DTIC ADA204287: Monte Carlo Approximations in Bayesian pdf

DTIC ADA204287: Monte Carlo Approximations in Bayesian

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In decision-making problems, the Bayesian action and its posterior expected loss usually can not be obtained analytically. This paper studies a Monte Carlo method for approximating the Bayesian action and its posterior expected loss. The Monte Carlo approximation to the Bayesian action is obtained through approximating the posterior expected loss function by using the Monte Carlo integration method and searching the minimum of the approximated posterior expected loss function. As the Monte Carlo sample size diverges to infinity, the Monte Carlo approximations are shown to be convergent in very general situations. The rates of the convergence are also obtained under some regularity conditions on the loss function. Two accuracy measures of the Monte Carlo approximations are proposed. Some examples are presented for illustration

• Creator/s: Defense Technical Information Center
• Date: 1/1/1989
• Year: 1989
• Book Topics/Themes: DTIC Archive, Shao, Jun, PURDUE UNIV LAFAYETTE IN DEPT OF STATISTICS, *APPROXIMATION(MATHEMATICS), *BAYES THEOREM, *MONTE CARLO METHOD, ACCURACY, DECISION THEORY, CONVERGENCE, LOSSES, RATES, DECISION MAKING, FUNCTIONS, INTEGRATION

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