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Unformatted text preview: unrecognizable. If the cost for rejects is not too high, rejection may be a desirable action. Let, Where is the loss incurred for choosing the (c+1) th action, rejection and is the loss incurred for making a substitution error. Show that the minimum risk is obtained if we decide if for all and if and reject otherwise. What happens if = 0? What happens if ? 4 Let the components of the vector x = (x 1 ,x d ) t be binary valued (0 or 1) and be the prior probability for the state of nature and j = 1,.c. Now define With the components of x i being statistically independent for all x in . Let x be distributed as described above, with c=2, d odd and (a) Show that the minimumerrorrate decision rule becomes: (b) Show that the minimum probability of error is given by (c) What is the limiting value of ? Explain. (d) Show that approaches zero as Explain....
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This note was uploaded on 07/20/2009 for the course CENG 564 taught by Professor John during the Spring '09 term at 東京大学.
 Spring '09
 John

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