Uses of Bayesian posterior modes in solving complex estimation problems in statistics Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/47429c49k

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  • In Bayesian analysis, means are commonly used to summarize Bayesian posterior distributions. Problems with a large number of parameters often require numerical integrations over many dimensions to obtain means. In this dissertation, posterior modes with respect to appropriate measures are used to summarize Bayesian posterior distributions, using the Newton-Raphson method to locate modes. Further inference of modes relies on the normal approximation, using asymptotic multivariate normal distributions to approximate posterior distributions. These techniques are applied to two statistical estimation problems. First, Bayesian sequential dose selection procedures are developed for Bioassay problems using Ramsey's prior [28]. Two adaptive designs for Bayesian sequential dose selection and estimation of the potency curve are given. The relative efficiency is used to compare the adaptive methods with other non-Bayesian methods (Spearman-Karber, up-and-down, and Robbins-Monro) for estimating the ED50 . Second, posterior distributions of the order of an autoregressive (AR) model are determined following Robb's method (1980). Wolfer's sunspot data is used as an example to compare the estimating results with FPE, AIC, BIC, and CIC methods. Both Robb's method and the normal approximation for estimation of the order have full posterior results.
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