L3 - EE7750 MACHINERECOGNITIONOFPATTERNS...

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EE7750 MACHINE RECOGNITION OF PATTERNS Lecture 3: Bayesian Decision Theory
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Bayesian Decision Theory Return to the fish example. There are two categories. Denote these categories as w 1 for sea bass and w 2 for salmon. Assume that there is some prior probability (or simply prior) P(w 1 ) that the next fish is sea bass, and some prior probability that P(w 2 ) that it is salmon. Suppose that we make a decision without making a measurement. The logical decision rule is Decide w 1 if P(w 1 ) > P(w 2 ); otherwise decide w 2
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Bayesian Decision Theory Suppose that we have a feature vector x; now the decision rule is Decide w 1 if P(w 1 | x) > P(w 2 | x); otherwise decide w 2 Using the Bayes formula P(x) does not have any effect in the decision, and can be eliminated. ( | )( ) (| ) () ii i p wPw Pw p = x x x
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Bayesian Decision Theory Rearranging the previous formula, we get the likelihood ratio test:
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Bayesian Decision Theory Define a set of discriminant functions g i (x), i=1,…,c (| )( ) ) () ii i p wPw Pw p = x x x ( | ) ( ) i gp w P w = xx () l n ( | ) l n ( ) i w P w =+ or
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This note was uploaded on 09/21/2010 for the course EE EE7750 taught by Professor Bahadirgunturk during the Fall '10 term at LSU.

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L3 - EE7750 MACHINERECOGNITIONOFPATTERNS...

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