Murder and (of?) the likelihood principle: A Trialogue
Ward Edwards, David A. Schum, Robert L. Winkler · Journal of Behavioral Decision Making · 1990
Abstract The Likelihood Principle of Bayesian inference asserts that only likelihoods matter to single‐stage inference. A likelihood is the probability of evidence given a hypothesis multiplied by a positive constant. The constant cancels out of simple versions of Bayes's Theorem, and so is irrelevant to single‐stage inferences. Most non‐statistical inferences require a multi‐stage path from evidence to hypotheses; testimony that an event occurred does not guarantee that in fact it did. Hierarchical Bayesian models explicate such cases. For such models, the Likelihood Principle applies to a collection of data elements treated as a single datum conditionally independent of other similar collections. It does not necessarily apply to a single data element taken alone. This has unfortunate implications; in particular, it does not permit the inputs to Bayesian arithmetic at all levels to be likelihood ratios. These issues are sorted out in the context of a trial in which one author is accused of murdering another, with the third as a key witness.