The geometry of Bayes theorem

17 Jun, 2022 at 10:50 | Posted in Statistics & Econometrics | 1 Comment

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An informative visualization of a theorem that shows how to update probabilities — calculating conditional probabilities — when new information/evidence becomes available.

But …

Although Bayes’ theorem is mathematically unquestionable, that doesn’t qualify it as indisputably applicable to scientific questions. Bayesian statistics is one thing, and Bayesian epistemology is something else. Science is not reducible to betting, and scientific inference is not a branch of probability theory. It always transcends mathematics. The unfulfilled dream of constructing an inductive logic of probabilism — the Bayesian Holy Grail — will always remain unfulfilled.

Bayesian probability calculus is far from the automatic inference engine that its protagonists maintain it is. That probabilities may work for expressing uncertainty when we pick balls from an urn, does not automatically make it relevant for making inferences in science. Where do the priors come from? Wouldn’t it be better in science if we did some scientific experimentation and observation if we are uncertain, rather than starting to make calculations based on often vague and subjective personal beliefs? People have a lot of beliefs, and when they are plainly wrong, we shall not do any calculations whatsoever on them. We simply reject them. Is it, from an epistemological point of view, really credible to think that the Bayesian probability calculus makes it possible to somehow fully assess people’s subjective beliefs? And are — as many Bayesians maintain — all scientific controversies and disagreements really possible to explain in terms of differences in prior probabilities? I strongly doubt it.