |
5,611 | Are there any good movies involving mathematics or probability? | 'A Beautiful Mind' naturally has a bit of game theory in it. | Are there any good movies involving mathematics or probability? | 'A Beautiful Mind' naturally has a bit of game theory in it. | Are there any good movies involving mathematics or probability?
'A Beautiful Mind' naturally has a bit of game theory in it. | Are there any good movies involving mathematics or probability?
'A Beautiful Mind' naturally has a bit of game theory in it. |
5,612 | Are there any good movies involving mathematics or probability? | MONEYBALL!
It's a movie where the statisticians win!
This is probably the most inspiring major motion picture about the power of quantitative methods. (if only because the plot is a little formulaic). And it shows quantitative methods (sabrmetrics) eventually coming to dominate over the backward and untested techniqu... | Are there any good movies involving mathematics or probability? | MONEYBALL!
It's a movie where the statisticians win!
This is probably the most inspiring major motion picture about the power of quantitative methods. (if only because the plot is a little formulaic | Are there any good movies involving mathematics or probability?
MONEYBALL!
It's a movie where the statisticians win!
This is probably the most inspiring major motion picture about the power of quantitative methods. (if only because the plot is a little formulaic). And it shows quantitative methods (sabrmetrics) event... | Are there any good movies involving mathematics or probability?
MONEYBALL!
It's a movie where the statisticians win!
This is probably the most inspiring major motion picture about the power of quantitative methods. (if only because the plot is a little formulaic |
5,613 | Are there any good movies involving mathematics or probability? | Not a movie, but a TV series:
Numb3rs | Are there any good movies involving mathematics or probability? | Not a movie, but a TV series:
Numb3rs | Are there any good movies involving mathematics or probability?
Not a movie, but a TV series:
Numb3rs | Are there any good movies involving mathematics or probability?
Not a movie, but a TV series:
Numb3rs |
5,614 | Are there any good movies involving mathematics or probability? | The mathematical movie database has some great suggestions with over 800 movies (though most tenuously linked to maths) already listed. In the navy, from 1941, is probably my favourite. | Are there any good movies involving mathematics or probability? | The mathematical movie database has some great suggestions with over 800 movies (though most tenuously linked to maths) already listed. In the navy, from 1941, is probably my favourite. | Are there any good movies involving mathematics or probability?
The mathematical movie database has some great suggestions with over 800 movies (though most tenuously linked to maths) already listed. In the navy, from 1941, is probably my favourite. | Are there any good movies involving mathematics or probability?
The mathematical movie database has some great suggestions with over 800 movies (though most tenuously linked to maths) already listed. In the navy, from 1941, is probably my favourite. |
5,615 | Are there any good movies involving mathematics or probability? | N Is a Number: A Portrait of Paul Erdős | Are there any good movies involving mathematics or probability? | N Is a Number: A Portrait of Paul Erdős | Are there any good movies involving mathematics or probability?
N Is a Number: A Portrait of Paul Erdős | Are there any good movies involving mathematics or probability?
N Is a Number: A Portrait of Paul Erdős |
5,616 | Are there any good movies involving mathematics or probability? | Proof was pretty good. | Are there any good movies involving mathematics or probability? | Proof was pretty good. | Are there any good movies involving mathematics or probability?
Proof was pretty good. | Are there any good movies involving mathematics or probability?
Proof was pretty good. |
5,617 | Are there any good movies involving mathematics or probability? | The Cube | Are there any good movies involving mathematics or probability? | The Cube | Are there any good movies involving mathematics or probability?
The Cube | Are there any good movies involving mathematics or probability?
The Cube |
5,618 | Are there any good movies involving mathematics or probability? | 21 - based on the book Bringing Down the House (MIT Blackjack team)
Near the beginning they discuss the Monty Hall Problem. However after that there isn't much actual math/probability. | Are there any good movies involving mathematics or probability? | 21 - based on the book Bringing Down the House (MIT Blackjack team)
Near the beginning they discuss the Monty Hall Problem. However after that there isn't much actual math/probability. | Are there any good movies involving mathematics or probability?
21 - based on the book Bringing Down the House (MIT Blackjack team)
Near the beginning they discuss the Monty Hall Problem. However after that there isn't much actual math/probability. | Are there any good movies involving mathematics or probability?
21 - based on the book Bringing Down the House (MIT Blackjack team)
Near the beginning they discuss the Monty Hall Problem. However after that there isn't much actual math/probability. |
5,619 | Are there any good movies involving mathematics or probability? | I have not seen this yet, but it seems somewhat geeky:
Fermat's Room | Are there any good movies involving mathematics or probability? | I have not seen this yet, but it seems somewhat geeky:
Fermat's Room | Are there any good movies involving mathematics or probability?
I have not seen this yet, but it seems somewhat geeky:
Fermat's Room | Are there any good movies involving mathematics or probability?
I have not seen this yet, but it seems somewhat geeky:
Fermat's Room |
5,620 | Are there any good movies involving mathematics or probability? | Early in The Social Network begins with a one night hackathon where Mark Zuckerberg uses the Elo rating system algorithm to
... create a website that rates the attractiveness of female students
when compared to each other. ... in a few hours, using an algorithm for
ranking chess players supplied by his best friend... | Are there any good movies involving mathematics or probability? | Early in The Social Network begins with a one night hackathon where Mark Zuckerberg uses the Elo rating system algorithm to
... create a website that rates the attractiveness of female students
whe | Are there any good movies involving mathematics or probability?
Early in The Social Network begins with a one night hackathon where Mark Zuckerberg uses the Elo rating system algorithm to
... create a website that rates the attractiveness of female students
when compared to each other. ... in a few hours, using an a... | Are there any good movies involving mathematics or probability?
Early in The Social Network begins with a one night hackathon where Mark Zuckerberg uses the Elo rating system algorithm to
... create a website that rates the attractiveness of female students
whe |
5,621 | Are there any good movies involving mathematics or probability? | There are several movie versions of Flatland. And there's The Great $\pi$/e Debate. | Are there any good movies involving mathematics or probability? | There are several movie versions of Flatland. And there's The Great $\pi$/e Debate. | Are there any good movies involving mathematics or probability?
There are several movie versions of Flatland. And there's The Great $\pi$/e Debate. | Are there any good movies involving mathematics or probability?
There are several movie versions of Flatland. And there's The Great $\pi$/e Debate. |
5,622 | Are there any good movies involving mathematics or probability? | Good Will Hunting is also a classic. Discrete mathematics at MIT. | Are there any good movies involving mathematics or probability? | Good Will Hunting is also a classic. Discrete mathematics at MIT. | Are there any good movies involving mathematics or probability?
Good Will Hunting is also a classic. Discrete mathematics at MIT. | Are there any good movies involving mathematics or probability?
Good Will Hunting is also a classic. Discrete mathematics at MIT. |
5,623 | Are there any good movies involving mathematics or probability? | The documentary about Andrew Wiles proof of Fermat's Last Theorem is fantastic:
http://www.pbs.org/wgbh/nova/proof/
Available on youtube:
http://www.youtube.com/watch?v=7FnXgprKgSE | Are there any good movies involving mathematics or probability? | The documentary about Andrew Wiles proof of Fermat's Last Theorem is fantastic:
http://www.pbs.org/wgbh/nova/proof/
Available on youtube:
http://www.youtube.com/watch?v=7FnXgprKgSE | Are there any good movies involving mathematics or probability?
The documentary about Andrew Wiles proof of Fermat's Last Theorem is fantastic:
http://www.pbs.org/wgbh/nova/proof/
Available on youtube:
http://www.youtube.com/watch?v=7FnXgprKgSE | Are there any good movies involving mathematics or probability?
The documentary about Andrew Wiles proof of Fermat's Last Theorem is fantastic:
http://www.pbs.org/wgbh/nova/proof/
Available on youtube:
http://www.youtube.com/watch?v=7FnXgprKgSE |
5,624 | Are there any good movies involving mathematics or probability? | BBC Horizon - The Bible Code. It shows, that whatever codes people found in Bible, so far they didn't prove to be statistically significant. | Are there any good movies involving mathematics or probability? | BBC Horizon - The Bible Code. It shows, that whatever codes people found in Bible, so far they didn't prove to be statistically significant. | Are there any good movies involving mathematics or probability?
BBC Horizon - The Bible Code. It shows, that whatever codes people found in Bible, so far they didn't prove to be statistically significant. | Are there any good movies involving mathematics or probability?
BBC Horizon - The Bible Code. It shows, that whatever codes people found in Bible, so far they didn't prove to be statistically significant. |
5,625 | Are there any good movies involving mathematics or probability? | The Man Who Knew Infinity is based on the life of Srinivasa Ramanujan.
It's a beautiful movie directed by Matthew Brown. Mathematicians Manjul Bhargava and Ken Ono collaborated on the film. | Are there any good movies involving mathematics or probability? | The Man Who Knew Infinity is based on the life of Srinivasa Ramanujan.
It's a beautiful movie directed by Matthew Brown. Mathematicians Manjul Bhargava and Ken Ono collaborated on the film. | Are there any good movies involving mathematics or probability?
The Man Who Knew Infinity is based on the life of Srinivasa Ramanujan.
It's a beautiful movie directed by Matthew Brown. Mathematicians Manjul Bhargava and Ken Ono collaborated on the film. | Are there any good movies involving mathematics or probability?
The Man Who Knew Infinity is based on the life of Srinivasa Ramanujan.
It's a beautiful movie directed by Matthew Brown. Mathematicians Manjul Bhargava and Ken Ono collaborated on the film. |
5,626 | Are there any good movies involving mathematics or probability? | Rounders. A very watchable drama about poker players.
http://www.imdb.com/title/tt0128442/ | Are there any good movies involving mathematics or probability? | Rounders. A very watchable drama about poker players.
http://www.imdb.com/title/tt0128442/ | Are there any good movies involving mathematics or probability?
Rounders. A very watchable drama about poker players.
http://www.imdb.com/title/tt0128442/ | Are there any good movies involving mathematics or probability?
Rounders. A very watchable drama about poker players.
http://www.imdb.com/title/tt0128442/ |
5,627 | Are there any good movies involving mathematics or probability? | There is a published a documentary about Srinivasa Ramanujan whose life, as we know, is tremendously interesting. However, the film is Indian and I haven't actually seen it. I recall an Indian math historian speaking about this film at our university colloquium several years ago. He boasted, "Ben Kingsley was intereste... | Are there any good movies involving mathematics or probability? | There is a published a documentary about Srinivasa Ramanujan whose life, as we know, is tremendously interesting. However, the film is Indian and I haven't actually seen it. I recall an Indian math hi | Are there any good movies involving mathematics or probability?
