Bayesian hypothesis testing: A reference approach

Summary For any probability model M={p(x|θ, ω), θeΘ, ωeΩ} assumed to describe the probabilistic behaviour of data xeX, it is argued that testing whether or not the available data are compatible with the hypothesis H0={θ=θ0} is best considered as a formal decision problem on whether to use (a0), or not to use (a0), the simpler probability model (or null model) M0={p(x|θ0, ω), ωeΩ}, where the loss difference L(a0, θ, ω) –L(a0, θ, ω) is proportional to the amount of information δ(θ0, ω), which would be lost if the simplified model M0 were used as a proxy for the assumed model M. For any prior distribution π(θ, ω), the appropriate normative solution is obtained by rejecting the null model M0 wh…