Scientific Decisions and Bayesian Reasoning

In deciding whether to accept or reject one theory rather than another, scientists often look at the evidence that agrees or disagrees with each theory. We formalize this method of comparison in terms of a 2-by-2 matrix where rows are the theories being compared and the columns the extent of agreement or disagreement with evidence. Illustrating this approach with two examples from the history of science, we show under what conditions scientific decisions to support a theory conform with Bayes’ theorem. For example, when a scientist decides that the theory with the most empirical support, or the fewest empirical failures, is the correct one, are they conforming to the rules of Bayesian confirmation? We show by a random simulation that often only a single comparison of agreements or disagreements, successes or failures, is consistent with Bayes’ theorem. This means that many scientists’ decisions to support or reject theories are consistent with Bayes’ theorem without their being aware of it.