There is a published a documentary about Srinivasa Ramanujan whose life, as we know, is tremendously interesting. However, the film is Indian and I haven't actually seen it. I recall an Indian math historian speaking about this film at our university collo... | Are there any good movies involving mathematics or probability?
There is a published a documentary about Srinivasa Ramanujan whose life, as we know, is tremendously interesting. However, the film is Indian and I haven't actually seen it. I recall an Indian math hi |
5,628 | Are there any good movies involving mathematics or probability? | Sofia Kovalevskaya - biopic about Russian female mathematician. You don't have too many movies about these folks. One of the recent ones is The Imitation Game about Alan Turing, a British mathematician and computer scientist (allegedly) murdered by his government. | Are there any good movies involving mathematics or probability? | Sofia Kovalevskaya - biopic about Russian female mathematician. You don't have too many movies about these folks. One of the recent ones is The Imitation Game about Alan Turing, a British mathematicia | Are there any good movies involving mathematics or probability?
Sofia Kovalevskaya - biopic about Russian female mathematician. You don't have too many movies about these folks. One of the recent ones is The Imitation Game about Alan Turing, a British mathematician and computer scientist (allegedly) murdered by his gov... | Are there any good movies involving mathematics or probability?
Sofia Kovalevskaya - biopic about Russian female mathematician. You don't have too many movies about these folks. One of the recent ones is The Imitation Game about Alan Turing, a British mathematicia |
5,629 | Are there any good movies involving mathematics or probability? | Stand and Deliver is a good film about the Bolivian-born math teacher Jaime Escalante. Inspiring! See this commentary | Are there any good movies involving mathematics or probability? | Stand and Deliver is a good film about the Bolivian-born math teacher Jaime Escalante. Inspiring! See this commentary | Are there any good movies involving mathematics or probability?
Stand and Deliver is a good film about the Bolivian-born math teacher Jaime Escalante. Inspiring! See this commentary | Are there any good movies involving mathematics or probability?
Stand and Deliver is a good film about the Bolivian-born math teacher Jaime Escalante. Inspiring! See this commentary |
5,630 | Are there any good movies involving mathematics or probability? | 12 angry men (1957, with Henry Fonda): a great film about a decision procedure and the strength of evidences | Are there any good movies involving mathematics or probability? | 12 angry men (1957, with Henry Fonda): a great film about a decision procedure and the strength of evidences | Are there any good movies involving mathematics or probability?
12 angry men (1957, with Henry Fonda): a great film about a decision procedure and the strength of evidences | Are there any good movies involving mathematics or probability?
12 angry men (1957, with Henry Fonda): a great film about a decision procedure and the strength of evidences |
5,631 | Are there any good movies involving mathematics or probability? | travelling salesman is a good one. | Are there any good movies involving mathematics or probability? | travelling salesman is a good one. | Are there any good movies involving mathematics or probability?
travelling salesman is a good one. | Are there any good movies involving mathematics or probability?
travelling salesman is a good one. |
5,632 | What is your favorite statistical graph? | I think that Anscombe's quartet deserves a place here as an example and reminder to always plot your data because datasets with the same numeric summaries can have very different relationships:
Anscombe, Francis J. (1973) Graphs in statistical analysis.
American Statistician, 27, 17-21. | What is your favorite statistical graph? | I think that Anscombe's quartet deserves a place here as an example and reminder to always plot your data because datasets with the same numeric summaries can have very different relationships:
Ansco | What is your favorite statistical graph?
I think that Anscombe's quartet deserves a place here as an example and reminder to always plot your data because datasets with the same numeric summaries can have very different relationships:
Anscombe, Francis J. (1973) Graphs in statistical analysis.
American Statistician, 2... | What is your favorite statistical graph?
I think that Anscombe's quartet deserves a place here as an example and reminder to always plot your data because datasets with the same numeric summaries can have very different relationships:
Ansco |
5,633 | What is your favorite statistical graph? | I always enjoy reading this Sankey diagram (a type of flow map) on the French invasion of Russia by Charles Joseph Minard in 1812:
Charles Joseph Minard's famous graph showing the decreasing size of
the Grande Armée as it marches to Moscow (brown line, from left to
right) and back (black line, from right to left) ... | What is your favorite statistical graph? | I always enjoy reading this Sankey diagram (a type of flow map) on the French invasion of Russia by Charles Joseph Minard in 1812:
Charles Joseph Minard's famous graph showing the decreasing size of
| What is your favorite statistical graph?
I always enjoy reading this Sankey diagram (a type of flow map) on the French invasion of Russia by Charles Joseph Minard in 1812:
Charles Joseph Minard's famous graph showing the decreasing size of
the Grande Armée as it marches to Moscow (brown line, from left to
right) a... | What is your favorite statistical graph?
I always enjoy reading this Sankey diagram (a type of flow map) on the French invasion of Russia by Charles Joseph Minard in 1812:
Charles Joseph Minard's famous graph showing the decreasing size of
|
5,634 | What is your favorite statistical graph? | I hope not to push things here too far toward the humorous side with an early response that's in that vein (+1 for @GregSnow's theoretical answer!), but since I already have an entry in the favorite cartoons thread, I'll add a graph here.
By Jorge Cham of Piled Higher and Deeper infamy, as per the © on on the botto... | What is your favorite statistical graph? | I hope not to push things here too far toward the humorous side with an early response that's in that vein (+1 for @GregSnow's theoretical answer!), but since I already have an entry in the favorite c | What is your favorite statistical graph?
I hope not to push things here too far toward the humorous side with an early response that's in that vein (+1 for @GregSnow's theoretical answer!), but since I already have an entry in the favorite cartoons thread, I'll add a graph here.
By Jorge Cham of Piled Higher and De... | What is your favorite statistical graph?
I hope not to push things here too far toward the humorous side with an early response that's in that vein (+1 for @GregSnow's theoretical answer!), but since I already have an entry in the favorite c |
5,635 | What is your favorite statistical graph? | Another famous visualization of data (we can have a semantic argument about whether it should be called a graph) is John Snow's 1854 map of cholera cases in London: | What is your favorite statistical graph? | Another famous visualization of data (we can have a semantic argument about whether it should be called a graph) is John Snow's 1854 map of cholera cases in London: | What is your favorite statistical graph?
Another famous visualization of data (we can have a semantic argument about whether it should be called a graph) is John Snow's 1854 map of cholera cases in London: | What is your favorite statistical graph?
Another famous visualization of data (we can have a semantic argument about whether it should be called a graph) is John Snow's 1854 map of cholera cases in London: |
5,636 | What is your favorite statistical graph? | I like very much your examples!, but one shocking and simple graph for my point of view is that one:
propaganda nazi | What is your favorite statistical graph? | I like very much your examples!, but one shocking and simple graph for my point of view is that one:
propaganda nazi | What is your favorite statistical graph?
I like very much your examples!, but one shocking and simple graph for my point of view is that one:
propaganda nazi | What is your favorite statistical graph?
I like very much your examples!, but one shocking and simple graph for my point of view is that one:
propaganda nazi |
5,637 | What is your favorite statistical graph? | Thinking in terms of a figure that packs a lot of information, I like this one:
It comes from the main page of the R Project for Statistical Computing. It won the R homepage graphics competition to be so displayed. The R code to produce it can be found by clicking on the figure on the R homepage. | What is your favorite statistical graph? | Thinking in terms of a figure that packs a lot of information, I like this one:
It comes from the main page of the R Project for Statistical Computing. It won the R homepage graphics competition t | What is your favorite statistical graph?
Thinking in terms of a figure that packs a lot of information, I like this one:
It comes from the main page of the R Project for Statistical Computing. It won the R homepage graphics competition to be so displayed. The R code to produce it can be found by clicking on the fi... | What is your favorite statistical graph?
Thinking in terms of a figure that packs a lot of information, I like this one:
It comes from the main page of the R Project for Statistical Computing. It won the R homepage graphics competition t |
5,638 | Negative values for AICc (corrected Akaike Information Criterion) | All that matters is the difference between two AIC (or, better, AICc) values, representing the fit to two models. The actual value of the AIC (or AICc), and whether it is positive or negative, means nothing. If you simply changed the units the data are expressed in, the AIC (and AICc) would change dramatically. But th... | Negative values for AICc (corrected Akaike Information Criterion) | All that matters is the difference between two AIC (or, better, AICc) values, representing the fit to two models. The actual value of the AIC (or AICc), and whether it is positive or negative, means | Negative values for AICc (corrected Akaike Information Criterion)
All that matters is the difference between two AIC (or, better, AICc) values, representing the fit to two models. The actual value of the AIC (or AICc), and whether it is positive or negative, means nothing. If you simply changed the units the data are ... | Negative values for AICc (corrected Akaike Information Criterion)
All that matters is the difference between two AIC (or, better, AICc) values, representing the fit to two models. The actual value of the AIC (or AICc), and whether it is positive or negative, means |
5,639 | Negative values for AICc (corrected Akaike Information Criterion) | AIC = -2Ln(L)+ 2k
where L is the maximised value of Likelihood function for that model and k is the number of parameters in the model.
In your example -2Ln(L)+ 2k <0 means that the log-likelihood at the maximum was > 0
which means that the likelihood at the maximum was > 1.
There is no problem with a positive log-like... | Negative values for AICc (corrected Akaike Information Criterion) | AIC = -2Ln(L)+ 2k
where L is the maximised value of Likelihood function for that model and k is the number of parameters in the model.
In your example -2Ln(L)+ 2k <0 means that the log-likelihood at | Negative values for AICc (corrected Akaike Information Criterion)
AIC = -2Ln(L)+ 2k
where L is the maximised value of Likelihood function for that model and k is the number of parameters in the model.
In your example -2Ln(L)+ 2k <0 means that the log-likelihood at the maximum was > 0
which means that the likelihood at... | Negative values for AICc (corrected Akaike Information Criterion)
AIC = -2Ln(L)+ 2k
where L is the maximised value of Likelihood function for that model and k is the number of parameters in the model.
