  While statistics focusses on hypothesis testing and on estimating (properties
of) the true sampling distribution, in machine learning the performance of
learning algorithms on future data is the primary issue. In this paper we
bridge the gap with a general principle (PHI) that identifies hypotheses with
best predictive performance. This includes predictive point and interval
estimation, simple and composite hypothesis testing, (mixture) model selection,
and others as special cases. For concrete instantiations we will recover
well-known methods, variations thereof, and new ones. PHI nicely justifies,
reconciles, and blends (a reparametrization invariant variation of) MAP, ML,
MDL, and moment estimation. One particular feature of PHI is that it can
genuinely deal with nested hypotheses.
