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Department of Statistics

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https://hdl.handle.net/10217/100518
These digital collections include theses, dissertations, and datasets from the Department of Statistics. Due to departmental name changes, materials from the following historical department are also included here: Mathematics and Statistics.

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Browsing Department of Statistics by Subject "Bayesian statistical decision theory"

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    The pooling of prior distributions via logarithmic and supra-Bayesian methods with application to Bayesian inference in deterministic simulation models
    (Colorado State University. Libraries, 1998) Roback, Paul J., author; Givens, Geof, advisor; Hoeting, Jennifer, committee member; Howe, Adele, committee member; Tweedie, Richard, committee member
    We consider Bayesian inference when priors and likelihoods are both available for inputs and outputs of a deterministic simulation model. Deterministic simulation models are used frequently by scientists to describe natural systems, and the Bayesian framework provides a natural vehicle for incorporating uncertainty in a deterministic model. The problem of making inference about parameters in deterministic simulation models is fundamentally related to the issue of aggregating (i. e. pooling) expert opinion. Alternative strategies for aggregation are surveyed and four approaches are discussed in detail- logarithmic pooling, linear pooling, French-Lindley supra-Bayesian pooling, and Lindley-Winkler supra-Bayesian pooling. The four pooling approaches are compared with respect to three suitability factors-theoretical properties, performance in examples, and the selection and sensitivity of hyperparameters or weightings incorporated in each method and the logarithmic pool is found to be the most appropriate pooling approach when combining exp rt opinions in the context of deterministic simulation models. We develop an adaptive algorithm for estimating log pooled priors for parameters in deterministic simulation models. Our adaptive estimation approach relies on importance sampling methods, density estimation techniques for which we numerically approximate the Jacobian, and nearest neighbor approximations in cases in which the model is noninvertible. This adaptive approach is compared to a nonadaptive approach over several examples ranging from a relatively simple R1 → R1 example with normally distributed priors and a linear deterministic model, to a relatively complex R2 → R2 example based on the bowhead whale population model. In each case, our adaptive approach leads to better and more efficient estimates of the log pooled prior than the nonadaptive estimation algorithm. Finally, we extend our inferential ideas to a higher-dimensional, realistic model for AIDS transmission. Several unique contributions to the statistical discipline are contained in this dissertation, including: 1. the application of logarithmic pooling to inference in deterministic simulation models; 2. the algorithm for estimating log pooled priors using an adaptive strategy; 3. the Jacobian-based approach to density estimation in this context, especially in higher dimensions; 4. the extension of the French-Lindley supra-Bayesian methodology to continuous parameters; 5. the extension of the Lindley-Winkler supra-Bayesian methodology to multivariate parameters; and, 6. the proofs and illustrations of the failure of Relative Propensity Consistency under the French-Lindley supra-Bayesian approach.