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How do I develop an intuitive understanding of statistics?

Anonymous Mon 26 Oct 16:54:24 2020 No.12275423 View Reply Original Report

Quoted By: >>12276225 >>12276272 >>12276329 >>12276380 >>12276446 >>12279360 >>12279594 >>12282205 >>12288475

I know basic stuff like ANOVA, Hypothesis testing etc the basic first course undergrad content but how do I get to a level where I can deeply understand the mechanics of statistics ? My ultimate goal would be to get to a level where I can produce new theories and/or synthesize existing ones.

TD;DR What do I need to know to get on his level or at least close to it, If you dont know R Fisher, hes the father of stats

Anonymous

Anonymous Mon 26 Oct 2020 20:38:17 No.12276225 Report

Quoted By: >>12276272 >>12279354

>>12275423
Literally study maths and then go into statistics

Anonymous

Anonymous Mon 26 Oct 2020 20:50:32 No.12276272 Report

Quoted By: >>12276380 >>12276739

>>12275423
Basically this >>12276225

You will need to study real analysis, linear algebra, and differential equations. By then you will really be developing an deeper understanding of the inner workings of statistics. After than you would need to learn measure theory and stochastic calculus. Of course, you should also continue to use statistic in applied contexts. Mathematical biology and the applied areas of computer science (e.g. 'data analytics', 'informatics', 'machine learning', etc) are probably the best areas to get this kind of exposure - of course in other areas like psychology and sociology they also use statistics, and they can be interesting subjects, but the statistical methods they use are usually extremely rudimentary and they tend to exclude the details from publications.

By that point, if you know measure theory and stochastic calculus and you feel comfortable working with statistics in applied contexts (e.g. mathematical biology), then I would imagine you would probably be able to start reading and understanding a decent body of research literature. From that point, it would be up to you to begin specializing and looking deeper into specific research topics.

That being said, take everything I say with a grain of salt. I'm graduating with a math degree very shortly, but I never got really deep into statistics, because of course statistics really constitutes its own field of study.

Anonymous

Anonymous Mon 26 Oct 2020 21:06:33 No.12276329 Report

Quoted By: >>12276739

>>12275423
There's understanding the "mechanics" of statistics, which is just math like calculus, linear algebra, etc. Then there's understanding the intuition behind statistics, which is the justification of the mechanics and is equally important. For instance, one may ask why the mean of a sample from a normally distributed population is a good estimate of the population mean itself? Maximizing the likelihood function provides an intuitive explanation of this question and gives a reason for why the sample mean rather than say the 25th percentile is a better estimate of the population mean.

Getting this kind of intuition requires studying the mathematics and also meditating a bit on the reason behind the mathematics. As for the level of Fisher, you need experience analyzing actual problems. Most statistical breakthroughs are driven by necessity rather than arrived at through theory alone. Limitations are identified with current methodology, and people work on ways to remedy these limitations.

Anonymous

Anonymous Mon 26 Oct 2020 21:19:18 No.12276380 Report

Quoted By: >>12276739

>>12275423
When you say "produce new theories and/or synthesize existing ones." do you mean from a mathematical/statistical research point of view? Do you mean more machine learning? Do you mean coming up with arbitrarily specific statistical models for your own experiments in a STEM field of choice?

Each of these will lead to different recommendations. Imo this advice: >>12276272 is terrible unless you really want to go into mathematical stats research. Even then, you should start reading research before you have a deep understanding of analysis, measure theory or stochastic calc, and you should prioritize applications over those three courses along the way. measure theory and SDEs are subjects that typically aren't covered until PhD coursework, and unless you're doing theoretical research, you'll rarely use them. That doesn't mean they're not important, it's just that for doing stats they don't matter as much. Also for many applications applied functional analysis is more important than SDEs (e.g. Bayesian non-parametrics).

Imo the best way to get a good general stats background would be to just follow along a stats major from an Ivy League school. Look up syllabi, exercises, etc. Worry about highly theoretical stuff later. Focus on foundations and projects.

Anonymous

Anonymous Mon 26 Oct 2020 21:39:31 No.12276446 Report

Quoted By: >>12276478

>>12275423
Look up entropy and cross-entropy.

