The Art of Statistics: Learning from Data

by David Spiegelhalter

Which brings us to Bayes’ second key contribution: a result in probability theory that allows us to continuously revise our current probabilities in the light of new evidence. This has become known as Bayes’ theorem, and essentially provides a formal mechanism for learning from experience, which is an extraordinary achievement for an obscure clergyman from a small English spa town. Bayes’ legacy is the fundamental insight that the data does not speak for itself – our external knowledge, and even our judgement, has a central role. This may seem to be incompatible with the scientific process, but of course background knowledge and understanding has always been an element in learning from data, and the difference is that in the Bayesian approach it is handled in a formal and mathematical way. The implications of Bayes’ work have been deeply contested, with many statisticians and philosophers objecting to the idea that subjective judgement has any role in statistical science. So it is only fair that I make my personal position clear: I was introduced into a ‘subjectivist’ Bayesian school of statistical reasoning at the start of my career,fn2 and it still remains for me the most satisfying approach.

Bayes theorem is based on subjectivity+data