The **Bayes factor** is used in Bayesian statistics to measure the relative probability of alternatives based on some form of observed data. For a simple H_{0} vs H_{1} alternative (e.g. human vs Martian), the Bayes factor is the ratio of the odds for the two alternatives: P(H_{1} | observed data) / P(H_{0} | observed data). However, if H_{0} vs H_{1} is more complex (e.g. mean = 0 vs any other value), then calculating the Bayes factor involves averaging over the alternative possibilities weighted by the prior probability distribution.

Defined on page 75

Used on pages 75, 76, 100, 101