Anonymous

Anonymous Mon 26 Oct 2020 21:47:44 No.12276478 Report

Quoted By:

>>12276446
some insights:
maximizing likelihood is equivalent to minimizing the cross entropy (or again equivalently, the Kullback–Leibler divergence) of the model distribution with the empirical distribution

The Uniform distribution (a,b) has maximum entropy (i.e. least informative) among all distributions with support (a.b)
The Normal distribution ?, ?^2 is the maximum entropy distribution among all distributions with support (-infinity, infinity), expected value ? and variance ?^2.
And that's why we always use them. They're Occam's razor.

Anonymous

Anonymous Mon 26 Oct 2020 22:50:47 No.12276739 Report

Quoted By: >>12276752 >>12276891 >>12277512

Wow great answers in this thread thank you!

>>12276272
>course statistics really constitutes its own field of study.
How and why? Isnt it just a subset of applied math?

>>12276329
>most statistical breakthroughs are driven by necessity rather than arrived at through theory alone.
Wow now that I think about it you're right, its less theoretical and more real world. Never realized that before.

>>12276380
>Do you mean coming up with arbitrarily specific statistical models for your own experiments in a STEM field of choice?
Yes

For context this is my degree syllabus for my degree https://www.unisa.ac.za/sites/corporate/default/Register-to-study-through-Unisa/Undergraduate-&-honours-qualifications/Find-your-qualification-&-choose-your-modules/All-qualifications/Bachelor-of-Commerce-in-Quantitative-Management-Revised-Curriculum-2019-(98311-%E2%80%93-QMA)

>inb4 not science
Its got stats an math courses. Am I just waiting my time learning more because someone with a pure math degree will always out do me? Thats the feeling I have

Anonymous

Anonymous Mon 26 Oct 2020 22:54:49 No.12276752 Report

Quoted By: >>12276780

>>12276739
Well, Fisher was a biologist.

Anonymous

Anonymous Mon 26 Oct 2020 23:10:58 No.12276780 Report

Quoted By:

>>12276752
Holy shit you're right I can apply stats to the things I like...

Anonymous

Anonymous Mon 26 Oct 2020 23:52:37 No.12276891 Report

Quoted By:

>>12276739
Cool, then 100% don't follow the advice of the anon I quoted. I also dgaf that it's not stem –people on this board are so pretentious and ridiculous.

wrt stats stuff, I'll still stick to my advice about filling in your holes with, e.g. Stanford's stats major curriculum type resources. Maybe more important though is to pick up some projects to fuck around with, and read papers that use interesting statistical methodologies in your field. That last point in particular is super important.

Also, a really fun, light, but still incredibly valuable resource is MclReath's Statistical Rethinking. It has basically no mathematical prereqs, it'll give you a wonderful overview of bayesian approaches, and most importantly, it'll change the way you look at statistics. He also has great lectures on line

Do you know calc and linear algebra? It looks like you do, but if you don't, I'd start with MIT OCW single/multivariable calc and the Strang course on LA while following the Mclreath book before you do any of the syllabus following stuff I was saying

Anonymous

Anonymous Tue 27 Oct 2020 03:47:32 No.12277512 Report

Quoted By:

>>12276739
Yes statistics is a subfield of applied math, but it has grown so large that it has basically become its own discipline. The same thing happened with logic/theoretical computer science.

Anonymous

Anonymous Tue 27 Oct 2020 17:51:23 No.12279354 Report

Quoted By: >>12279701

>>12276225
How do you study math?

Anonymous

Anonymous Tue 27 Oct 2020 17:52:48 No.12279360 Report

Quoted By:

>>12275423
By being biased toward one side

Anonymous

Anonymous Tue 27 Oct 2020 18:50:50 No.12279594 Report

Quoted By: >>12285217

>>12275423

Statistics is different. Most people who are not good at maths, are good at statistics.

Those who are really good at maths, hate statistics.

For example, a lot of lawyers would be good at statistics. It is theory based, and you make judgements often qualitative judgements.

I thought that Nightingale woman was the founder of statistics.

Anonymous

Anonymous Tue 27 Oct 2020 19:16:55 No.12279701 Report

Quoted By: >>12279837

>>12279354
you open up a textbook and read it

Anonymous

Anonymous Tue 27 Oct 2020 20:07:08 No.12279837 Report

Quoted By: >>12279855

>>12279701
Not a good answer

Anonymous

Anonymous Tue 27 Oct 2020 20:12:28 No.12279855 Report

Quoted By: >>12281785

>>12279837
That's how I did it and it worked really well.
You open up a textbook and read the whole thing. If you have questions, you google them. Simple as.

