The Author Problem: Bayesian Inference with Two Hypotheses

Abstract

The “Author Problem” provides a concrete example of Bayesian inference. This chapter draws on work by Frederick Mosteller and David Wallace, who used Bayesian inference to assign authorship for unsigned Federalist Papers. The Federalist Papers were a collection of papers known to be written during the American Revolution. However, some papers were unsigned by the author, resulting in disputed authorship. The chapter provides a very basic Bayesian analysis of the unsigned “Paper 54,” which was written by Alexander Hamilton or James Madison. The example illustrates the principles of Bayesian inference for two competing hypotheses, including the concepts of alternative hypothesis, prior probability distribution, posterior probability distribution, prior probability of a hypothesis, likelihood of the observed data, and posterior probability of a hypothesis.