Assume that is a sequential sample from the density and that it is desired to test versus The cost of each observation is c, and the decision loss is "0- Ki" loss. Let 1Ti denote the prior...

Assume that

is a sequential sample from the density

and that it is desired to test

versus

The cost of each observation is c, and the decision loss is "0- Ki" loss. Let 1Ti denote the prior probability of Hi.

(a) Show that the Bayes sequential procedure is one of the procedures d_J
(Ja nonnegative integer) defined as follows. The procedure d_o
is simply the immediate Bayes decision. For

is the procedure which starts sampling; stops sampling when stage n = J is reached, deciding and deciding HI otherwise; and at stage n <>

(b) For d_J
J

show that

and that

(c) if

, show that, for small enough c, the Bayes sequential procedure is d_J*, where