Bayesian Boxes: A colored calculator for picturing posteriors

Abstract

The need for Bayesian inference arises in military intelligence, medical diagnosis and many other practical applications. The problem is that human inferences are generally conservative by Bayesian standards, i.e., people fail to extract all the certainty they should from the data they are given. Here I present a diagram called "Bayesian Boxes" designed to correct conservatism, The diagram uses colored lines and boxes to illustrate the Bayesian posterior and the underlying principle. Compared to other diagrams, Bayesian Boxes is novel in illustrating the conceptual features (e.g., hypotheses and evidence) and computational structure (e.g., products and ratio) of Bayesian inference.