(New page: Decision Rule: A map from values of x to Ho or H1 if x E R, say H1 else if x does not contain R say Ho Max-likelihood Rule: Pick hypothesis that maxes conditional PDF ML Rule: say H1 i...) |
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| + | =Binary Hypothesis Testing= | ||
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Decision Rule: A map from values of x to Ho or H1 | Decision Rule: A map from values of x to Ho or H1 | ||
if x E R, say H1 | if x E R, say H1 | ||
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Probability of Type I : Pr(x E R|H0) | Probability of Type I : Pr(x E R|H0) | ||
Probablitiy of Type II: Pr(X E Rc|H1) | Probablitiy of Type II: Pr(X E Rc|H1) | ||
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| + | [[Main_Page_ECE302Fall2008sanghavi|Back to ECE302 Fall 2008 Prof. Sanghavi]] | ||
Latest revision as of 12:43, 22 November 2011
Binary Hypothesis Testing
Decision Rule: A map from values of x to Ho or H1 if x E R, say H1 else if x does not contain R say Ho
Max-likelihood Rule:
Pick hypothesis that maxes conditional PDF
ML Rule: say H1 if fx|theta(x|theta1) > fx|theta0)
H0 if fx|theta(x|theta1) <= fx|theta(theta|theta0)
Rml = {X such that fx|theta(x|theta1) > fx|theta(x|theta0}
Type I : Say H1 when truth is Ho Type II: say H0 when truth is H1
Probability of Type I : Pr(x E R|H0) Probablitiy of Type II: Pr(X E Rc|H1)
