nostalgebraist - bayes: a kinda-sorta masterpost

by Kaj_Sotala1 min read4th Sep 201819 comments


Bayes' Theorem / Bayesianism

Extended criticism of "Bayesianism" as discussed on LW. An excerpt from the first section of the post:

Like most terms ending in -ism, [Bayesianism] can mean a number of different things.  In its most limited sense, “Bayesianism” is a collection of technical/mathematical machinery, analogous to a tool or toolbox.  This collection, which I will call “the Bayesian machinery,” uses a particular way of representing knowledge, and if you can represent your knowledge in that way, the machinery tells you how to alter it when presented with new evidence.
The Bayesian machinery is frequently used in statistics and machine learning, and some people in these fields believe it is very frequently the right tool for the job.  I’ll call this position “weak Bayesianism.”  There is a more extreme and more philosophical position, which I’ll call “strong Bayesianism,” that says that the Bayesian machinery is the single correct way to do not only statistics, but science and inductive inference in general – that it’s the “aspirin in willow bark” that makes science, and perhaps all speculative thought, work insofar as it does work.  (I.e., if you’re doing these things right, you’re being Bayesian, whether you realize it or not.)
Strong Bayesianism is what E. T. Jaynes and Eliezer Yudkowsky mean when they say they are Bayesians.  It is usually what I am talking about when I say I “don’t like” Bayesianism.  I think strong Bayesianism is dead wrong.  I think weak Bayesianism may well be true, in that the Bayesian machinery may well be a very powerful set of tools – but I want to understand why, in a way that defines the power of a tool by some metric other than how Bayesian it is.

Contents of the post:

0. What is “Bayesianism”?

1. What is the Bayesian machinery?

1a. Synchronic Bayesian machinery

1b. Diachronic Bayesian machinery

3.  What is Bayes’ Theorem?

4. How does the Bayesian machinery relate to the more classical approach to statistics?

5. Why is the Bayesian machinery supposed to be so great?

6. Get to the goddamn point already.  What’s wrong with Bayesianism?

7. The problem of ignored hypotheses with known relations

7b. Okay, but why is this a problem?

8. The problem of new ideas

8b. The natural selection analogy

9. Where do priors come from?

10. It’s just regularization, dude

11. Bayesian “Occam factors”