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. There seems to be no natural Bayesian counterpart to the testing of a null hypothesis against a vague alternative which is just its negation. For a discussion of this and related matters see Cox and Hinkley (1974, p. 392).