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Unformatted text preview: The Bayes Estimators Suppose that X 1 ,X 2 ,...,X n is a sample from a distribution with an unknown parameter . Bayes estimators are based on the idea of viewing as being a particular value of a random variable. We postulate a prior distribution on : a prior density if is viewed as continu ous random variable; a prior pmf if can take values in a discrete set. Then we use the Bayes formula to compute the posterior density of . The observations X 1 ,X 2 ,...,X n can be dis crete or continuous, not necessarily of the same kind as . Discrete observations Suppose that X 1 ,X 2 ,...,X n are iid discrete ran dom variables with a pmf p X ( x i ; ). Case 1 : the unknown parameter can take only discrete values 1 ,..., k . We view as a value of a discrete random variable, , with a prior pmf p . Then ( ,X 1 ,X 2 ,...,X n ) is an ( n +1)dimensional discrete random vector....
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 Fall '10
 SAMORODNITSKY

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