“The subjectivist (i.e. Bayesian) states his judgements, whereas the objectivist sweeps them under the carpet by calling assumptions knowledge, and he basks in the glorious objectivity of science.” – I.J. Good
Irving J. Good was a mathematician and a statistician of the Bayesian variety. During the war, he worked with Alan Turing at Bletchley Park and later was a research professor of statistics at Virginia Tech. Good was convinced of the utility of Bayesian methods when most of the academy was dead set against it; that took a certain amount of courage and foresight.
One the delightful aspects of this book is that Good’d humor and sarcasm are so clearly on display. For instance, one of the chapters is called 46656 Varieties of Bayesians, where he derives this number using a combinatorial argument.
In the above quote, Good zooms in on what he considers to be the difference between the frequentist (objectivist) and Bayesian schools. This argument seems to hold to this day. In my experience interacting with
The key insight is that nothing precludes Frequentists from working with likelihoods directly, and many do, but I bet that most don’t.
Another subtle difference is that people, being naturally Bayesian, generally rely on prior probabilities when making judgments. Priors are always there, even under the Frequentist framework, but some very famous and very clever Frequentists failed to take them into account, as demonstrated by this amusing bit from Good:
