Introduction to Modern Statistics • Hacker News Board

Re: Introduction to Modern Statistics

#131

Post by obscurette » Fri, Oct 13, 2023, 7:24 PM UTC

Novosell wrote: post #106

obscurette wrote: post #79

Earlier quoted context omitted.

> It's seems very rare for someone to openly say "I'm bad at [my native language]" or "writing". It is actually even fashionable in non-english countries. Declaring "I'm bad at [my native language], I only use english anyway" makes you a better person somehow. And it's not rare in other areas either – in post-truth world it's trendy not to know things.

In non-english countries? All of them? Source? I, as a person from one of said non-english countries, disagree.

I didn't mean that in all of them and everyone in any of them. But it has been always the case everywhere in the world. It's the mechanism how languages die - gravitation to the bigger languages. Hundreds of languages die in Russia not only because of limited education in regional languages, but because it's more fashionable to be russian than representative of smaller nation. In world level this gravitation is towards english mainly.

In my country it's especially fashionable not to know a native language for a people in tech. "It's impossible to talk about tech anyway in native languages, so we all should use english anyway in future" is very common. I tried to fight with it localizing/translating software for many years, but I've given up for now.

Re: Introduction to Modern Statistics

#132

Post by mmplxx » Sat, Oct 14, 2023, 12:35 AM UTC

thefringthing wrote: post #102

wespiser_2018 wrote: post #81

Earlier quoted context omitted.

The difficulty of teaching statistics is that the maths you need to prove things are right and gain an intuitive understanding of the methods are far more advanced than what is presented in a basic stats course. Gosset came up with the t-test and proved to the world it made sense, yet we teach students to apply it in a black box way without a fundamental understanding of why it's right. That's not great pedagogy. IMO…

> There's a Curry-Howard isomorphism [between] logic [and Bayesian statistical inference]. This is an odd way of putting it. I think it's better to say that, given some mostly uncontroversial assumptions, if one is willing to assign real number degrees of belief to uncertain claims, then Bayesian statistical inference is the only way of reasoning about those claims that's compatible with classical propositional logic…

The will to assign real numbers to degrees of belief is the controversial assumption. Converted bayesians tend to gloss over this fact. Many, as in a sibling comment, state that MLE is bayesian statistics with a uniform prior, but this isn't true of most if not all frequentist inference, based on frequentist NHT and CI, not MAP. Modeling uncertainty with uniform priors (or even more sophisticated non-informative priors a la Jaynes) is a recipe for paradoxes and there is no alternative practical proposal that I know of. I have no issue with bayesian modeling in a ML context of model selection and validation based on resampling methods, but IMO it's not up to the foundational claims its proponents often do.

Re: Introduction to Modern Statistics

#133

Post by tnecniv » Sat, Oct 14, 2023, 2:24 AM UTC

trealira wrote: post #112

fallat wrote: post #85

Earlier quoted context omitted.

> I'm hoping to see, over time, a shift away from ad-hoc null hypothesis testing in favour of linear models (yes, in introductory courses, from the start-- see link below) and Bayesian-by-default approaches. Is there anything where I can start today, as a guinea pig? My statistics education is basically zero.

There's this great series of lectures I watched during my intro to statistics and probability course: https://youtube.com/playlist?list=PLQfiOKXnQpw_l0rbiV_QW8lwl... It goes over Bayes' Theorem early on, which I assume is Bayesian-by-default. I didn't realize this isn't universal. I watched it because my professor seemed to be teaching from the same textbook, so it followed the same general course structure. The text…

Bayes Theorem is universal. It’s one of the most fundamental results in probability.

Bayesian statistics is not. Most basic intro courses go the frequentist routes for historical reasons, but really both methods have their pros and cons.

Re: Introduction to Modern Statistics

#134

Post by tnecniv » Sat, Oct 14, 2023, 8:12 AM UTC

growingkittens wrote: post #46

Is there a "pre-statistics" book that teaches the thinking skills and concepts needed to understand statistics?

An undergrad (non-measure theoretic) probability book with basic linear algebra and calculus is the best preparation. If you solidly understand the basic tools of probability, you can learn statistics quite easily in my experience. Without that understanding, statistics will likely seem like a bunch of recipes. However, if you are comfortable with probability, you can write down the actual problem you have and find the statistical tool you’re after with a little googling.

Re: Introduction to Modern Statistics

#135

Post by growingkittens » Sat, Oct 14, 2023, 9:52 AM UTC

tnecniv wrote: post #134

growingkittens wrote: post #46

Is there a "pre-statistics" book that teaches the thinking skills and concepts needed to understand statistics?

An undergrad (non-measure theoretic) probability book with basic linear algebra and calculus is the best preparation. If you solidly understand the basic tools of probability, you can learn statistics quite easily in my experience. Without that understanding, statistics will likely seem like a bunch of recipes. However, if you are comfortable with probability, you can write down the actual problem you have and find t…

Thank you for the guide! It's very helpful. This comment [1] describes my background with math.

