Statistical Rethinking
"Statistical Rethinking: A Bayesian Course with Examples in R and Stan builds readers’ knowledge of and confidence in statistical modeling. Reflecting the need for even minor programming in today’s model-based statistics, the book pushes readers to perform step-by-step calculations that are usually automated. This unique computational approach ensures that readers understand enough of the details to make reasonable choices and interpretations in their own modeling work. The text presents generalized linear multilevel models from a Bayesian perspective, relying on a simple logical interpretation of Bayesian probability and maximum entropy. It covers from the basics of regression to multilevel models. The author also discusses measurement error, missing data, and Gaussian process models for spatial and network autocorrelation." --Publisher's website.
Stats for nerds
81recommend
113mentions
92people
2016–2026years
88% recommend12% neutral1% critical
Mentions per year
What Hacker News says
- How would it overlap or differ from 'Statistical Rethinking'?
This is widely regarded as the most accessible intro textbook to Bayesian statistics.
- Hi, I would read it if it came with a GitHub of python code that I can modify for my own use. The fewest dependencies, the better.
I like Statistical Rethinking, but unfortunately the solver was very slow and I didn't end up using it much - not the author's fault, it's probably my computer that's way too old.
- McElreath's Statistical Rethinking is also a great reference for causal thinking and modeling.
- I said before that the function shape changes as you're updating the parameters that govern the function but that's actually very misleading, (sorry), since the kernel parameters are only indirectly governing the function. What the parameters directly govern is the joint probability distribution P(f(x1), f(x2), ..., f(xn)). So the function f is implicitly defined by how likely the entire sequence of f values are.
So how does it change shape? Well this part is actually something I don't fully grasp myself yet. But I can sketch a crude bayesian interpretation, which is how I think of it. Not completely correct but works as a placeholder until I fully work out the math of updating the parameters.
Basically, from a bayesian perspective we can condition the joint distribution of function outputs as a likelihood conditioned on the kernel parameters theta: p(f(x1), f(x2), ... | theta).
Then we can derive the posterior distribution over theta p(theta | f(x1), f(x2), ...) like so:
p(theta | f(x1), f(x2), ...) ≈ p(f(x1), f(x2), ... | theta) p(theta).
So we fit the theta parameters based on how well it fits the observed data we feed our bayesian model.
FWIW, I recommend chapter 14 of Richard McElreath's Statistical Rethinking for a better introduction of GPs. This article kind of glosses over a lot of the intuition and introductory concepts that you need to really grok it.
- Highly recommend Statistical Rethinking for anyone looking for practical/applied/intuitive approach to Bayesian Statistics. For example the 2023 lecture series: https://youtu.be/FdnMWdICdRs?is=KycmwPL-cn8clOK5
- Get a book on applied statistics, such as
Think Stats: Probability and Statistics for Programmers (https://allendowney.github.io/ThinkStats/)
Computer Age Statistical Inference (https://hastie.su.domains/CASI/)
Statistical Rethinking (https://xcelab.net/rm/)
An Introduction to Statistical Learning (https://www.statlearning.com/)
Obviously maths is going to be involved to do the subject justice. These recommendations are more about applied statistics, but that's the foundation. From there it is a small transition to statistical process control.
Related
Regression and Other Stories
11 recommend · 20
Computer Age Statistical Inference
14 recommend · 20
Doing Bayesian Data Analysis
22 recommend · 33
Introduction to Statistical Learning
85 recommend · 120
Data analysis using regression and multilevel/hierarchical models
10 recommend · 13
2019–2025
Bayesian Statistics the Fun Way
1 recommend · 3
