List of arguments for Bayesianism

7Radford Neal

9cubefox

4Dagon

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An additional technical reason involves the concept of an "admissible" decision procedure - one which isn't "dominated" by some other decision procedure, which is at least as good in all possible situations and better in some. It turns out that (ignoring a few technical details involving infinities or zero probabilities) the set of admissible decision procedures is the same as the set of Bayesian decision procedures.

However, the real reason for using Bayesian statistical methods is that they work well in practice. And this is also how one comes to sometimes not use Bayesian methods, because there are problems in which the computations for Bayesian methods are infeasible and/or the intellectual labour in defining a suitable prior is excessive.

I've been trying to list out for myself the various arguments people give for going with Bayesian (or at least probabilistic) epistemology. Here's what I have so far:

Intuitive representation for degrees of belief:It seems pretty obvious that beliefs come in degrees. Representing degrees of belief as numbers between 0 and 1 that follow probability theory (including Bayes' Theorem) seems intuitively straightforward.Cox's Theorem:Given some very plausible desiderata for rational thinking with degrees of belief, probability theory (including updating using Bayes' Theorem) follows.von Neumann - Morgenstern (VNM) Representation Theorem:Any agent following certain very plausible desiderata for rational decision making can be represented as a Bayesian utility maximizer for some (perhaps extremely complicated) utility function.Dutch Book arguments:Any agent violating Bayesian decision making can be "Dutch booked" with a set of deals that will result in a guaranteed loss for the agent.Philosophy of science:Many philosophers of science think that science is (ideally) just Bayesian reasoning, in that it is trying to infer the probability that a theory is correct given the evidence. Alternative approaches to philosophy of science (e.g., Popperian falsificationism) have serious problems.The Bayesian Brain hypothesis:Many cognitive scientists think that biological brains instantiate Bayesian reasoning as one of if not the primary thinking algorithm.Evidence from superforecasting:Phil Tetlock and colleagues found that the best forecasters use (mostly intuitive versions of) Bayesian reasoning, among other techniques.Paradoxes:Probabilistic reasoning helps resolve a bunch of philosophical paradoxes related to epistemology (e.g., Lottery Paradox, Preface Paradox, Raven Paradox).I'm pretty sure I'm missing some arguments though. What did I leave out?

(Of course, there are also counterarguments to these given by opponents of Bayesianism, and there is also a long list of arguments people use *against* Bayesianism. But that's for next steps. At the moment I'm just trying to list out arguments people give *for* Bayesianism / Probabilism.)