## NEYMAN-PEARSON LEMMA

In this section we study the Bayesian strategy of choosing an optimal test among all the admissible tests and a practical method which enables us to find a best test of a given size. The latter is due to Neyman and Pearson

figure 9.4 A set of admissible characteristics

and is stated in the lemma that bears their names. A Bayesian interpretation of the Neyman-Pearson lemma will be pedagogically useful here.

We first consider how the Bayesian would solve the problem of hypothesis testing. For her it is a matter of choosing between HQ and Hx given the posterior probabilities P(H0 | x) and P{H | x) where x is the observed value of X. Suppose the loss of making a wrong decision is as given in Table 9.2. For example, if we choose H0 when Hx is in fact true, we incur a loss y2.

Assu...

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