In your example -2Ln(L)+ 2k <0 means that the log-likelihood at |
5,640 | Negative values for AICc (corrected Akaike Information Criterion) | Generally, it is assumed that AIC (and so AICc) is defined up to adding a constant, so the fact if it is negative or positive is not meaningful at all. So the answer is yes, it is valid. | Negative values for AICc (corrected Akaike Information Criterion) | Generally, it is assumed that AIC (and so AICc) is defined up to adding a constant, so the fact if it is negative or positive is not meaningful at all. So the answer is yes, it is valid. | Negative values for AICc (corrected Akaike Information Criterion)
Generally, it is assumed that AIC (and so AICc) is defined up to adding a constant, so the fact if it is negative or positive is not meaningful at all. So the answer is yes, it is valid. | Negative values for AICc (corrected Akaike Information Criterion)
Generally, it is assumed that AIC (and so AICc) is defined up to adding a constant, so the fact if it is negative or positive is not meaningful at all. So the answer is yes, it is valid. |
5,641 | Negative values for AICc (corrected Akaike Information Criterion) | Yes it's valid to compare negative AICc values, in the same way as you would negative AIC values. The correction factor in the AICc can become large with small sample size and relatively large number of parameters, and penalize heavier than the AIC. So positive AIC values can correspond to negative AICc values. | Negative values for AICc (corrected Akaike Information Criterion) | Yes it's valid to compare negative AICc values, in the same way as you would negative AIC values. The correction factor in the AICc can become large with small sample size and relatively large number | Negative values for AICc (corrected Akaike Information Criterion)
Yes it's valid to compare negative AICc values, in the same way as you would negative AIC values. The correction factor in the AICc can become large with small sample size and relatively large number of parameters, and penalize heavier than the AIC. So... | Negative values for AICc (corrected Akaike Information Criterion)
Yes it's valid to compare negative AICc values, in the same way as you would negative AIC values. The correction factor in the AICc can become large with small sample size and relatively large number |
5,642 | Negative values for AICc (corrected Akaike Information Criterion) | Yes. It's valid to compare AIC values regardless they are positive or negative. That's because AIC is defined be a linear function (-2) of log-likelihood. If the likelihood is large, your AIC will be likely negative but it says nothing about the model itself.
AICc is similar, the fact that the values are now adjusted c... | Negative values for AICc (corrected Akaike Information Criterion) | Yes. It's valid to compare AIC values regardless they are positive or negative. That's because AIC is defined be a linear function (-2) of log-likelihood. If the likelihood is large, your AIC will be | Negative values for AICc (corrected Akaike Information Criterion)
Yes. It's valid to compare AIC values regardless they are positive or negative. That's because AIC is defined be a linear function (-2) of log-likelihood. If the likelihood is large, your AIC will be likely negative but it says nothing about the model it... | Negative values for AICc (corrected Akaike Information Criterion)
Yes. It's valid to compare AIC values regardless they are positive or negative. That's because AIC is defined be a linear function (-2) of log-likelihood. If the likelihood is large, your AIC will be |
5,643 | How seriously should I think about the different philosophies of statistics? | I think that the main takeaway here is this: the mere fact that there are these different philosophies of statistics and disagreement over them implies that translating the "hard numbers" that one gets from applying statistical formulae into "real world" decisions is a non-trivial problem and is fraught with interpreti... | How seriously should I think about the different philosophies of statistics? | I think that the main takeaway here is this: the mere fact that there are these different philosophies of statistics and disagreement over them implies that translating the "hard numbers" that one get | How seriously should I think about the different philosophies of statistics?
I think that the main takeaway here is this: the mere fact that there are these different philosophies of statistics and disagreement over them implies that translating the "hard numbers" that one gets from applying statistical formulae into "... | How seriously should I think about the different philosophies of statistics?
I think that the main takeaway here is this: the mere fact that there are these different philosophies of statistics and disagreement over them implies that translating the "hard numbers" that one get |
5,644 | How seriously should I think about the different philosophies of statistics? | A preliminary note on my nomenclature: As a preliminary matter, I note that I have never liked the terms "frequentist school" for the philosophy and set of methods it designates, and so I instead refer to this school of thought as "classical". Both Bayesians and classical statisticians agree entirely on the relevant t... | How seriously should I think about the different philosophies of statistics? | A preliminary note on my nomenclature: As a preliminary matter, I note that I have never liked the terms "frequentist school" for the philosophy and set of methods it designates, and so I instead refe | How seriously should I think about the different philosophies of statistics?
A preliminary note on my nomenclature: As a preliminary matter, I note that I have never liked the terms "frequentist school" for the philosophy and set of methods it designates, and so I instead refer to this school of thought as "classical".... | How seriously should I think about the different philosophies of statistics?
A preliminary note on my nomenclature: As a preliminary matter, I note that I have never liked the terms "frequentist school" for the philosophy and set of methods it designates, and so I instead refe |
5,645 | How seriously should I think about the different philosophies of statistics? | I try to add something to the already existing answers that are worthwhile to read.
I do think that the foundations discussion touch basic questions that are important to think about as statisticians, particularly "what do we mean by probability?" Also understanding "inferential logic" when running, say, tests, confid... | How seriously should I think about the different philosophies of statistics? | I try to add something to the already existing answers that are worthwhile to read.
I do think that the foundations discussion touch basic questions that are important to think about as statisticians | How seriously should I think about the different philosophies of statistics?
I try to add something to the already existing answers that are worthwhile to read.
I do think that the foundations discussion touch basic questions that are important to think about as statisticians, particularly "what do we mean by probabil... | How seriously should I think about the different philosophies of statistics?
I try to add something to the already existing answers that are worthwhile to read.
I do think that the foundations discussion touch basic questions that are important to think about as statisticians |
5,646 | How seriously should I think about the different philosophies of statistics? | What you shouldn't do is align yourself with one in the sense of declaring one of them "right" and the other one "wrong". They are just two different viewpoints on the same thing, giving you alternative "tools of the trade". As an expert, you should be conversant in both. You may choose, for practical reasons, to speci... | How seriously should I think about the different philosophies of statistics? | What you shouldn't do is align yourself with one in the sense of declaring one of them "right" and the other one "wrong". They are just two different viewpoints on the same thing, giving you alternati | How seriously should I think about the different philosophies of statistics?
What you shouldn't do is align yourself with one in the sense of declaring one of them "right" and the other one "wrong". They are just two different viewpoints on the same thing, giving you alternative "tools of the trade". As an expert, you ... | How seriously should I think about the different philosophies of statistics?
What you shouldn't do is align yourself with one in the sense of declaring one of them "right" and the other one "wrong". They are just two different viewpoints on the same thing, giving you alternati |
5,647 | How seriously should I think about the different philosophies of statistics? | Many people have given way better answers than I possibly could, but there are two things I wanted to add.
The field, hypothesis, and type of data you are working with can heavily influence which philosophy you use. The hypothesis "The mass of a neutron is 1.001 times the mass of a proton" definitely has a true or fal... | How seriously should I think about the different philosophies of statistics? | Many people have given way better answers than I possibly could, but there are two things I wanted to add.
The field, hypothesis, and type of data you are working with can heavily influence which phi | How seriously should I think about the different philosophies of statistics?
Many people have given way better answers than I possibly could, but there are two things I wanted to add.
The field, hypothesis, and type of data you are working with can heavily influence which philosophy you use. The hypothesis "The mass o... | How seriously should I think about the different philosophies of statistics?
Many people have given way better answers than I possibly could, but there are two things I wanted to add.
The field, hypothesis, and type of data you are working with can heavily influence which phi |
5,648 | How seriously should I think about the different philosophies of statistics? | The data itself is often the same for both approaches. In practice, the Bayesian or frequentist philosophies determine different estimators to analyze that data. Conversely, some estimators can be rationalized by either philosophy. Within each approach, modeling choices are needed to take the model to data, that can so... | How seriously should I think about the different philosophies of statistics? | The data itself is often the same for both approaches. In practice, the Bayesian or frequentist philosophies determine different estimators to analyze that data. Conversely, some estimators can be rat | How seriously should I think about the different philosophies of statistics?
The data itself is often the same for both approaches. In practice, the Bayesian or frequentist philosophies determine different estimators to analyze that data. Conversely, some estimators can be rationalized by either philosophy. Within each... | How seriously should I think about the different philosophies of statistics?
The data itself is often the same for both approaches. In practice, the Bayesian or frequentist philosophies determine different estimators to analyze that data. Conversely, some estimators can be rat |
5,649 | Approximate $e$ using Monte Carlo Simulation | The simple and elegant way to estimate $e$ by Monte Carlo is described in this paper. The paper is actually about teaching $e$. Hence, the approach seems perfectly fitting for your goal. The idea's based on an exercise from a popular Ukrainian textbook on probability theory by Gnedenko.
See ex.22 on p.183
It happens so... | Approximate $e$ using Monte Carlo Simulation | The simple and elegant way to estimate $e$ by Monte Carlo is described in this paper. The paper is actually about teaching $e$. Hence, the approach seems perfectly fitting for your goal. The idea's ba | Approximate $e$ using Monte Carlo Simulation
The simple and elegant way to estimate $e$ by Monte Carlo is described in this paper. The paper is actually about teaching $e$. Hence, the approach seems perfectly fitting for your goal. The idea's based on an exercise from a popular Ukrainian textbook on probability theory ... | Approximate $e$ using Monte Carlo Simulation
The simple and elegant way to estimate $e$ by Monte Carlo is described in this paper. The paper is actually about teaching $e$. Hence, the approach seems perfectly fitting for your goal. The idea's ba |
5,650 | Approximate $e$ using Monte Carlo Simulation | I suggest upvoting Aksakal's answer. It is unbiased and relies only on a method of generating unit uniform deviates.
My answer can be made arbitrarily precise, but still is biased away from the true value of $e$.
Xi'an's answer is correct, but I think its dependence on either the $\log$ function or a way of generating ... | Approximate $e$ using Monte Carlo Simulation | I suggest upvoting Aksakal's answer. It is unbiased and relies only on a method of generating unit uniform deviates.
My answer can be made arbitrarily precise, but still is biased away from the true v | Approximate $e$ using Monte Carlo Simulation
I suggest upvoting Aksakal's answer. It is unbiased and relies only on a method of generating unit uniform deviates.
My answer can be made arbitrarily precise, but still is biased away from the true value of $e$.
Xi'an's answer is correct, but I think its dependence on eithe... | Approximate $e$ using Monte Carlo Simulation
I suggest upvoting Aksakal's answer. It is unbiased and relies only on a method of generating unit uniform deviates.
