On the​ emptiness of Bayesian probabilism

15 Jan, 2019 at 17:49 | Posted in Statistics & Econometrics | 1 Comment

A major attraction of the personalistic [Bayesian] view is that it aims to address uncertainty that is not directly based on statistical data, in the narrow sense of that term​. Clearly much uncertainty is of this broader kind. Yet when we come to specific issues I believe that a snag in the theory emerges. To take an example that concerns me at the moment: what is the evidence that the signals from mobile telephones or transmission base stations are a major health hazard? Because such telephones are relatively new and the latency period for the development of, say, brain tumours is long the direct epidemiological evidence is slender; we rely largely on the interpretation of animal and cellular studies and to some extent on theoretical calculations about the energy levels that are needed to induce certain changes. What ​is the probability that conclusions drawn from such indirect studies have relevance for human health? Now I can elicit what my personal probability actually is at the moment, at least approximately. But that is not the issue. I want to know what my personal probability ought to be, partly because I want to behave sensibly and much more importantly because I am involved in the writing of a report which wants to be generally convincing. I come to the conclusion that my personal probability is of little interest to me and of no interest whatever to anyone else unless it is based on serious and so far as feasible explicit information. For example, how often have very broadly comparable laboratory studies been misleading as regards human health? How distant are the laboratory studies from a direct process affecting health? The issue is not to elicit how much weight I actually put on such considerations but how much I ought to put. Now of course in the personalistic approach having (good) information is better than having none but the point is that in my view the personalistic probability is virtually worthless for reasoned discussion​ unless it is based on information, often directly or indirectly of a broadly frequentist kind. The personalistic approach as usually presented is in danger of putting the cart before the horse.

David Cox

The nodal point here is that although Bayes’ theorem is mathematically unquestionable, that doesn’t qualify it as indisputably applicable to scientific questions. 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’ll be dipped!