Bayesian Hypothesis Testing
Definition
Bayesian hypothesis testing can be framed as a special case of model comparison where a model refers to a likelihood function and a prior distribution.
How it works
Given two competing hypotheses and some relevant data, Bayesian hypothesis testing begins by specifying separate prior distributions to quantitatively describe each hypothesis. The combination of the likelihood function for the observed data with each of the prior distributions yields hypothesis-specific models. For each of the hypothesis-specific models, averaging (ie, integrating) the likelihood with respect to the prior distribution across the entire parameter space yields the probability of the data under the model and, therefore, the corresponding hypothesis. This quantity is more commonly referred to as the marginal likelihood and represents the average fit of the model to the data. The ratio of the marginal likelihoods for both hypothesis-specific models is known as the Bayes factor.
References
Baig, S. A., PhD. (2020). Bayesian Inference: An Introduction to Hypothesis Testing Using Bayes Factors. Nicotine & Tobacco Research, 22(7), 1244-1246. Link