My answer can be made arbitrarily precise, but still is biased away from the true v |
5,651 | Approximate $e$ using Monte Carlo Simulation | Solution 1:
For a Poisson $\mathcal{P}(\lambda)$ distribution, $$\mathbb{P}(X=k)=\frac{\lambda^k}{k!}\,e^{-\lambda}$$Therefore, if $X\sim\mathcal{P}(1)$,
$$\mathbb{P}(X=0)=\mathbb{P}(X=1)=e^{-1}$$which means you can estimate $e^{-1}$ by a Poisson simulation. And Poisson simulations can be derived from an exponential di... | Approximate $e$ using Monte Carlo Simulation | Solution 1:
For a Poisson $\mathcal{P}(\lambda)$ distribution, $$\mathbb{P}(X=k)=\frac{\lambda^k}{k!}\,e^{-\lambda}$$Therefore, if $X\sim\mathcal{P}(1)$,
$$\mathbb{P}(X=0)=\mathbb{P}(X=1)=e^{-1}$$whic | Approximate $e$ using Monte Carlo Simulation
Solution 1:
For a Poisson $\mathcal{P}(\lambda)$ distribution, $$\mathbb{P}(X=k)=\frac{\lambda^k}{k!}\,e^{-\lambda}$$Therefore, if $X\sim\mathcal{P}(1)$,
$$\mathbb{P}(X=0)=\mathbb{P}(X=1)=e^{-1}$$which means you can estimate $e^{-1}$ by a Poisson simulation. And Poisson simu... | Approximate $e$ using Monte Carlo Simulation
Solution 1:
For a Poisson $\mathcal{P}(\lambda)$ distribution, $$\mathbb{P}(X=k)=\frac{\lambda^k}{k!}\,e^{-\lambda}$$Therefore, if $X\sim\mathcal{P}(1)$,
$$\mathbb{P}(X=0)=\mathbb{P}(X=1)=e^{-1}$$whic |
5,652 | Approximate $e$ using Monte Carlo Simulation | Not a solution ... just a quick comment that is too long for the comment box.
Aksakal
Aksakal posted a solution where we calculate the expected number of standard Uniform drawings that must be taken, such that their sum will exceed 1. In Mathematica, my first formulation was:
mrM := NestWhileList[(Random[] + #) &, Rand... | Approximate $e$ using Monte Carlo Simulation | Not a solution ... just a quick comment that is too long for the comment box.
Aksakal
Aksakal posted a solution where we calculate the expected number of standard Uniform drawings that must be taken, | Approximate $e$ using Monte Carlo Simulation
Not a solution ... just a quick comment that is too long for the comment box.
Aksakal
Aksakal posted a solution where we calculate the expected number of standard Uniform drawings that must be taken, such that their sum will exceed 1. In Mathematica, my first formulation was... | Approximate $e$ using Monte Carlo Simulation
Not a solution ... just a quick comment that is too long for the comment box.
Aksakal
Aksakal posted a solution where we calculate the expected number of standard Uniform drawings that must be taken, |
5,653 | Approximate $e$ using Monte Carlo Simulation | Here is another way it can be done, though it is quite slow. I make no claim to efficiency, but offer this alternative in the spirit of completeness.
Contra Xi'an's answer, I will assume for the purposes of this question that you are able to generate and use a sequence of $n$ uniform pseudo-random variables $U_1, \cdo... | Approximate $e$ using Monte Carlo Simulation | Here is another way it can be done, though it is quite slow. I make no claim to efficiency, but offer this alternative in the spirit of completeness.
Contra Xi'an's answer, I will assume for the purp | Approximate $e$ using Monte Carlo Simulation
Here is another way it can be done, though it is quite slow. I make no claim to efficiency, but offer this alternative in the spirit of completeness.
Contra Xi'an's answer, I will assume for the purposes of this question that you are able to generate and use a sequence of $... | Approximate $e$ using Monte Carlo Simulation
Here is another way it can be done, though it is quite slow. I make no claim to efficiency, but offer this alternative in the spirit of completeness.
Contra Xi'an's answer, I will assume for the purp |
5,654 | Approximate $e$ using Monte Carlo Simulation | Method requiring an ungodly amount of samples
First you need to be able to sample from a normal distribution. Assuming you are going to exclude the use of the function $f(x) = e^x$, or look up tables derived from that function, you can produce approximate samples from the normal distribution via the CLT. For example, i... | Approximate $e$ using Monte Carlo Simulation | Method requiring an ungodly amount of samples
First you need to be able to sample from a normal distribution. Assuming you are going to exclude the use of the function $f(x) = e^x$, or look up tables | Approximate $e$ using Monte Carlo Simulation
Method requiring an ungodly amount of samples
First you need to be able to sample from a normal distribution. Assuming you are going to exclude the use of the function $f(x) = e^x$, or look up tables derived from that function, you can produce approximate samples from the no... | Approximate $e$ using Monte Carlo Simulation
Method requiring an ungodly amount of samples
First you need to be able to sample from a normal distribution. Assuming you are going to exclude the use of the function $f(x) = e^x$, or look up tables |
5,655 | Approximate $e$ using Monte Carlo Simulation | If you do not have a calculator (ie you can not compute the exponential 'e' indirectly by using some related functions like computing a sample from a normal distribution or exponential distribution) and you have only coin flips or dice rolls* available to you, then you could use the following puzzle to estimate the num... | Approximate $e$ using Monte Carlo Simulation | If you do not have a calculator (ie you can not compute the exponential 'e' indirectly by using some related functions like computing a sample from a normal distribution or exponential distribution) a | Approximate $e$ using Monte Carlo Simulation
If you do not have a calculator (ie you can not compute the exponential 'e' indirectly by using some related functions like computing a sample from a normal distribution or exponential distribution) and you have only coin flips or dice rolls* available to you, then you could... | Approximate $e$ using Monte Carlo Simulation
If you do not have a calculator (ie you can not compute the exponential 'e' indirectly by using some related functions like computing a sample from a normal distribution or exponential distribution) a |
5,656 | Approximate $e$ using Monte Carlo Simulation | $$\int_1^2 \frac{1}{x}dx = \ln{2}$$
So if you draw uniformly from $[1,2]^2$, the fraction of points whose product is less than $1$ would converge to $\ln{2}$ by the LLN.
You can then get to $e$ by
$$2^{\frac{1}{\ln{2}}} = e$$
One might raise the issue that exponentiation might require knowledge of $e$ itself. I don’t h... | Approximate $e$ using Monte Carlo Simulation | $$\int_1^2 \frac{1}{x}dx = \ln{2}$$
So if you draw uniformly from $[1,2]^2$, the fraction of points whose product is less than $1$ would converge to $\ln{2}$ by the LLN.
You can then get to $e$ by
$$2 | Approximate $e$ using Monte Carlo Simulation
$$\int_1^2 \frac{1}{x}dx = \ln{2}$$
So if you draw uniformly from $[1,2]^2$, the fraction of points whose product is less than $1$ would converge to $\ln{2}$ by the LLN.
You can then get to $e$ by
$$2^{\frac{1}{\ln{2}}} = e$$
One might raise the issue that exponentiation mig... | Approximate $e$ using Monte Carlo Simulation
$$\int_1^2 \frac{1}{x}dx = \ln{2}$$
So if you draw uniformly from $[1,2]^2$, the fraction of points whose product is less than $1$ would converge to $\ln{2}$ by the LLN.
You can then get to $e$ by
$$2 |
5,657 | Approximate $e$ using Monte Carlo Simulation | The Python version of this is the following if anyone is curious:
import random
print("Number of iterations: ", end="")
n = int(input())
sum_total = 0
for _ in range(n):
temp = 0
counter = 0
while temp < 1:
temp += random.random()
counter += 1
sum_total += counter
print(sum_total/n) | Approximate $e$ using Monte Carlo Simulation | The Python version of this is the following if anyone is curious:
import random
print("Number of iterations: ", end="")
n = int(input())
sum_total = 0
for _ in range(n):
temp = 0
counter = 0 | Approximate $e$ using Monte Carlo Simulation
The Python version of this is the following if anyone is curious:
import random
print("Number of iterations: ", end="")
n = int(input())
sum_total = 0
for _ in range(n):
temp = 0
counter = 0
while temp < 1:
temp += random.random()
counter += 1
... | Approximate $e$ using Monte Carlo Simulation
The Python version of this is the following if anyone is curious:
import random
print("Number of iterations: ", end="")
n = int(input())
sum_total = 0
for _ in range(n):
temp = 0
counter = 0 |
5,658 | McFadden's Pseudo-$R^2$ Interpretation | So I figured I'd sum up what I've learned about McFadden's pseudo $R^2$ as a proper answer.
The seminal reference that I can see for McFadden's pseudo $R^2$ is: McFadden, D. (1974) “Conditional logit analysis of qualitative choice behavior.” Pp. 105-142 in P. Zarembka (ed.), Frontiers in Econometrics. Academic Press. ... | McFadden's Pseudo-$R^2$ Interpretation | So I figured I'd sum up what I've learned about McFadden's pseudo $R^2$ as a proper answer.
The seminal reference that I can see for McFadden's pseudo $R^2$ is: McFadden, D. (1974) “Conditional logit | McFadden's Pseudo-$R^2$ Interpretation
So I figured I'd sum up what I've learned about McFadden's pseudo $R^2$ as a proper answer.
The seminal reference that I can see for McFadden's pseudo $R^2$ is: McFadden, D. (1974) “Conditional logit analysis of qualitative choice behavior.” Pp. 105-142 in P. Zarembka (ed.), Fron... | McFadden's Pseudo-$R^2$ Interpretation
So I figured I'd sum up what I've learned about McFadden's pseudo $R^2$ as a proper answer.
The seminal reference that I can see for McFadden's pseudo $R^2$ is: McFadden, D. (1974) “Conditional logit |
5,659 | McFadden's Pseudo-$R^2$ Interpretation | McFadden's $R^2$ is defined as $1 - LL_{mod} / LL_0$, where $LL_{mod}$ is the log likelihood value for the fitted model and $LL_0$ is the log likelihood for the null model which includes only an intercept as predictor (so that every individual is predicted the same probability of 'success').
For a logistic regression m... | McFadden's Pseudo-$R^2$ Interpretation | McFadden's $R^2$ is defined as $1 - LL_{mod} / LL_0$, where $LL_{mod}$ is the log likelihood value for the fitted model and $LL_0$ is the log likelihood for the null model which includes only an inter | McFadden's Pseudo-$R^2$ Interpretation
McFadden's $R^2$ is defined as $1 - LL_{mod} / LL_0$, where $LL_{mod}$ is the log likelihood value for the fitted model and $LL_0$ is the log likelihood for the null model which includes only an intercept as predictor (so that every individual is predicted the same probability of ... | McFadden's Pseudo-$R^2$ Interpretation
McFadden's $R^2$ is defined as $1 - LL_{mod} / LL_0$, where $LL_{mod}$ is the log likelihood value for the fitted model and $LL_0$ is the log likelihood for the null model which includes only an inter |
5,660 | McFadden's Pseudo-$R^2$ Interpretation | I did some more focused research on this topic, and I found that interpretations of McFadden's pseudo $R^2$ (also known as likelihood-ratio index) are not clear; however, it can range from 0 to 1, but will never reach or exceed 1 as a result of its calculation.
