[ 3 / biz / cgl / ck / diy / fa / ic / jp / lit / sci / vr / vt ] [ index / top / reports ] [ become a patron ] [ status ]
2023-11: Warosu is now out of extended maintenance.

/sci/ - Science & Math


View post   

File: 131 KB, 999x375, Screenshot 2023-12-16 111410.png [View same] [iqdb] [saucenao] [google]
15926364 No.15926364 [Reply] [Original]

You guys don't really come to /sci/ without a basic understanding of probability and statistics, right?

>> No.15926367

>>15926364
>category theory
>basic understanding of probability

>> No.15926372

>>15926367
There's no category theory here. It's just a discrete random variable with k possible states and specified respective probabilities.

The KL divergence thing is a bit different and somewhat outside of standard statistics (really it's an information theory thing that statisticians borrow for hypothesis testing information bounds).

>> No.15926373

>>15926364
>probability and statistics
are what made me give up biotechnology studies and put my life on the track of 15 years incel failure, and counting.

>> No.15926374

>>15926372
It says categorical random variable

>> No.15926379

>>15926374
Yes, the word categorical is used, that doesn't mean you need category theory to describe the random variable.

It just means that the random variable is in one of k states. You could think of this like corresponding to being associated to a unit vector in one of k directions in R^k. You don't need category theory for this.

You need, at most, some linear algebra, a bit of experience with series simplifications, and some patience.

>> No.15926413

>>15926379
You mean a geometric series has nothing to do with geometry?

If I read the word "geometric", my 90IQ-Braine know, "ah, its about bodies"

>> No.15926606

>>15926413
The geometric series does actually have something to do with geometry believe it or not.

If you take any three consecutive terms in a geometric series, the one in the middle is the geometric mean of the two on either side of it. Meaning, the middle term is the side-length of a square whose total area is given by the product of the two terms on either end.

>> No.15926714

>>15926364
i do

>> No.15926725

>>15926364
Divide 2 observation points by 2 and create a new one, statistics is the physics of mathematics.

>> No.15926810

>>15926373
I'm proud of you

>> No.15927535

>>15926725
If you mean that both of them are fundamentally about inferences and modeling, yes.

>> No.15927556

>>15926364
Statistics is a brainlet field. With that being said you can still make a ton of money if you study it.

>> No.15927564

>>15926364
I'd rather kill myself than finish reading this problem. I hated statistics so much it's unreal.

>> No.15927580

My probability class was awful.
Any recommendations of some good books?
My class didn't even go over central limit theorem.

>> No.15927584

>homework thread

>> No.15928626
File: 325 KB, 682x923, IMG_5451.png [View same] [iqdb] [saucenao] [google]
15928626

>>15926364
what’s a decent book on probability where most results are derived and proven? i know nothing of the subject.

is this a good book to start with?
https://probability4datascience.com/

>> No.15928631

>>15926364
the people on this board are morons larping as gigabrains, they dont understand anything outside of hs level

>> No.15928707
File: 30 KB, 360x360, IMG_5452.jpg [View same] [iqdb] [saucenao] [google]
15928707

>>15928626
>>15926364
is this a better alternative?

https://archive.org/details/lev-tarasov-the-world-is-built-on-probability-mir-2023

>> No.15928711

>>15926379
>>15926364
Can you post an infographic on learning probability from scratch? is multivariable calculus needed?

>> No.15928720

>>15928711
>>15928707
A really good resource for undergrad to early grad level probability is Bertsekas's Introduction to Probability.

It's super easy to find a PDF of the book as well as the associated MIT courseware and doesn't ask much of students in terms of prerequisites except for a familiarity with some multivariable calculus and a little bit of linear algebra towards the end.

I remember an anon asked me to make a infographic on the whole "how do I start with probability" thing and I was working on it and got a bit sidetracked. I'm less busy between semesters so I can try to put something together.

>> No.15928787

>>15928720
Nice, looking forward to it. What's your background by the way?

