Bayes factor

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.