A rule of thumb that I found to be quite helpful is that a... | McFadden's Pseudo-$R^2$ Interpretation | I did some more focused research on this topic, and I found that interpretations of McFadden's pseudo $R^2$ (also known as likelihood-ratio index) are not clear; however, it can range from 0 to 1, but | McFadden's Pseudo-$R^2$ Interpretation
I did some more focused research on this topic, and I found that interpretations of McFadden's pseudo $R^2$ (also known as likelihood-ratio index) are not clear; however, it can range from 0 to 1, but will never reach or exceed 1 as a result of its calculation.
A rule of thumb tha... | McFadden's Pseudo-$R^2$ Interpretation
I did some more focused research on this topic, and I found that interpretations of McFadden's pseudo $R^2$ (also known as likelihood-ratio index) are not clear; however, it can range from 0 to 1, but |
5,661 | McFadden's Pseudo-$R^2$ Interpretation | In case anyone is still interested in finding McFadden's own word, here is the link. In a footnote, McFadden (1977, p.35) wrote that "values of .2 to .4 for [$\rho^2$] represent an excellent fit." The paper is available online.
http://cowles.yale.edu/sites/default/files/files/pub/d04/d0474.pdf | McFadden's Pseudo-$R^2$ Interpretation | In case anyone is still interested in finding McFadden's own word, here is the link. In a footnote, McFadden (1977, p.35) wrote that "values of .2 to .4 for [$\rho^2$] represent an excellent fit." T | McFadden's Pseudo-$R^2$ Interpretation
In case anyone is still interested in finding McFadden's own word, here is the link. In a footnote, McFadden (1977, p.35) wrote that "values of .2 to .4 for [$\rho^2$] represent an excellent fit." The paper is available online.
http://cowles.yale.edu/sites/default/files/files/pu... | McFadden's Pseudo-$R^2$ Interpretation
In case anyone is still interested in finding McFadden's own word, here is the link. In a footnote, McFadden (1977, p.35) wrote that "values of .2 to .4 for [$\rho^2$] represent an excellent fit." T |
5,662 | R - Confused on Residual Terminology | As requested, I illustrate using a simple regression using the mtcars data:
fit <- lm(mpg~hp, data=mtcars)
summary(fit)
Call:
lm(formula = mpg ~ hp, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-5.7121 -2.1122 -0.8854 1.5819 8.2360
Coefficients:
Estimate Std. Error t value Pr(>|t... | R - Confused on Residual Terminology | As requested, I illustrate using a simple regression using the mtcars data:
fit <- lm(mpg~hp, data=mtcars)
summary(fit)
Call:
lm(formula = mpg ~ hp, data = mtcars)
Residuals:
Min 1Q Median | R - Confused on Residual Terminology
As requested, I illustrate using a simple regression using the mtcars data:
fit <- lm(mpg~hp, data=mtcars)
summary(fit)
Call:
lm(formula = mpg ~ hp, data = mtcars)
Residuals:
Min 1Q Median 3Q Max
-5.7121 -2.1122 -0.8854 1.5819 8.2360
Coefficients:
... | R - Confused on Residual Terminology
As requested, I illustrate using a simple regression using the mtcars data:
fit <- lm(mpg~hp, data=mtcars)
summary(fit)
Call:
lm(formula = mpg ~ hp, data = mtcars)
Residuals:
Min 1Q Median |
5,663 | R - Confused on Residual Terminology | The original poster asked for an "explain like I'm 5" answer. Let's say your school teacher invites you and your schoolmates to help guess the teacher's table width. Each of the 20 students in class can choose a device (ruler, scale, tape, or yardstick) and is allowed to measure the table 10 times. You all are asked... | R - Confused on Residual Terminology | The original poster asked for an "explain like I'm 5" answer. Let's say your school teacher invites you and your schoolmates to help guess the teacher's table width. Each of the 20 students in class | R - Confused on Residual Terminology
The original poster asked for an "explain like I'm 5" answer. Let's say your school teacher invites you and your schoolmates to help guess the teacher's table width. Each of the 20 students in class can choose a device (ruler, scale, tape, or yardstick) and is allowed to measure t... | R - Confused on Residual Terminology
The original poster asked for an "explain like I'm 5" answer. Let's say your school teacher invites you and your schoolmates to help guess the teacher's table width. Each of the 20 students in class |
5,664 | R - Confused on Residual Terminology | I also feel all the terms are very confusing. I strongly feel it is necessary to explain why we have these many metrics.
Here is my note on SSE and RMSE:
First metric: Sum of Squared Errors (SSE). Other names, Residual Sum of Squares (RSS), Sum of Squared Residuals (SSR).
If we are in optimization community, SSE is wid... | R - Confused on Residual Terminology | I also feel all the terms are very confusing. I strongly feel it is necessary to explain why we have these many metrics.
Here is my note on SSE and RMSE:
First metric: Sum of Squared Errors (SSE). Oth | R - Confused on Residual Terminology
I also feel all the terms are very confusing. I strongly feel it is necessary to explain why we have these many metrics.
Here is my note on SSE and RMSE:
First metric: Sum of Squared Errors (SSE). Other names, Residual Sum of Squares (RSS), Sum of Squared Residuals (SSR).
If we are ... | R - Confused on Residual Terminology
I also feel all the terms are very confusing. I strongly feel it is necessary to explain why we have these many metrics.
Here is my note on SSE and RMSE:
First metric: Sum of Squared Errors (SSE). Oth |
5,665 | Why is multiple comparison a problem? | You've stated something that is a classic counter argument to Bonferroni corrections. Shouldn't I adjust my alpha criterion based on every test I will ever make? This kind of ad absurdum implication is why some people do not believe in Bonferroni style corrections at all. Sometimes the kind of data one deals with in... | Why is multiple comparison a problem? | You've stated something that is a classic counter argument to Bonferroni corrections. Shouldn't I adjust my alpha criterion based on every test I will ever make? This kind of ad absurdum implication | Why is multiple comparison a problem?
You've stated something that is a classic counter argument to Bonferroni corrections. Shouldn't I adjust my alpha criterion based on every test I will ever make? This kind of ad absurdum implication is why some people do not believe in Bonferroni style corrections at all. Someti... | Why is multiple comparison a problem?
You've stated something that is a classic counter argument to Bonferroni corrections. Shouldn't I adjust my alpha criterion based on every test I will ever make? This kind of ad absurdum implication |
5,666 | Why is multiple comparison a problem? | Well-respected statisticians have taken a wide variety of positions on multiple comparisons. It's a subtle subject. If someone thinks it's simple, I'd wonder how much they've thought about it.
Here's an interesting Bayesian perspective on multiple testing from Andrew Gelman: Why we don't (usually) worry about multiple... | Why is multiple comparison a problem? | Well-respected statisticians have taken a wide variety of positions on multiple comparisons. It's a subtle subject. If someone thinks it's simple, I'd wonder how much they've thought about it.
Here's | Why is multiple comparison a problem?
Well-respected statisticians have taken a wide variety of positions on multiple comparisons. It's a subtle subject. If someone thinks it's simple, I'd wonder how much they've thought about it.
Here's an interesting Bayesian perspective on multiple testing from Andrew Gelman: Why w... | Why is multiple comparison a problem?
Well-respected statisticians have taken a wide variety of positions on multiple comparisons. It's a subtle subject. If someone thinks it's simple, I'd wonder how much they've thought about it.
Here's |
5,667 | Why is multiple comparison a problem? | Related to the comment earlier, what the fMRI researcher should remember is that clinically-important outcomes are what matter, not the density shift of a single pixel on a fMRI of the brain. If it doesn't result in a clinical improvement/detriment, it doesn't matter. That is one way of reducing the concern about multi... | Why is multiple comparison a problem? | Related to the comment earlier, what the fMRI researcher should remember is that clinically-important outcomes are what matter, not the density shift of a single pixel on a fMRI of the brain. If it do | Why is multiple comparison a problem?
Related to the comment earlier, what the fMRI researcher should remember is that clinically-important outcomes are what matter, not the density shift of a single pixel on a fMRI of the brain. If it doesn't result in a clinical improvement/detriment, it doesn't matter. That is one w... | Why is multiple comparison a problem?
Related to the comment earlier, what the fMRI researcher should remember is that clinically-important outcomes are what matter, not the density shift of a single pixel on a fMRI of the brain. If it do |
5,668 | Why is multiple comparison a problem? | To fix ideas: I will take the case when you obverse, $n$ independent random variables $(X_i)_{i=1,\dots,n}$ such that for $i=1,\dots,n$ $X_i$ is drawn from $\mathcal{N}(\theta_i,1)$. I assume that you want to know which one have non zero mean, formally you want to test:
$H_{0i} : \theta_i=0$ Vs $H_{1i} : \theta_i\neq ... | Why is multiple comparison a problem? | To fix ideas: I will take the case when you obverse, $n$ independent random variables $(X_i)_{i=1,\dots,n}$ such that for $i=1,\dots,n$ $X_i$ is drawn from $\mathcal{N}(\theta_i,1)$. I assume that yo | Why is multiple comparison a problem?
To fix ideas: I will take the case when you obverse, $n$ independent random variables $(X_i)_{i=1,\dots,n}$ such that for $i=1,\dots,n$ $X_i$ is drawn from $\mathcal{N}(\theta_i,1)$. I assume that you want to know which one have non zero mean, formally you want to test:
$H_{0i} : ... | Why is multiple comparison a problem?
To fix ideas: I will take the case when you obverse, $n$ independent random variables $(X_i)_{i=1,\dots,n}$ such that for $i=1,\dots,n$ $X_i$ is drawn from $\mathcal{N}(\theta_i,1)$. I assume that yo |
5,669 | Why is multiple comparison a problem? | An illustrating (and funny) article (http://www.jsur.org/ar/jsur_ben102010.pdf) about the need to correct for multiple testing in some practical study evolving many variables e.g. functional MRI (fMRI). This short citation contains most of the message:
"[...] we completed an fMRI scanning session with a post-mortem... | Why is multiple comparison a problem? | An illustrating (and funny) article (http://www.jsur.org/ar/jsur_ben102010.pdf) about the need to correct for multiple testing in some practical study evolving many variables e.g. functional MRI (fMR | Why is multiple comparison a problem?
