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. / Graduation date: 1992
| Identifer | oai:union.ndltd.org:ORGSU/oai:ir.library.oregonstate.edu:1957/36872 |
| Date | 17 March 1992 |
| Creators | Lin, Lie-fen |
| Contributors | Ramsey, Fred L. |
| Source Sets | Oregon State University |
| Language | en_US |
| Detected Language | English |
| Type | Thesis/Dissertation |
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