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Unformatted text preview: UC Berkeley Department of Statistics STAT 210A: Introduction to Mathematical Statistics Problem Set 5 Fall 2007 Issued: Thursday, September 27 Due: Thursday, October 4 Reading: For this problem set: Chapter 9 of Keener (Bayesian methods); § 3.1, 3.2 of Bickel and Doksum. Problem 5.1 Find conjugate distributions for the following family of distributions: (a) the gamma family of distribution functions Γ( λ,p ) (b) the beta family of distribution functions β ( λ,p ) (c) the family defined on the parameters β 1 and β 2 by the linear regression y i = β 1 + β 2 x i + ε with ε ∼ N (0 ,σ 2 ) and σ 2 known. Problem 5.2 This problem addresses the issue of implementing Bayes estimators for exponential family models. Suppose that we have a (conditional) exponential family model p ( x | θ ) = h ( x ) exp ( d X i =1 θ i T i ( x )- A ( θ ) ) , where x = ( x 1 ,...,x n ) and the random vector Θ has density λ ( · )....
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- Fall '08
- Statistics, Probability theory, Estimation theory, Bayesian probability, Bayesian statistics