An illustrating (and funny) article (http://www.jsur.org/ar/jsur_ben102010.pdf) about the need to correct for multiple testing in some practical study evolving many variables e.g. functional MRI (fMRI). This short citation contains most of the message:
"[...] we completed an fM... | Why is multiple comparison a problem?
An illustrating (and funny) article (http://www.jsur.org/ar/jsur_ben102010.pdf) about the need to correct for multiple testing in some practical study evolving many variables e.g. functional MRI (fMR |
5,670 | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | You can write your own function based on what we know about the mechanics of the two-sample $t$-test. For example, this will do the job:
# m1, m2: the sample means
# s1, s2: the sample standard deviations
# n1, n2: the same sizes
# m0: the null value for the difference in means to be tested for. Default is 0.
# equal.... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | You can write your own function based on what we know about the mechanics of the two-sample $t$-test. For example, this will do the job:
# m1, m2: the sample means
# s1, s2: the sample standard deviat | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
You can write your own function based on what we know about the mechanics of the two-sample $t$-test. For example, this will do the job:
# m1, m2: the sample means
# s1, s2: the sample standard deviations
# n1, n2: the same ... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
You can write your own function based on what we know about the mechanics of the two-sample $t$-test. For example, this will do the job:
# m1, m2: the sample means
# s1, s2: the sample standard deviat |
5,671 | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | You just calculate it by hand:
$$
t = \frac{(\text{mean}_f - \text{mean}_m) - \text{expected difference}}{SE} \\
~\\
~\\
SE = \sqrt{\frac{sd_f^2}{n_f} + \frac{sd_m^2}{n_m}} \\
~\\
~\\
\text{where, }~~~df = n_m + n_f - 2
$$
The expected difference is probably zero.
If you want the p-value simply use the pt() function:... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | You just calculate it by hand:
$$
t = \frac{(\text{mean}_f - \text{mean}_m) - \text{expected difference}}{SE} \\
~\\
~\\
SE = \sqrt{\frac{sd_f^2}{n_f} + \frac{sd_m^2}{n_m}} \\
~\\
~\\
\text{where, } | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
You just calculate it by hand:
$$
t = \frac{(\text{mean}_f - \text{mean}_m) - \text{expected difference}}{SE} \\
~\\
~\\
SE = \sqrt{\frac{sd_f^2}{n_f} + \frac{sd_m^2}{n_m}} \\
~\\
~\\
\text{where, }~~~df = n_m + n_f - 2
$$... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
You just calculate it by hand:
$$
t = \frac{(\text{mean}_f - \text{mean}_m) - \text{expected difference}}{SE} \\
~\\
~\\
SE = \sqrt{\frac{sd_f^2}{n_f} + \frac{sd_m^2}{n_m}} \\
~\\
~\\
\text{where, } |
5,672 | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | You can do the calculations based on the formula in the book (on the web page), or you can generate random data that has the properties stated (see the mvrnorm function in the MASS package) and use the regular t.test function on the simulated data. | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | You can do the calculations based on the formula in the book (on the web page), or you can generate random data that has the properties stated (see the mvrnorm function in the MASS package) and use th | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
You can do the calculations based on the formula in the book (on the web page), or you can generate random data that has the properties stated (see the mvrnorm function in the MASS package) and use the regular t.test functio... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
You can do the calculations based on the formula in the book (on the web page), or you can generate random data that has the properties stated (see the mvrnorm function in the MASS package) and use th |
5,673 | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | The question asks about R, but the issue can arise with any other statistical software. Stata for example has various so-called immediate commands, which allow calculations from summary statistics alone. See http://www.stata.com/manuals13/rttest.pdf for the particular case of the ttesti command, which applies here. | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | The question asks about R, but the issue can arise with any other statistical software. Stata for example has various so-called immediate commands, which allow calculations from summary statistics alo | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
The question asks about R, but the issue can arise with any other statistical software. Stata for example has various so-called immediate commands, which allow calculations from summary statistics alone. See http://www.stata... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
The question asks about R, but the issue can arise with any other statistical software. Stata for example has various so-called immediate commands, which allow calculations from summary statistics alo |
5,674 | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | Another possible solution is to simulate the datasets and then use the standard t test function. It may be less efficient, computationally speaking, but it is very simple.
t.test.from.summary.data <- function(mean1, sd1, n1, mean2, sd2, n2, ...) {
data1 <- scale(1:n1)*sd1 + mean1
data2 <- scale(1:n2)*sd2 + mean... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data? | Another possible solution is to simulate the datasets and then use the standard t test function. It may be less efficient, computationally speaking, but it is very simple.
t.test.from.summary.data <- | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
Another possible solution is to simulate the datasets and then use the standard t test function. It may be less efficient, computationally speaking, but it is very simple.
t.test.from.summary.data <- function(mean1, sd1, n1,... | How to perform two-sample t-tests in R by inputting sample statistics rather than the raw data?
Another possible solution is to simulate the datasets and then use the standard t test function. It may be less efficient, computationally speaking, but it is very simple.
t.test.from.summary.data <- |
5,675 | When should I use a variational autoencoder as opposed to an autoencoder? | VAE is a framework that was proposed as a scalable way to do variational EM (or variational inference in general) on large datasets. Although it has an AE like structure, it serves a much larger purpose.
Having said that, one can, of course, use VAEs to learn latent representations. VAEs are known to give representatio... | When should I use a variational autoencoder as opposed to an autoencoder? | VAE is a framework that was proposed as a scalable way to do variational EM (or variational inference in general) on large datasets. Although it has an AE like structure, it serves a much larger purpo | When should I use a variational autoencoder as opposed to an autoencoder?
VAE is a framework that was proposed as a scalable way to do variational EM (or variational inference in general) on large datasets. Although it has an AE like structure, it serves a much larger purpose.
Having said that, one can, of course, use ... | When should I use a variational autoencoder as opposed to an autoencoder?
VAE is a framework that was proposed as a scalable way to do variational EM (or variational inference in general) on large datasets. Although it has an AE like structure, it serves a much larger purpo |
5,676 | When should I use a variational autoencoder as opposed to an autoencoder? | The standard autoencoder can be illustrated using the following graph:
As stated in the previous answers it can be viewed as just a nonlinear extension of PCA.
But compared to the variational autoencoder the vanilla autoencoder has the following drawback:
The fundamental problem with autoencoders, for generation, is ... | When should I use a variational autoencoder as opposed to an autoencoder? | The standard autoencoder can be illustrated using the following graph:
As stated in the previous answers it can be viewed as just a nonlinear extension of PCA.
But compared to the variational autoenc | When should I use a variational autoencoder as opposed to an autoencoder?
The standard autoencoder can be illustrated using the following graph:
As stated in the previous answers it can be viewed as just a nonlinear extension of PCA.
But compared to the variational autoencoder the vanilla autoencoder has the following... | When should I use a variational autoencoder as opposed to an autoencoder?
The standard autoencoder can be illustrated using the following graph:
As stated in the previous answers it can be viewed as just a nonlinear extension of PCA.
But compared to the variational autoenc |
5,677 | When should I use a variational autoencoder as opposed to an autoencoder? | TenaliRaman had some good points but he missed a lot of fundamental concepts as well. First it should be noted that the primary reason to use an AE-like framework is the latent space that allows us to compress the information and hopefully get independent factors out of it that represent high-level features of the dat... | When should I use a variational autoencoder as opposed to an autoencoder? | TenaliRaman had some good points but he missed a lot of fundamental concepts as well. First it should be noted that the primary reason to use an AE-like framework is the latent space that allows us t | When should I use a variational autoencoder as opposed to an autoencoder?
TenaliRaman had some good points but he missed a lot of fundamental concepts as well. First it should be noted that the primary reason to use an AE-like framework is the latent space that allows us to compress the information and hopefully get i... | When should I use a variational autoencoder as opposed to an autoencoder?
TenaliRaman had some good points but he missed a lot of fundamental concepts as well. First it should be noted that the primary reason to use an AE-like framework is the latent space that allows us t |
5,678 | When should I use a variational autoencoder as opposed to an autoencoder? | Choosing the distribution of the code in VAE allows for a better unsupervised representation learning where samples of the same class end up close to each other in the code space. Also this way, finding a semantic for the regions in the code space becomes easier. E.g, you would know from each area what class can be ge... | When should I use a variational autoencoder as opposed to an autoencoder? | Choosing the distribution of the code in VAE allows for a better unsupervised representation learning where samples of the same class end up close to each other in the code space. Also this way, findi | When should I use a variational autoencoder as opposed to an autoencoder?
Choosing the distribution of the code in VAE allows for a better unsupervised representation learning where samples of the same class end up close to each other in the code space. Also this way, finding a semantic for the regions in the code spa... | When should I use a variational autoencoder as opposed to an autoencoder?
Choosing the distribution of the code in VAE allows for a better unsupervised representation learning where samples of the same class end up close to each other in the code space. Also this way, findi |
5,679 | K-fold vs. Monte Carlo cross-validation | $k$-Fold Cross Validation
Suppose you have 100 data points. For $k$-fold cross validation, these 100 points are divided into $k$ equal sized and mutually-exclusive 'folds'. For $k$=10, you might assign points 1-10 to fold #1, 11-20 to fold #2, and so on, finishing by assigning points 91-100 to fold #10. Next, we select... | K-fold vs. Monte Carlo cross-validation | $k$-Fold Cross Validation
Suppose you have 100 data points. For $k$-fold cross validation, these 100 points are divided into $k$ equal sized and mutually-exclusive 'folds'. For $k$=10, you might assig | K-fold vs. Monte Carlo cross-validation
$k$-Fold Cross Validation
Suppose you have 100 data points. For $k$-fold cross validation, these 100 points are divided into $k$ equal sized and mutually-exclusive 'folds'. For $k$=10, you might assign points 1-10 to fold #1, 11-20 to fold #2, and so on, finishing by assigning po... | K-fold vs. Monte Carlo cross-validation
$k$-Fold Cross Validation
Suppose you have 100 data points. For $k$-fold cross validation, these 100 points are divided into $k$ equal sized and mutually-exclusive 'folds'. For $k$=10, you might assig |
5,680 | K-fold vs. Monte Carlo cross-validation | Let's assume $ N $ is the size of the dataset, $k$ is the number of the $k$-fold subsets , $n_t$ is the size of the training set and $n_v$ is the size of the validation set. Therefore, $N = k \times n_v$ for $k$-fold cross-validation and $N = n_t + n_v$ for Monte Carlo cross-validation.
