The removal of coherent noise generated by surface waves in land based seismic is a prerequisite to imaging the subsurface. These surface waves, termed as ground roll, overlay important reflector information in both the t-x and f-k domains. Standard techniques of ground roll removal commonly alter reflector information as a consequence of the ground roll removal. We propose the combined use of the curvelet domain as a sparsifying basis in which to perform signal separation techniques that can preserve reflector information while increasing ground roll removal. We examine two signal separation techniques, a block-coordinate relaxation method and a Bayesian separation method. The derivations and background for both methods are presented and the parameter sensitivity is examined. Both methods are shown to be effective in certain situations regarding synthetic data and erroneous surface wave predictions. The block-coordinate relaxation method is shown to have major weaknesses when dealing with seismic signal separation in the presence of noise and with the production of artifacts and reflector degradation. The Bayesian separation method is shown to improve overall separation for both seismic and real data. The Bayesian separation scheme is used on a real data set with a surface wave prediction containing reflector information. It is shown to improve the signal separation by recovering reflector information while improving the surface wave removal. The abstract contains a separate real data example where both the block-coordinate relaxation method and the Bayesian separation method are compared.

Clustering microarray data is a helpful way of identifying genes which are biologically related. Unfortunately, when attempting to cluster microarray data, certain issues must be considered including: the uncertainty in the number of true clusters; the expression of a given gene is often a ected by the expression of other genes; and microarray data is usually high dimensional. This thesis outlines a Bayesian in nite Gaussian mixture model which addresses the issues outlined above by: not requiring the researcher to specify the number of clusters expected, applying a non-diagonal covariance structure, and using mixtures of factor analyzers and extensions thereof to structure the covariance matrix such that it is based on a few latent variables. This approach will be illustrated on real and simulated data.

The credibility of the scientific methodology of mathematical models and their adequacy to form the basis of public policy decisions has frequently been challenged. Skeptical views of the scientific value of modelling argue that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure. The purpose of this work was to first advance the Bayesian calibration of process-based models for guiding the water quality criteria setting process in Hamilton Harbour, Ontario, Canada. The analysis suggests that the water quality targets for total phosphorus and chlorophyll a concentrations will likely be met, if the recommendation for phosphorus loading at the level of 142 kg day-1 is achieved. My dissertation also examines how the Bayesian approach can effectively support the decision making process by synthesizing the predictions of different models developed for the same system. The model averaging approach consolidates the finding that the existing total phosphorus goal is most likely unattainable. The discrepancy between the chlorophyll a predictions of the two models pinpoints the need to delve into the dynamics of phosphorus in the sediment-water column interface. This work also aims to examine statistical formulations that explicitly accommodate the covariance among the process error terms for various model endpoints. The analysis suggests that the statistical characterization of the model error can be influential to the inference drawn by a modelling exercise. Finally, my dissertation challenges the capacity of the ecological foundation of eutrophication models to predict the role of nutrient regeneration. It shows that the recycled nutrients can be significant drivers in low as well as in high-productivity ecosystems depending on the period of the year examined. My dissertation also discusses several prescriptive guidelines that should be helpful towards a structural and methodological improvement of eutrophication modelling.

This thesis consists of three chapters in Bayesian financial econometrics. The first chapter proposes new dynamic component models of returns and realized covariance (RCOV) matrices based on timevarying Wishart distributions. Bayesian estimation and model comparison is conducted with a range of multivariate GARCH models and existing RCOV models from the literature. The main method of model comparison consists of a term-structure of density forecasts of returns for multiple forecast horizons. The new joint return-RCOV models provide superior density forecasts for returns from forecast horizons of 1 day to 3 months ahead as well as improved point forecasts for realized covariances. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out. The second chapter proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates on commodity prices for 3 commodity-exporting countries: Canada, Australia and New Zealand. I examine the predictive effect of exchange rates on the entire distribution of commodity prices and how this effect changes over time. A time-dependent infinite mixture of normal linear regression model is proposed for the conditional distribution of the commodity price index. The mixing weights of the mixture follow a Probit stick-breaking prior and are hence time-varying. As a result, I allow the conditional distribution of the commodity price index given exchange rates to change over time nonparametrically. The empirical study shows some new results on the predictive power of exchange rates on commodity prices. The third chapter proposes a flexible way of modeling heterogeneous breakdowns in the volatility dynamics of multivariate financial time series within the framework of MGARCH models. During periods of normal market activities, volatility dynamics are modeled by a MGARCH specification. I refer to any significant temporary deviation of the conditional covariance matrix from its implied GARCH dynamics as a covariance breakdown, which is captured through a stochastic component that allows for changes in the whole conditional covariance matrix. Bayesian inference is used and I propose an efficient posterior sampling procedure. Empirical studies show the model can capture complex and erratic temporary structural change in the volatility dynamics.

