Pooling of prior distributions via logarithmic and supra-Bayesian methods with application to Bayesian inference in deterministic simulation models, The

1998 Summer.Includes bibliographic references.Covers not scanned.Print version deaccessioned 2022.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

Judicious use of multiple hypothesis tests

When analyzing a table of statistical results, one must first decide whether adjustment of significance levels is appropriate. If the main goal is hypothesis generation or initial screening for potential conservation problems, then it may be appropriate to use the standard comparisonwise significance level to avoid Type 2 errors (not detecting real differences or trends). If, however, the main goal is rigorous testing of a hypothesis, then an adjustment for multiple tests is needed. To control the familywise Type 1 error rate (the probability of rejecting at least one true null hypothesis), sequential modifications of the standard Bonferroni Method, such as Holm’s method, will provide more statistical power than the standard Bonferroni method. Additional power may be achieved by using procedures that control the False Discovery Rate (the expected proportion of false positives among tests found to be significant). When the Holm’s method and two different false discovery rate procedures (FDR and pFDR) were applied to the results of multiple regression analyses of the relationship between habitat variables and abundance for 25 species of forest birds in Japan, the pFDR procedures provided the greatest statistical power

Acute effects of fluoxetine versus placebo on functional health and well-being in late-life depression

In a randomized 6-week trial comparing fluoxetine with placebo, the Medical Outcomes Study 36-Item Short-Form Health Status Survey (SF-36) scales were used to measure the effects of treatment on functional health and well-being among elderly (age \u3e or = 60 years) outpatients with major depression. In the fluoxetine and placebo groups, 261 and 271 patients, respectively, completed the SF-36 before treatment and at Weeks 3 and 6. Compared with national norms for individuals over age 60, study patients before treatment exhibited baseline decrements on the following SF-36 scales: mental health, role limitations due to emotional problems, social functioning, vitality, role limitations due to physical problems, and bodily pain. Analyses of SF-36 changed scores from baseline to Week 6 revealed that the fluoxetine group improved more than the placebo group across all scales. Differences in changes of scores between groups were significant (p \u3c .05), favoring the fluoxetine group for the scales of mental health, role limitations due to emotional problems, physical functioning, and bodily pain. Improvements observed in the fluoxetine group were both clinically and socially significant

Estimates of ambient groundwater velocity in the alluvium south of Yucca Mountain from single-well tracer tests.

The saturated alluvium located south of Yucca Mountain, Nevada is expected to serve as the final barrier to radionuclide transport from the proposed high-level nuclear waste repository at Yucca Mountain. The alluvium will act as a barrier if radionuclides breach the engineered barriers in the repository, move through the unsaturated zone beneath the repository to the water table, and then migrate through saturated volcanic tuffs to the alluvium. Three single-well injection-withdrawal tracer tests were conducted between December 2000 and April 2001 in the saturated alluviuni at NC-EWDP-19D1, a Nye County-Early Warning Drilling Program well located about 18 km south of Yucca Mountain. The tests had the objectives of (1) distinguishing between a single- and a dual-porosity conceptual radionuclide transport model for the alluvium, and (2) obtaining estimates of ambient groundwater velocity in the alluvium