$k$-fold cross-validation (kFCV... | K-fold vs. Monte Carlo cross-validation | Let's assume $ N $ is the size of the dataset, $k$ is the number of the $k$-fold subsets , $n_t$ is the size of the training set and $n_v$ is the size of the validation set. Therefore, $N = k \times | K-fold vs. Monte Carlo cross-validation
Let's assume $ N $ is the size of the dataset, $k$ is the number of the $k$-fold subsets , $n_t$ is the size of the training set and $n_v$ is the size of the validation set. Therefore, $N = k \times n_v$ for $k$-fold cross-validation and $N = n_t + n_v$ for Monte Carlo cross-val... | K-fold vs. Monte Carlo cross-validation
Let's assume $ N $ is the size of the dataset, $k$ is the number of the $k$-fold subsets , $n_t$ is the size of the training set and $n_v$ is the size of the validation set. Therefore, $N = k \times |
5,681 | K-fold vs. Monte Carlo cross-validation | The other two answers are great, I'll just add a two pictures as well as one synonym.
K-fold cross-validation (kFCV):
Monte Carlo cross-validation (MCCV) = Repeated random sub-sampling validation (RRSSV):
References:
The pictures come from (1) (pages 64 and 65), and the synonym is mentioned in (1) and (2).
(1) Re... | K-fold vs. Monte Carlo cross-validation | The other two answers are great, I'll just add a two pictures as well as one synonym.
K-fold cross-validation (kFCV):
Monte Carlo cross-validation (MCCV) = Repeated random sub-sampling validation ( | K-fold vs. Monte Carlo cross-validation
The other two answers are great, I'll just add a two pictures as well as one synonym.
K-fold cross-validation (kFCV):
Monte Carlo cross-validation (MCCV) = Repeated random sub-sampling validation (RRSSV):
References:
The pictures come from (1) (pages 64 and 65), and the syno... | K-fold vs. Monte Carlo cross-validation
The other two answers are great, I'll just add a two pictures as well as one synonym.
K-fold cross-validation (kFCV):
Monte Carlo cross-validation (MCCV) = Repeated random sub-sampling validation ( |
5,682 | K-fold vs. Monte Carlo cross-validation | What about in practice?
In certain situations (smaller data), I combine both Monte Carlo and K-Fold CV, into repeated, nested cross-validation:
Inner K-fold CV for hyperparameter selection
Outer K-fold CV for estimating generalization performance
Now, repeat steps 1 and 2 many times (Monte Carlo).
If for 2. you use K... | K-fold vs. Monte Carlo cross-validation | What about in practice?
In certain situations (smaller data), I combine both Monte Carlo and K-Fold CV, into repeated, nested cross-validation:
Inner K-fold CV for hyperparameter selection
Outer K-fo | K-fold vs. Monte Carlo cross-validation
What about in practice?
In certain situations (smaller data), I combine both Monte Carlo and K-Fold CV, into repeated, nested cross-validation:
Inner K-fold CV for hyperparameter selection
Outer K-fold CV for estimating generalization performance
Now, repeat steps 1 and 2 many t... | K-fold vs. Monte Carlo cross-validation
What about in practice?
In certain situations (smaller data), I combine both Monte Carlo and K-Fold CV, into repeated, nested cross-validation:
Inner K-fold CV for hyperparameter selection
Outer K-fo |
5,683 | K-fold vs. Monte Carlo cross-validation | k-fold CV trains on more data than are held out for validation; this is a problem. MCCV has great potential to correct this error; for details, see below, but the validation set should always be at least as big as the training set, and not the other way around.
According to Jun Shao's seminal 1993 paper, "Linear Model... | K-fold vs. Monte Carlo cross-validation | k-fold CV trains on more data than are held out for validation; this is a problem. MCCV has great potential to correct this error; for details, see below, but the validation set should always be at l | K-fold vs. Monte Carlo cross-validation
k-fold CV trains on more data than are held out for validation; this is a problem. MCCV has great potential to correct this error; for details, see below, but the validation set should always be at least as big as the training set, and not the other way around.
According to Jun ... | K-fold vs. Monte Carlo cross-validation
k-fold CV trains on more data than are held out for validation; this is a problem. MCCV has great potential to correct this error; for details, see below, but the validation set should always be at l |
5,684 | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | Wang, Kaijun, Baijie Wang, and Liuqing Peng. "CVAP: Validation for cluster analyses." Data Science Journal 0 (2009): 0904220071.:
To measure the quality of clustering results, there are two kinds of
validity indices: external indices and internal indices.
An external
index is a measure of agreement between two partiti... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | Wang, Kaijun, Baijie Wang, and Liuqing Peng. "CVAP: Validation for cluster analyses." Data Science Journal 0 (2009): 0904220071.:
To measure the quality of clustering results, there are two kinds of
| Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
Wang, Kaijun, Baijie Wang, and Liuqing Peng. "CVAP: Validation for cluster analyses." Data Science Journal 0 (2009): 0904220071.:
To measure the quality of clustering results, there are two kinds of
validity indices: ex... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
Wang, Kaijun, Baijie Wang, and Liuqing Peng. "CVAP: Validation for cluster analyses." Data Science Journal 0 (2009): 0904220071.:
To measure the quality of clustering results, there are two kinds of
|
5,685 | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | An outline of internal clustering criteria (internal cluster validation indices)
This is the excerpt from my documentation of a number of popular internal clustering criteria I've programmed, as a user, for SPSS Statistics (see my web page).
1. Reflections
Internal clustering criteria or indices exist to assess interna... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | An outline of internal clustering criteria (internal cluster validation indices)
This is the excerpt from my documentation of a number of popular internal clustering criteria I've programmed, as a use | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
An outline of internal clustering criteria (internal cluster validation indices)
This is the excerpt from my documentation of a number of popular internal clustering criteria I've programmed, as a user, for SPSS Statisti... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
An outline of internal clustering criteria (internal cluster validation indices)
This is the excerpt from my documentation of a number of popular internal clustering criteria I've programmed, as a use |
5,686 | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | There are some internal clustering methods. In particular with respect to the distances of objects in the data set. See for example Silhouette coefficient [on Wikipedia].
You must however be aware that there are algorithms such as k-means that try to optimize exactly these parameters, and as such you introduce a partic... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | There are some internal clustering methods. In particular with respect to the distances of objects in the data set. See for example Silhouette coefficient [on Wikipedia].
You must however be aware tha | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
There are some internal clustering methods. In particular with respect to the distances of objects in the data set. See for example Silhouette coefficient [on Wikipedia].
You must however be aware that there are algorith... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
There are some internal clustering methods. In particular with respect to the distances of objects in the data set. See for example Silhouette coefficient [on Wikipedia].
You must however be aware tha |
5,687 | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | If your problem is to evaluate the clustering result among a list of clustering algorithms (i.e choosing the best clustering algorithm for a certain input dataset) another idea is to use an evaluation metric that someone else used as evaluation function to maximize, in order to create his clustering algorithm.
A very ... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate] | If your problem is to evaluate the clustering result among a list of clustering algorithms (i.e choosing the best clustering algorithm for a certain input dataset) another idea is to use an evaluatio | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
If your problem is to evaluate the clustering result among a list of clustering algorithms (i.e choosing the best clustering algorithm for a certain input dataset) another idea is to use an evaluation metric that someon... | Evaluation measures of goodness or validity of clustering (without having truth labels) [duplicate]
If your problem is to evaluate the clustering result among a list of clustering algorithms (i.e choosing the best clustering algorithm for a certain input dataset) another idea is to use an evaluatio |
5,688 | Fake uniform random numbers: More evenly distributed than true uniform data | Yes, there are many ways to produce a sequence of numbers that are more evenly distributed than random uniforms. In fact, there is a whole field dedicated to this question; it is the backbone of quasi-Monte Carlo (QMC). Below is a brief tour of the absolute basics.
Measuring uniformity
There are many ways to do this, b... | Fake uniform random numbers: More evenly distributed than true uniform data | Yes, there are many ways to produce a sequence of numbers that are more evenly distributed than random uniforms. In fact, there is a whole field dedicated to this question; it is the backbone of quasi | Fake uniform random numbers: More evenly distributed than true uniform data
Yes, there are many ways to produce a sequence of numbers that are more evenly distributed than random uniforms. In fact, there is a whole field dedicated to this question; it is the backbone of quasi-Monte Carlo (QMC). Below is a brief tour of... | Fake uniform random numbers: More evenly distributed than true uniform data
Yes, there are many ways to produce a sequence of numbers that are more evenly distributed than random uniforms. In fact, there is a whole field dedicated to this question; it is the backbone of quasi |
5,689 | Fake uniform random numbers: More evenly distributed than true uniform data | One way to do this would be to generate uniform random numbers, then test for "closeness" using any method you like and then delete random items that are too close to others and choose another set of random uniforms to make up for them.
Would such a distribution pass every test of uniformity? I sure hope not! It's no l... | Fake uniform random numbers: More evenly distributed than true uniform data | One way to do this would be to generate uniform random numbers, then test for "closeness" using any method you like and then delete random items that are too close to others and choose another set of | Fake uniform random numbers: More evenly distributed than true uniform data
One way to do this would be to generate uniform random numbers, then test for "closeness" using any method you like and then delete random items that are too close to others and choose another set of random uniforms to make up for them.
Would s... | Fake uniform random numbers: More evenly distributed than true uniform data
One way to do this would be to generate uniform random numbers, then test for "closeness" using any method you like and then delete random items that are too close to others and choose another set of |
5,690 | Fake uniform random numbers: More evenly distributed than true uniform data | This is known as a "hard-core" poisson point process - so named by Brian Ripley in the 1970s; i.e. you want it to be random, but you don't want any points to be too close together. The "hard-core" can be imagined as a buffer zone around which other points cannot intrude.