The credibility of the scientific methodology of mathematical models and their adequacy to form the basis of public policy decisions has frequently been challenged. Skeptical views of the scientific value of modelling argue that there is no true model of an ecological system, but rather several adequate descriptions of different conceptual basis and structure. The purpose of this work was to first advance the Bayesian calibration of process-based models for guiding the water quality criteria setting process in Hamilton Harbour, Ontario, Canada. The analysis suggests that the water quality targets for total phosphorus and chlorophyll a concentrations will likely be met, if the recommendation for phosphorus loading at the level of 142 kg day-1 is achieved. My dissertation also examines how the Bayesian approach can effectively support the decision making process by synthesizing the predictions of different models developed for the same system. The model averaging approach consolidates the finding that the existing total phosphorus goal is most likely unattainable. The discrepancy between the chlorophyll a predictions of the two models pinpoints the need to delve into the dynamics of phosphorus in the sediment-water column interface. This work also aims to examine statistical formulations that explicitly accommodate the covariance among the process error terms for various model endpoints. The analysis suggests that the statistical characterization of the model error can be influential to the inference drawn by a modelling exercise. Finally, my dissertation challenges the capacity of the ecological foundation of eutrophication models to predict the role of nutrient regeneration. It shows that the recycled nutrients can be significant drivers in low as well as in high-productivity ecosystems depending on the period of the year examined. My dissertation also discusses several prescriptive guidelines that should be helpful towards a structural and methodological improvement of eutrophication modelling.

Genes, the fundamental building blocks of life, act together (often through their derived proteins) in modules such as protein complexes and molecular pathways to achieve a cellular function such as DNA repair and cellular transport. A current emphasis in genomics research is to identify gene modules from gene profiles, which are measurements (such as a mutant phenotype or an expression level), associated with the individual genes under conditions of interest; genes in modules often have similar gene profiles. Clustering groups of genes with similar profiles can hence deliver candidate gene modules. Pairwise similarity measures derived from these profiles are used as input to the popular hierarchical agglomerative clustering algorithms; however, these algorithms offer little guidance on how to choose candidate modules and how to improve a clustering as new data becomes available. As an alternative, there are methods based on thresholding the similarity values to obtain a graph; such a graph can be analyzed through (probabilistic) methods developed in the social sciences. However, thresholding the data discards valuable information and choosing the threshold is difficult. Extending binary relational analysis, we exploit ranked relational data as the basis for two distinct approaches for identifying modules from genomic data, both based on the theory of random graph processes. We propose probabilistic models for ranked relational data that allow candidate modules to be accompanied by objective confidence scores and that permit an elegant integration of external information on gene-gene relationships. We first followed theoretical work by Ling to objectively select exceptionally isolated groups as candidate gene modules. Secondly, inspired by stochastic block models used in the social sciences, we construct a novel model for ranked relational data, where all genes have hidden module parameters which govern the strength of all gene-gene relationships. Adapting a classical likelihood often used for the analysis of horse races, clustering is performed by estimating the module parameters using standard Bayesian methods. The method allows the incorporation of prior information on gene-gene relationships; the utility of using prior information in the form of protein-protein interaction data in clustering of yeast mutant phenotype profiles is demonstrated.

The removal of coherent noise generated by surface waves in land based seismic is a prerequisite to imaging the subsurface. These surface waves, termed as ground roll, overlay important reflector information in both the t-x and f-k domains. Standard techniques of ground roll removal commonly alter reflector information as a consequence of the ground roll removal. We propose the combined use of the curvelet domain as a sparsifying basis in which to perform signal separation techniques that can preserve reflector information while increasing ground roll removal. We examine two signal separation techniques, a block-coordinate relaxation method and a Bayesian separation method. The derivations and background for both methods are presented and the parameter sensitivity is examined. Both methods are shown to be effective in certain situations regarding synthetic data and erroneous surface wave predictions. The block-coordinate relaxation method is shown to have major weaknesses when dealing with seismic signal separation in the presence of noise and with the production of artifacts and reflector degradation. The Bayesian separation method is shown to improve overall separation for both seismic and real data. The Bayesian separation scheme is used on a real data set with a surface wave prediction containing reflector information. It is shown to improve the signal separation by recovering reflector information while improving the surface wave removal. The abstract contains a separate real data example where both the block-coordinate relaxation method and the Bayesian separation method are compared.

Thesis (Ph. D.)--Oregon State University, 1999. / Typescript (photocopy). Includes bibliographical references (leaves 71-73). Also available on the World Wide Web.

Thesis (M.S.)--George Mason University, 2007. / Vita: p. 192. Thesis director: Kathryn Blackmond Laskey. Submitted in partial fulfillment of the requirements for the degree of Master of Science in Systems Engineering. Title from PDF t.p. (viewed Aug. 13, 2008). Additional zip folders contain software, thesis defense powerpoint and analysis documents. Includes bibliographical references (p. 190-191). Also issued in print.

Thesis--University of Wisconsin--Madison. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 191-197).