Bayesian Testing of a Point Null Hypothesis Based on the Latent Information Prior

Bayesian testing of a point null hypothesis is considered. The null hypothesis is that an observation, x, is distributed according to the normal distribution with a mean of zero and known variance σ. The alternative hypothesis is that x is distributed according to a normal distribution with an unknown nonzero mean, μ, and variance σ. The testing problem is formulated as a prediction problem. Bayesian testing based on priors constructed by using conditional mutual information is investigated.