Imagine you're recording the position of some c... | Fake uniform random numbers: More evenly distributed than true uniform data | This is known as a "hard-core" poisson point process - so named by Brian Ripley in the 1970s; i.e. you want it to be random, but you don't want any points to be too close together. The "hard-core" ca | Fake uniform random numbers: More evenly distributed than true uniform data
This is known as a "hard-core" poisson point process - so named by Brian Ripley in the 1970s; i.e. you want it to be random, but you don't want any points to be too close together. The "hard-core" can be imagined as a buffer zone around which ... | Fake uniform random numbers: More evenly distributed than true uniform data
This is known as a "hard-core" poisson point process - so named by Brian Ripley in the 1970s; i.e. you want it to be random, but you don't want any points to be too close together. The "hard-core" ca |
5,691 | Fake uniform random numbers: More evenly distributed than true uniform data | With respect to batch generation in advance, I would generate a large number of sets of pseudorandom variates, and then test them with a test such as the Kolmogorov-Smirnov test. You will want to select the set that has the highest p-value (i.e., $p \approx 1$ is ideal). Note that this will be slow, but as $N$ gets l... | Fake uniform random numbers: More evenly distributed than true uniform data | With respect to batch generation in advance, I would generate a large number of sets of pseudorandom variates, and then test them with a test such as the Kolmogorov-Smirnov test. You will want to sel | Fake uniform random numbers: More evenly distributed than true uniform data
With respect to batch generation in advance, I would generate a large number of sets of pseudorandom variates, and then test them with a test such as the Kolmogorov-Smirnov test. You will want to select the set that has the highest p-value (i.... | Fake uniform random numbers: More evenly distributed than true uniform data
With respect to batch generation in advance, I would generate a large number of sets of pseudorandom variates, and then test them with a test such as the Kolmogorov-Smirnov test. You will want to sel |
5,692 | Fake uniform random numbers: More evenly distributed than true uniform data | I would formalize your problem this way: You want a distribution over $[0,1]^n$ such that the density is $f(x) \propto e^{\left(\frac1k\sum_{ij}\lvert x_i-x_j \rvert^{k}\right)^{\frac1k}}$ for some $k<0$ quantifying the repulsion of points.
One easy way to generate such vectors is to do Gibbs sampling. | Fake uniform random numbers: More evenly distributed than true uniform data | I would formalize your problem this way: You want a distribution over $[0,1]^n$ such that the density is $f(x) \propto e^{\left(\frac1k\sum_{ij}\lvert x_i-x_j \rvert^{k}\right)^{\frac1k}}$ for some $ | Fake uniform random numbers: More evenly distributed than true uniform data
I would formalize your problem this way: You want a distribution over $[0,1]^n$ such that the density is $f(x) \propto e^{\left(\frac1k\sum_{ij}\lvert x_i-x_j \rvert^{k}\right)^{\frac1k}}$ for some $k<0$ quantifying the repulsion of points.
On... | Fake uniform random numbers: More evenly distributed than true uniform data
I would formalize your problem this way: You want a distribution over $[0,1]^n$ such that the density is $f(x) \propto e^{\left(\frac1k\sum_{ij}\lvert x_i-x_j \rvert^{k}\right)^{\frac1k}}$ for some $ |
5,693 | What is the difference between finite and infinite variance | $\DeclareMathOperator{\E}{E} \DeclareMathOperator{\var}{var}$
What does it mean for a random variable to have "infinite variance"? What does it mean for a random variable to have infinite expectation? The explanation in both cases are rather similar, so let us start with the case of expectation, and then variance aft... | What is the difference between finite and infinite variance | $\DeclareMathOperator{\E}{E} \DeclareMathOperator{\var}{var}$
What does it mean for a random variable to have "infinite variance"? What does it mean for a random variable to have infinite expectation | What is the difference between finite and infinite variance
$\DeclareMathOperator{\E}{E} \DeclareMathOperator{\var}{var}$
What does it mean for a random variable to have "infinite variance"? What does it mean for a random variable to have infinite expectation? The explanation in both cases are rather similar, so let ... | What is the difference between finite and infinite variance
$\DeclareMathOperator{\E}{E} \DeclareMathOperator{\var}{var}$
What does it mean for a random variable to have "infinite variance"? What does it mean for a random variable to have infinite expectation |
5,694 | What is the difference between finite and infinite variance | Variance is the measure of dispersion of the distribution of values of a random variable. It's not the only such measure, e.g. mean absolute deviation is one of alternatives.
The infinite variance means that random values don't tend to concentrate around the mean too tightly. It could mean that there's large enough pro... | What is the difference between finite and infinite variance | Variance is the measure of dispersion of the distribution of values of a random variable. It's not the only such measure, e.g. mean absolute deviation is one of alternatives.
The infinite variance mea | What is the difference between finite and infinite variance
Variance is the measure of dispersion of the distribution of values of a random variable. It's not the only such measure, e.g. mean absolute deviation is one of alternatives.
The infinite variance means that random values don't tend to concentrate around the m... | What is the difference between finite and infinite variance
Variance is the measure of dispersion of the distribution of values of a random variable. It's not the only such measure, e.g. mean absolute deviation is one of alternatives.
The infinite variance mea |
5,695 | What is the difference between finite and infinite variance | An alternative way to look at is by the quantile function.
$$Q(F(x)) = x$$
Then we can compute a moment or expectation
$$E(T(x)) = \int_{-\infty}^\infty T(x) f(x) dx\\$$
alternatively as (replacing $f(x)dx = dF$):
$$E(T(x)) = \int_{0}^1 T(Q(F)) dF \\$$
Say we wish to compute the first moment then $T(x) = x$. In the i... | What is the difference between finite and infinite variance | An alternative way to look at is by the quantile function.
$$Q(F(x)) = x$$
Then we can compute a moment or expectation
$$E(T(x)) = \int_{-\infty}^\infty T(x) f(x) dx\\$$
alternatively as (replacing | What is the difference between finite and infinite variance
An alternative way to look at is by the quantile function.
$$Q(F(x)) = x$$
Then we can compute a moment or expectation
$$E(T(x)) = \int_{-\infty}^\infty T(x) f(x) dx\\$$
alternatively as (replacing $f(x)dx = dF$):
$$E(T(x)) = \int_{0}^1 T(Q(F)) dF \\$$
Say w... | What is the difference between finite and infinite variance
An alternative way to look at is by the quantile function.
$$Q(F(x)) = x$$
Then we can compute a moment or expectation
$$E(T(x)) = \int_{-\infty}^\infty T(x) f(x) dx\\$$
alternatively as (replacing |
5,696 | What is the difference between finite and infinite variance | Most distributions you encounter probably have finite variance. Here is a discrete example $X$ that has infinite variance but finite mean:
Let its probability mass function be $ p(k) = c/|k|^3$, for $k \in \mathbb{Z} \setminus\{0\}$, $p(0) = 0$, where $c = (2\zeta(3))^{-1} := (2\sum_{k=1}^\infty 1/k^3)^{-1} < \infty$.... | What is the difference between finite and infinite variance | Most distributions you encounter probably have finite variance. Here is a discrete example $X$ that has infinite variance but finite mean:
Let its probability mass function be $ p(k) = c/|k|^3$, for | What is the difference between finite and infinite variance
Most distributions you encounter probably have finite variance. Here is a discrete example $X$ that has infinite variance but finite mean:
Let its probability mass function be $ p(k) = c/|k|^3$, for $k \in \mathbb{Z} \setminus\{0\}$, $p(0) = 0$, where $c = (2... | What is the difference between finite and infinite variance
Most distributions you encounter probably have finite variance. Here is a discrete example $X$ that has infinite variance but finite mean:
Let its probability mass function be $ p(k) = c/|k|^3$, for |
5,697 | How is Naive Bayes a Linear Classifier? | In general the naive Bayes classifier is not linear, but if the likelihood factors $p(x_i \mid c)$ are from exponential families, the naive Bayes classifier corresponds to a linear classifier in a particular feature space. Here is how to see this.
You can write any naive Bayes classifier as*
$$p(c = 1 \mid \mathbf{x}) ... | How is Naive Bayes a Linear Classifier? | In general the naive Bayes classifier is not linear, but if the likelihood factors $p(x_i \mid c)$ are from exponential families, the naive Bayes classifier corresponds to a linear classifier in a par | How is Naive Bayes a Linear Classifier?
In general the naive Bayes classifier is not linear, but if the likelihood factors $p(x_i \mid c)$ are from exponential families, the naive Bayes classifier corresponds to a linear classifier in a particular feature space. Here is how to see this.
You can write any naive Bayes cl... | How is Naive Bayes a Linear Classifier?
In general the naive Bayes classifier is not linear, but if the likelihood factors $p(x_i \mid c)$ are from exponential families, the naive Bayes classifier corresponds to a linear classifier in a par |
5,698 | How is Naive Bayes a Linear Classifier? | It is linear only if the class conditional variance matrices are the same for both classes. To see this write down the ration of the log posteriors and you'll only get a linear function out of it if the corresponding variances are the same.
Otherwise it is quadratic. | How is Naive Bayes a Linear Classifier? | It is linear only if the class conditional variance matrices are the same for both classes. To see this write down the ration of the log posteriors and you'll only get a linear function out of it if t | How is Naive Bayes a Linear Classifier?
It is linear only if the class conditional variance matrices are the same for both classes. To see this write down the ration of the log posteriors and you'll only get a linear function out of it if the corresponding variances are the same.
Otherwise it is quadratic. | How is Naive Bayes a Linear Classifier?
It is linear only if the class conditional variance matrices are the same for both classes. To see this write down the ration of the log posteriors and you'll only get a linear function out of it if t |
5,699 | How is Naive Bayes a Linear Classifier? | I'd like add one additional point: the reason for some of the confusion rests on what it means to be performing "Naive Bayes classification".
Under the broad topic of "Gaussian Discriminant Analysis (GDA)" there are several techniques: QDA, LDA, GNB, and DLDA (quadratic DA, linear DA, gaussian naive bayes, diagonal L... | How is Naive Bayes a Linear Classifier? | I'd like add one additional point: the reason for some of the confusion rests on what it means to be performing "Naive Bayes classification".
Under the broad topic of "Gaussian Discriminant Analysis | How is Naive Bayes a Linear Classifier?
I'd like add one additional point: the reason for some of the confusion rests on what it means to be performing "Naive Bayes classification".
Under the broad topic of "Gaussian Discriminant Analysis (GDA)" there are several techniques: QDA, LDA, GNB, and DLDA (quadratic DA, lin... | How is Naive Bayes a Linear Classifier?
I'd like add one additional point: the reason for some of the confusion rests on what it means to be performing "Naive Bayes classification".
Under the broad topic of "Gaussian Discriminant Analysis |
5,700 | Test for bimodal distribution | Another possible approach to this issue is to think about what might be going on behind the scenes that is generating the data you see. That is, you can think in terms of a mixture model, for example, a Gaussian mixture model. For instance, you might believe that your data are drawn from either a single normal popula... | Test for bimodal distribution | Another possible approach to this issue is to think about what might be going on behind the scenes that is generating the data you see. That is, you can think in terms of a mixture model, for example | Test for bimodal distribution
Another possible approach to this issue is to think about what might be going on behind the scenes that is generating the data you see. That is, you can think in terms of a mixture model, for example, a Gaussian mixture model. For instance, you might believe that your data are drawn from... | Test for bimodal distribution
Another possible approach to this issue is to think about what might be going on behind the scenes that is generating the data you see. That is, you can think in terms of a mixture model, for example |
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