>> No.15928809

>>15926379
How do series make an appearance in probability, besides the usual gimmick of approximating difficult to integrate functions via power series

>> No.15928824

>>15928809
A partial geometric series describes the probability of waiting x \leq k trials before the first successful trial of a binary/Bernoulli random variable of probability p (as an example).

Infinite series give you the way of calculating probabilities and expectations of (countable) infinite length random variables.

>>15928787
PhD in EE with a concentration in adaptive statistical estimation/detection. My job is basically just probability and stochastic processes but for statistical signal processing applications.

>> No.15928852

looks like category theory is still for trannies. containment zone of math

>> No.15928860

>>15926364
its clearly just n*D(p||q)

>> No.15928866

>>15926364
>basic understanding of probability and statistics
it's 50-50.
it either happens or it doesn't
qed.

>> No.15928872

How does physics reconcile classical mechanics (deterministic) with quantum mechanics (probabilistic)? wtf is going on.

>> No.15928879

>>15928872
A V E R A G E S

>> No.15928925

>>15928809
one very specific example that I used recently is finding the causal representation of some ARMA processes

>> No.15928931

>>15928872
Based binary maximum entropy enjoyer

>> No.15928945

>>15928931
Was meant to reply to >>15928866

Oops

>> No.15929666

>>15928720
>I remember an anon asked me to make a infographic on the whole "how do I start with probability" thing and I was working on it and got a bit sidetracked. I'm less busy between semesters so I can try to put something together.
Based. Any recommendations for now as far as math foundations?

>> No.15929834

>>15926372
Fuck you for bringing up the KL divergence, my information theory final is today

>> No.15929879

>>15929834
You've got this brother! I have faith in you. Did you use use Cover and Thomas or MacKay (or, god help you, Gallagher/Gray)?

>> No.15929882

>>15929666
If you want to do probability/statistics at an undergraduate STEM major level, you need to be pretty comfortable with multivariable calculus, ordinary differential equations/Fourier/Laplace transforms (for moment generating functions/characteristic functions) and linear algebra (for linear estimation).

If you aren't comfortable with those, that's where you want to start. Some discrete mathematics for infinite series will also be very helpful.

>> No.15929997

>>15929879
Thanks anon.
None of the above, We used my professor's own book.

>> No.15930015
File: 52 KB, 1024x663, 1689717661910537.jpg [View same] [iqdb] [saucenao] [google]
15930015

>>15926364
Probability and statistics are only limited to a single closed dataset and have a very niche application, for the entire universe as a system they are useless and the probability of anything happening at any given moment is 50/50

>> No.15930091

>>15926364
People on this board barely understand algebra.

>> No.15930143
File: 11 KB, 165x216, 3157RrL4eHL.jpg [View same] [iqdb] [saucenao] [google]
15930143

>>15929882
Would you say that Hubbard & Hubbard: Vector Calculus, Linear Algebra and Differential Forms is sufficient for a one-stop math undergrad? And then pursue with probability?

https://www.amazon.com/Vector-Calculus-Linear-Algebra-Differential/dp/0971576688/ref=sr_1_1?crid=13EWROUK9LKZ&keywords=hubbard+forms&qid=1702931103&sprefix=hubbard+forms%2Caps%2C99&sr=8-1

>> No.15930152

>>15930143
Linear Algebra and vector calc are a lot more important in statistics than probability.

I'm not familiar with the book you've linked, but if you can handle convolution integrals, Laplace/Fourier transforms, some basics of combinatorics and changes of variables, you've got pretty much everything you need for a basic undergraduate probability course.

The only way to know for certain is to give some problems a try.

>> No.15930153

>>15928872
That's not a question the field of statistics and probability can answer.

>> No.15930267

>>15928707
I'm reading from here, but this doesn't contain exercises. Can you post some exercises for beginners? Thanks OP.

>> No.15930710

>>15926364
What's there to understand? It either happens or it doesn'.t 50/50.