Suppose that we wish to test the hypotheses (9.8.1). Let
Chapter 9, Problem 5(choose chapter or problem)
Suppose that we wish to test the hypotheses (9.8.1). Let the loss function have the form of (9.8.2). a. Prove that the posterior probability of = 0 is 0f0(x)/[0f0(x) + 1f1(x)]. b. Prove that a test that minimizes r() also minimizes the posterior expected value of the loss given X = x for all x. c. Prove that the following test is one of the tests described in part (b): reject H0 if Pr(H0 true|x) w1/(w0 + w1
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