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)
