  Bayesian approaches to data analysis and machine learning are widespread and
popular as they provide intuitive yet rigorous axioms for learning from data;
see Bernardo and Smith (2004) and Bishop (2006). However, this rigour comes
with a caveat that the Bayesian model is a precise reflection of Nature. There
has been a recent trend to address potential model misspecification by raising
the likelihood function to a power, primarily for robustness reasons, though
not exclusively. In this paper we provide a coherent specification of the power
parameter once the Bayesian model has been specified in the absence of a
perfect model.