Anonymous

Anonymous Tue 27 Oct 2020 20:16:06 No.12279866 Report

Quoted By:

Study the essential rules of probability theory, learn about how the different distributions relate to each other like binomial, poisson, normal etc.

Anonymous

Anonymous Wed 28 Oct 2020 10:20:53 No.12281785 Report

Quoted By: >>12282270

>>12279855
Where should I start with math?

Anonymous

Anonymous Wed 28 Oct 2020 10:35:16 No.12281809 Report

Quoted By:

I'm racist and that's how I intuitively know stats

Anonymous

Anonymous Wed 28 Oct 2020 14:19:51 No.12282205 Report

Quoted By:

>>12275423
bump

Anonymous

Anonymous Wed 28 Oct 2020 14:53:48 No.12282270 Report

Quoted By: >>12283175

>>12281785
Depends on your level. If you are at high-school level, then go to a good uni's math department website and find it's curricula and respective resources. Start with the first semester and keep going.

Anonymous

Anonymous Wed 28 Oct 2020 19:58:20 No.12283175 Report

Quoted By: >>12283230 >>12288659

>>12282270
Im first year uni this is my course https://www.unisa.ac.za/sites/corporate/default/Register-to-study-through-Unisa/Undergraduate-&-honours-qualifications/Find-your-qualification-&-choose-your-modules/All-qualifications/Bachelor-of-Commerce-in-Quantitative-Management-Revised-Curriculum-2019-(98311-%E2%80%93-QMA)

Anonymous

Anonymous Wed 28 Oct 2020 20:10:31 No.12283230 Report

Quoted By: >>12283465

>>12283175
I see.
You're not gonna learn/understand math properly the way your uni is gonna teach you, but on the other hand, you have other courses as well, so it's up to you to decide how to spend your time.

Anonymous

Anonymous Wed 28 Oct 2020 21:10:54 No.12283465 Report

Quoted By: >>12283643 >>12288362

>>12283230
how does one learn math /properly/ then?

Anonymous

Anonymous Wed 28 Oct 2020 21:54:05 No.12283638 Report

Quoted By: >>12283643 >>12285705

For the math you'll need on economics, I'd say study calculus, then linear algebra, then multivariable calculus, then probability and then statistics.

For calculus there's Spivak.
For Linear Algebra there's Hoffman&Kunze and Axler (I've only read Axler)
For Multivariable Calculus I guess Marsden&Tromba.
For Probability, I don't really know, but I see Sheldon Ross' book being recommended often. There's also some great lectures on from Harvard on youtube.
For Statistics, I am not sure either. There's Cassela, but it might be too autistic. For more on the machine learning side, which is essentially "modern statistics" there's Bishop and there's also Tibshirani et al.

There's also some other great resources like 3blue1brown's videos.
Also, any unergrad question you will think of, will have an answer in math.stackexchange.com

Anonymous

Anonymous Wed 28 Oct 2020 21:55:08 No.12283643 Report

Quoted By:

>>12283465
>>12283638

Anonymous

Anonymous Thu 29 Oct 2020 07:01:09 No.12285217 Report

Quoted By:

>>12279594
>Most people who are not good at maths, are good at statistics.
Holy shit no

Anonymous

Anonymous Thu 29 Oct 2020 11:59:23 No.12285705 Report

Quoted By: >>12287029

>>12283638
thank you

Anonymous

Anonymous Thu 29 Oct 2020 20:03:38 No.12287029 Report

Quoted By:

>>12285705
np fren

Anonymous

Anonymous Fri 30 Oct 2020 03:30:24 No.12288362 Report

Quoted By:

>>12283465
You sound like a retard. To learn you need to put in the work and you don't seem willing to do that.

Anonymous

Anonymous Fri 30 Oct 2020 04:17:05 No.12288475 Report

Quoted By:

>>12275423
Stats is completely made up bullshit, there's no right or wrong in it.
Take a bunch of numbers, plug them in to an equation you make up to get some new numbers, bam you're a statistician.

Anonymous

Anonymous Fri 30 Oct 2020 05:46:34 No.12288659 Report

Quoted By:

>>12283175
>Supertafe

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