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Simulating and Visualising the Central Limit Theorem

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Re: Simulating and Visualising the Central Limit Theorem

#61

Post by [deleted] »

godelski wrote: post #59
kazinator wrote: post #56

> I always avoided statistics subjects. I don't believe you. Even if you had a good control group, the fact that one subject engaged in fewer statistics subjects than the control group doesn't lead to the conclusion that there is an avoidance mechanism (or any mechanism). You need a sample of something like 30 or 40 more of you to detect a statistically valid pattern of diminished engagement with statistics subjects…

Are you okay? Seriously, I don't understand what this comment is. The OP just said when they were in college they were afraid of taking a statistics class. Your comment is... completely unrelated an nonsensical. Like you don't believe they avoided taking statistics classes? Then you make some odd response where you use the wrong kind of "subject". Is English not your first language? Are you drunk or high? Did you mis…

[deleted]

Re: Simulating and Visualising the Central Limit Theorem

#62

Post by globalnode »

k2enemy wrote: post #31
globalnode wrote: post #17

The definition under "A Brief Recap" seems incorrect. The sample size doesn't approach infinity, the number of samples does. I'm in a similar situation to the author, I skipped stats, so I could be wrong. Overall great article though.

It is correct in the article. As the sample size approaches infinity, the distribution of the sample means approaches normal. https://en.wikipedia.org/wiki/Central_limit_theorem

Not sure what you're stating but it seems to be made of straw.

Re: Simulating and Visualising the Central Limit Theorem

#64

Post by lottin »

ngriffiths wrote: post #49
lottin wrote: post #5

Looking at the R code in this article, I'm having a hard time understanding the appeal of tidyverse.

For me the appeal is less that tidyverse is great and more that the R standard library is horrible . It's full of esoteric names, inconsistent use and order of parameters, unreasonable default behavior, behavior that surprises you coming from other programming experience. It's all in a couple massive packages instead of broken up into manageable pieces. Tidyverse is imperfect and it feels heavy-handed and awkward to…

I think the R standard library is quite excellent. It pretty much follows the Unix philosophy of "doing one thing right". The only exception being `reshape` which tries to do too many things, but it can usually be avoided. It isn't inconsistent. I think the problem is the lack of tutorials that explain how to use all the data manipulation tools effectively, because there are quite a lot of functions and it isn't easy to figure out how to use them together to accomplish practical things. Tidyverse may be consistent with itself, but it's inconsistent with everything else. Either you only use tidyverse, or your program looks like an inconsistent mess.

Re: Simulating and Visualising the Central Limit Theorem

#65

Post by ngriffiths »

lottin wrote: post #64
ngriffiths wrote: post #49

Earlier quoted context omitted.

For me the appeal is less that tidyverse is great and more that the R standard library is horrible . It's full of esoteric names, inconsistent use and order of parameters, unreasonable default behavior, behavior that surprises you coming from other programming experience. It's all in a couple massive packages instead of broken up into manageable pieces. Tidyverse is imperfect and it feels heavy-handed and awkward to…

I think the R standard library is quite excellent. It pretty much follows the Unix philosophy of "doing one thing right". The only exception being `reshape` which tries to do too many things, but it can usually be avoided. It isn't inconsistent. I think the problem is the lack of tutorials that explain how to use all the data manipulation tools effectively, because there are quite a lot of functions and it isn't easy…

Honestly, it might partly be that I've used R somewhat irregularly and I put a lot of value in design choices that "make sense" and are easier to remember. I'm sure once you are intimately familiar with the whole base language you can be really happy and productive with it.

> I think the problem is the lack of tutorials that explain how to use all the data manipulation tools effectively, because there are quite a lot of functions and it isn't easy to figure out how to use them together to accomplish practical things.

Most languages solve this problem by not cramming quite a lot of functions in one package and using shared design concepts to make it easier to fit them together. I don't think tutorials would solve these problems effectively but I guess it makes sense that they affect newer users the most.

> Tidyverse may be consistent with itself, but it's inconsistent with everything else.

Yeah, totally agree and I really dislike this part.

Re: Simulating and Visualising the Central Limit Theorem

#66

Post by mturmon »

kqr wrote: post #43

This is a very neat illustration, but I want to leave a reminder that when we cherry-pick well-behaved distributions for illustrating the CLT, people get unrealistic expectations of what it means: https://entropicthoughts.com/it-takes-long-to-become-gaussia...

The article you link is not using the CLT correctly.

The CLT gives a result about a recentered and rescaled version of the sum of iid variates. CLT does not give a result about the sum itself, and the article is invoking such a result in the “files” and “lakes” examples.

I’m aware that it can appear that CLT does say something about the sum itself. The normal distribution of the recentered/rescaled sum can be translated into a distribution pertaining to the sum itself, due to the closure of Normals under linear transformation. But the limiting arguments don’t work any more.

What I mean by that statement: in the CLT, the errors of the distributional approximation go to zero as N gets large. For the sum, of course the error will not go to zero - the sum itself is diverging as N grows, and so is its distribution. (The point of centering and rescaling is to establish a non-diverging limit distribution.)

So for instance, the third central moment of the Gaussian is zero. But the third central moment of a sum of N iid exponentials will diverge quickly with N (it’s a gamma with shape parameter N). This third-moment divergence will happen for any base distribution with non-zero skew.

The above points out another fact about the CLT: it does not say anything about the tails of the limit distribution. Just about the core. So CLT does not help with large deviations or very low-probability events. This is another reason the post is mistaken, which you can see in the “files” example where it talks about the upper tail of the sum. The CLT does not apply there.

Re: Simulating and Visualising the Central Limit Theorem

#67

Post by mturmon »

mturmon wrote: post #66
kqr wrote: post #43

This is a very neat illustration, but I want to leave a reminder that when we cherry-pick well-behaved distributions for illustrating the CLT, people get unrealistic expectations of what it means: https://entropicthoughts.com/it-takes-long-to-become-gaussia...

The article you link is not using the CLT correctly. The CLT gives a result about a recentered and rescaled version of the sum of iid variates. CLT does not give a result about the sum itself, and the article is invoking such a result in the “files” and “lakes” examples. I’m aware that it can appear that CLT does say something about the sum itself. The normal distribution of the recentered/rescaled sum can be transla…

Postscript: looking at the lesswrong link referenced by the post above, you will notice that the “eyeball metric” density plots happen to be recentered and scaled so that they capture the mass of the density. This is the graphical counterpart of the algebraic scaling and centering needed in the CLT.
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