Unformatted text preview: p ð x j N Þ ¼ Prob f DLT j Dose ¼ x g then the likelihood function for r = [ g N ] given the data D k is L ð N j D k Þ ¼ P k i ¼ 1 p ð x i j N Þ y i f 1 ± p ð x i j N Þg 1 ± y i : Bayes’ theorem then implies that the joint posterior distribution of ( g , N ) given the data D k is C k ð g ; N j D k Þ ¼ L ð g ; N j D k Þ h ð g ; N Þ m L ð u j D k Þ h ð u Þ d u where the integral is over Q . To facilitate exposition, it will hereafter be assumed that the prior distribution h is deﬁned on some set G ² V containing the parameter space Q such that g 2 G and N 2 V with prior probability 1. Whenever necessary, this will entail extending h from Q to G ² V by deﬁning h to be identically equal to zero on the diﬀerence ( G ² V )\ Q . This convention will simplify ensuing formulations without a loss of Copyright n 2004 by Marcel Dekker, Inc. All Rights Reserved....
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- Spring '11
- Physics, posterior distribution