ABSTRACT
In the non-Bayes approach to hypothesis testing a sharp distinction is usually made between the null hypothesis and alternative hypotheses. The null hypothesis holds a special place, a notion which is reinforced by the terminology 'testing of hypotheses'. The Bayes approach, or at least the Bayes decision theoretic approach, is different, emphasis being on the choice between hypotheses rather than one being singled out for special attention. From the point of view of decision theory the essential difference between point estimation and choosing between hypotheses is in the form of the loss function. From past data an estimate of the prior distribution is made, and it replaces the actual prior distribution in the Bayes decision rule, thus producing an EB decision rule. Any non-simple hypothesis will be referred to as a composite hypothesis. The prior distribution implied by these alternatives have the appearance of the two 'tails' of a distribution, the central portion having been removed.
