Bayes Factor

What is Bayes Factor

• The Bayes factor is a measure used in Bayesian statistics to compare the evidence provided by data for two competing hypotheses.
• Given two hypotheses $H_0$ (the null hypothesis) and $H_1$ (the alternative hypothesis), the Bayes factor $B{F}_{10}$​ is calculated as: $$BF_{1,0} = \frac{P(D|H_1)}{P(D|H_0)}$$, where $P(D|H_1)$ is the probability of the data D given that the alternative hypothesis H1​ is true, and $P(D|H_0)$ is the probability of the data D given that the alternative hypothesis H0​ is true.
• It is like a Likelihood ratio test, except we integrate out the parameters, which allows us to compare models of different complexity.

Interpreting Bayes factors: Jeffreys scale of evidence

• $1\le B{F}_{1,0}<3$​: anecdotal evidence for H1​
• $3\le B{F}_{1,0}<10$: Moderate evidence for H1​
• $B{F}_{1,0}>10$: Strong evidence for H1​
• $B{F}_{1,0}>100$: Very strong evidence for H1​