Adventures in Probability
buttondown.com
buttondown.com
So many of my college math classes had some version of this professor who took a fascinating subject like linear algebra, statistics or algorithms and made it into a slog. The fact that most stats is taught by getting students to just memorize random ideas rather than building up a holistic and intuitive view really is a travesty.
Also makes sense why so many people, even though they took stats in college, hav e such a poor understanding of probability.
We don't need first principals thinking for every thing. Granted, this comment is a bit vague, so I don't know how exactly you were taught or which type of class we're talking about, but generally, you can accept some axioms in applied mathematics classes. If we're talking the bare minimum classes like in the article (for apparently a business degree), this is likely a general applied prob/stat. Things tend to get more in depth with more advanced pure mathematics courses.
A great statistics textbook along these lines is Principles of Statistics by MG Bulmer. It's one of those Dover classic textbooks that you can get for cheap. This book assumes you already know basic calculus and combinatorics. It then goes through a series of practical problems, and shows how you can use calculus or combinatorics to solve them. And, along the way, an intuitive and holistic perspective on statistics begins to form.
The overall effect is great. It's a lot like a 3blue1brown video series, only from the 1960s, and with problem sets.
Additionally it's quite useful to have the background to understand the differences between Pearson correlation and Spearman rank, or why you might want to use Welch's t-test vs students, etc.
Not that you should know all of these things off the top of your head necessarily, but you should have the foundation to be able to quickly learn them, and you should know what assumptions the tests you're using actually make.
they want the professor to tell them the passwords they need to memorize. then on the exam they repeat the passwords and get an A. this is understandable though because they are under a lot of pressure and these days nobody can afford to fail.
if the teaching style deviates from this they become annoyed, leave poor course reviews, and that professor has a hard time.
the professor could overcome this by being "good" -- when the students say a professor is "good" they mean it is easy to get an A.
Incidentally, this also goes for the determinant of a matrix. It's got a lot of neat and desirable properties, and it turns out to be the only thing that does. When it was finally taught to me this way, those weird algorithms we use to compute this seemingly-arbitrary number finally made sense. (And, in fact, this is the easiest way to prove that all those algorithms have to be computing the same seemingly-arbitrary number. Because the algorithms preserve the properties that define The Determinant, and The Determinant is the unique thing that preserves all of those properties, so must those algorithms all be computing The Determinant, no matter how different they might look.)
So I can vouch that this style of explanation really does work, at least for people like me.
Do be warned that Algebra is a... high-octane... text written for serious math students and can be... powerful.
TL;DW the determinant represents how much you scale the area/volume/hypervolume (depending on dimension) of a shape by applying a matrix transformation to each point.
[0] https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQ...
[1] https://www.youtube.com/watch?v=Ip3X9LOh2dk&list=PLZHQObOWTQ...
1) product of eigenvalues
2) cofactor expansion (e.g., https://textbooks.math.gatech.edu/ila/determinants-cofactors...)
The second is the one I was taught first, in the context of linear system solution, but it does not seem obvious that it would be related to the product of eigenvalues. It’s kind of a weird pile of arithmetic manipulations.
Splitting a Poisson process into two lower rate processes is a neat trick. Even better is that you can do the same to convert a Poisson process into one with a variable rate, provided that rate is lower than the original (original may be variable as well).
And the fact that the partial sums of a bunch of exponential distributions results in the same distribution of values as picking Poisson(lambda * time) values uniformly at random is pure magic.
SELECT *
FROM Population
WHERE weight > 0
ORDER BY -LN(1.0 - RANDOM()) / weight
LIMIT 100 -- Sample size.
Either mathematically or just some python dice rolls.
Really good. Same ethos as fast.ai courses.
Finally that you can add tbe /3 and /5 to get a /8 distribution makes intuitive semsw to me. / means lambda.
This is because if you have people arriving to a train station you could split them by eye colour and there is no reason a particular eye colour cause there to be dependencies. (Assuming spherical cows: families arriving excepted. Assume it is downtown rush hour)
I think flawed examples lead to a great way of scaffolding towards the "true" nontrivial answer in a teaching setting at least... I am still exceptionally bitter at how I was taught and forced to learn stochastics and it was very much through a purely theoretical, proof driven, abstract lens with very crappy examples that were more of an afterthought... because of course the theory is all you need to make sense of it!
Further you can't process anything if the queue is empty. So it breaks down in this most obvious of cases.
For example, customers arrive at the grocery store in clusters due to traffic lights, schools getting out, etc. Even without direct signals, a NN could potentially pickup on these "rules" given other inputs, e.g. time of day, weather, etc.
?
You're kind of just describing seasonality components and exogenous regressors; RNNs do actually function quite well for demand forecasting of this type but even simple models (Holt-Winters or a Bayesian state space model or something) can be really effective
“A bunch” is actually a small enough number that brute forcing it works fine. If you have 20 methods in your head, you’re far ahead of most people.
You don’t even have to have them in your head. There’s an underutilized technology called a “list” where you just write things down one after another. Go down your list of methods. You’ll be able to throw out 90% of them because of something obvious.
You could be up to speed on this in a day of clicking though Wikipedia if you have some stats knowledge. Two days of you don’t. It’s how I did it myself, for whatever that’s worth.
I went for industrial engineering. we learned the math as pure math, then the math as free language problems, then how to identify and collect data to identify their attributes, then simulate and verify those processes, then test for variations in the underlying assumptions of those processes.
They never really did teach me to code well in a language that was useful, I had to pick that one up myself.
Edit: I remembered by stats class. merging poisson distributions requires Independent processes. since start and completion are dependent, its not mathematically valid.
but I am an engineer and it works, so whatever