Something related: I often feel like I'm doing math when I work with information, especially when drawing out concepts and their relationships. Like 3D Tetris, but with recursion. There are also patterns in categorization. One of my purposes in learning math is to be able to quantify relationships between concepts, and create models, etc. What would I need to know about in this case?

[1] https://news.ycombinator.com/item?id=37857050

Re: Introduction to Modern Statistics

#136

Post by epgui » Sun, Oct 15, 2023, 12:45 AM UTC

wespiser_2018 wrote: post #86

epgui wrote: post #57

Earlier quoted context omitted.

Probably most people who do statistics. R sucks as a language but it excels at that specific application, just because of its tremendous ecosystem (putting even python to shame in some niche areas).

R is fine, it's no more absurd than other non-typed languages like javascript. Most languages are very good at one or two things, then not so good or appropriate for other tasks. For R, that's statistics, modeling, and exploratory analysis, which it absolutely crushes at due to ecosystem effects.

Well… I also consider Javascript to be a horrible language. Python is horrible as well, but better than R. IMO python and javascript are in the same ballpark.

Not all non-typed languages are bad. Clojure, for example, is one if the most elegant languages I’ve worked with (despite my dislike of the JVM).

Re: Introduction to Modern Statistics

#137

Post by tnecniv » Sun, Oct 15, 2023, 1:33 AM UTC

growingkittens wrote: post #135

tnecniv wrote: post #134

Earlier quoted context omitted.

An undergrad (non-measure theoretic) probability book with basic linear algebra and calculus is the best preparation. If you solidly understand the basic tools of probability, you can learn statistics quite easily in my experience. Without that understanding, statistics will likely seem like a bunch of recipes. However, if you are comfortable with probability, you can write down the actual problem you have and find t…

Thank you for the guide! It's very helpful. This comment [1] describes my background with math. Something related: I often feel like I'm doing math when I work with information, especially when drawing out concepts and their relationships. Like 3D Tetris, but with recursion. There are also patterns in categorization. One of my purposes in learning math is to be able to quantify relationships between concepts, and cre…

I’m not sure what the best advice is for someone with a brain injury, however I feel for you. I didn’t realize I had an attention disorder until I was 25 and it explained why I would screw up signs and struggle to understand formulas.

However I will say that, as you learn more math, the intuition and big picture thinking is way more important than details. I normally forget the specifics of how something works, but I know what I’m trying to do and what thing I need to look up to do it. There is very little need to memorize things besides having enough “RAM” for the moment. You always have pen and paper to write stuff down!

Regarding modeling, the sky is kind of the limit. The more math you know, the more abstractions you learn and start to see in the world. Dynamical systems is a good field to look at but I’m biased because it’s my main topic. Despite its usual applications in physical modeling, an algorithm is basically a time-discrete dynamical system: you recursively apply a function to a state and that gives you a new state. I have certainly seen algorithms analyzed from that perspective before.

Another area you might find interesting is Algebra. This isn’t like the algebra you took in school but more about looking at a space of objects that interact via some operation and characterizing what you know about the space given that operation. A classic example is that rotation operations form an algebraic structure known as a “group” due to the fact that any two rotations gives you a third, rotations are invertible (you can cancel a rotation by rotating in the opposite manner), and they follow the associative property. There’s a book I’ve been meaning to read about how to use this kind of algebra to design safer and more intuitive APIs by considering the data structures of the APIs as objects and functions / methods as operators on those objects.

Re: Introduction to Modern Statistics

#138

Post by growingkittens » Sun, Oct 15, 2023, 7:20 PM UTC

tnecniv wrote: post #137

growingkittens wrote: post #135

Earlier quoted context omitted.

Thank you for the guide! It's very helpful. This comment [1] describes my background with math. Something related: I often feel like I'm doing math when I work with information, especially when drawing out concepts and their relationships. Like 3D Tetris, but with recursion. There are also patterns in categorization. One of my purposes in learning math is to be able to quantify relationships between concepts, and cre…

I’m not sure what the best advice is for someone with a brain injury, however I feel for you. I didn’t realize I had an attention disorder until I was 25 and it explained why I would screw up signs and struggle to understand formulas. However I will say that, as you learn more math, the intuition and big picture thinking is way more important than details. I normally forget the specifics of how something works, but I…

Any advice is good, I just have to start at the beginning in a way that most people don't. Beyond that, normal advice is fine. I can adjust that advice to the quirks of my systems.

Dynamical systems is a great new keyword! Algorithms are a perfect example. I am exploring system dynamics from a metacybernetic point of view (via the viable system model). My focus is the dynamics of humans in complex systems, how systems change human behavior and vice versa.

Does big picture thinking in math involve understanding/intuition of the implications of formulas, and how they interact with other formulas (or other mathematical entities, I don't know if formula is a general enough term for "group of math actions")?

Graph dynamical systems looks promising, because I draw similar pictures when showing relationships over time. Fractals are always good, drawing fractals taught me to think recursively.

Is this the definition of group in the algebra you mentioned? https://mathworld.wolfram.com/Group.html

I am also interested in the way models create understanding, and how technical models can be visually altered to aid in understanding. I have a background in visual psychology, and see many mistakes that cloud the meaning of what is being communicated.