Bernoulli trials and the weight of evidence in favour of a null hypothesis

Abstract

Suppose we want to test the null hypothesis that a parameter θ is equal to a predetermined constant against the vague alternative that θ is not equal to the null value. It is shown that for a certain family of distributions the last observation is uninformative if under the alternative hypothesis the posterior mean of θ obtained from the previous observations is equal to the null value. A special case is in Bernoulli sampling.