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 H0 vs H1 alternative (e.g. human vs Martian), the Bayes factor is the ratio of the odds for the two alternatives: P(H1 | observed data) / P(H0 | observed data). However, if H0 vs H1 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.
Context: For a simple H0 vs. H1 alternative (e.g., human vs. Martian) the Bayes factor is the ratio of the odds for the two alternatives: P(H1 | observed data) / P(H0 | observed data). However, if H0 vs. H1 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.
Also used in hcistats2e: Chap. 7: page 84; Chap. 9: pages 107, 108
Used in glossary entries: Bayesian statistics, prior distribution