Genetic data analysis has been capturing a lot of attentions for understanding the mechanism of the development and progressing of diseases like cancers, and is crucial in discovering genetic markers and treatment targets in medical research. This dissertation focuses on several important issues in genetic data analysis, graphical network modeling, feature selection, and covariance estimation. First, we develop a gene network modeling method for discrete gene expression data, produced by technologies such as serial analysis of gene expression and RNA sequencing experiment, which generate counts of mRNA transcripts in cell samples. We propose a generalized linear model to fit the discrete gene expression data and assume that the log ratios of the mean expression levels follow a Gaussian distribution. We derive the gene network structures by selecting covariance matrices of the Gaussian distribution with a hyper-inverse Wishart prior. We incorporate prior network models based on Gene Ontology information, which avails existing biological information on the genes of interest. Next, we consider a variable selection problem, where the variables have natural grouping structures, with application to analysis of chromosomal copy number data. The chromosomal copy number data are produced by molecular inversion probes experiments which measure probe-specific copy number changes. We propose a novel Bayesian variable selection method, the hierarchical structured variable se- lection (HSVS) method, which accounts for the natural gene and probe-within-gene architecture to identify important genes and probes associated with clinically relevant outcomes. We propose the HSVS model for grouped variable selection, where simultaneous selection of both groups and within-group variables is of interest. The HSVS model utilizes a discrete mixture prior distribution for group selection and group-specific Bayesian lasso hierarchies for variable selection within groups. We further provide methods for accounting for serial correlations within groups that incorporate Bayesian fused lasso methods for within-group selection. Finally, we propose a Bayesian method of estimating high-dimensional covariance matrices that can be decomposed into a low rank and sparse component. This covariance structure has a wide range of applications including factor analytical model and random effects model. We model the covariance matrices with the decomposition structure by representing the covariance model in the form of a factor analytic model where the number of latent factors is unknown. We introduce binary indicators for estimating the rank of the low rank component combined with a Bayesian graphical lasso method for estimating the sparse component. We further extend our method to a graphical factor analytic model where the graphical model of the residuals is of interest. We achieve sparse estimation of the inverse covariance of the residuals in the graphical factor model by employing a hyper-inverse Wishart prior method for a decomposable graph and a Bayesian graphical lasso method for an unrestricted graph.

This dissertation presents a Bayesian hierarchical model to combine two-resolution metrology data for inspecting the geometric quality of manufactured parts. The high- resolution data points are scarce, and thus scatter over the surface being measured, while the low-resolution data are pervasive, but less accurate or less precise. Combining the two datasets could supposedly make a better prediction of the geometric surface of a manufactured part than using a single dataset. One challenge in combining the metrology datasets is the misalignment which exists between the low- and high-resolution data points. This dissertation attempts to provide a Bayesian hierarchical model that can handle such misaligned datasets, and includes the following components: (a) a Gaussian process for modeling metrology data at the low-resolution level; (b) a heuristic matching and alignment method that produces a pool of candidate matches and transformations between the two datasets; (c) a linkage model, conditioned on a given match and its associated transformation, that connects a high-resolution data point to a set of low-resolution data points in its neighborhood and makes a combined prediction; and finally (d) Bayesian model averaging of the predictive models in (c) over the pool of candidate matches found in (b). This Bayesian model averaging procedure assigns weights to different matches according to how much they support the observed data, and then produces the final combined prediction of the surface based on the data of both resolutions. The proposed method improves upon the methods of using a single dataset as well as a combined prediction without addressing the misalignment problem. This dissertation demonstrates the improvements over alternative methods using both simulated data and the datasets from a milled sine-wave part, measured by two coordinate measuring machines of different resolutions, respectively.

<p>By concentrating materials and increasing the speed with which rainfall is conveyed off of the landscape, nearly all forms of land use change lead to predictable shifts in the hydrologic, thermal, and chemical regimes of receiving waters that can lead to the local extirpation of sensitive aquatic biota. In Central Appalachian river networks, alkaline mine drainage (AlkMD) derived from mountaintop removal mining for coal (MTM) noticeably simplifies macroinvertebrate communities. In this dissertation, I have used this distinct chemical regime shift as a platform to move beyond current understanding of chemical pollution in river networks. In Chapter Two, I applied a new model, the Hierarchical Diversity Decision Framework (HiDDeF) to a macroinvertebrate dataset along a gradient of AlkMD. By using this new modeling tool, I showed that current AlkMD water quality standards allow one-quarter of regional macroinvertebrates to decline to half of their maximum abundances. In Chapter Three, I conducted a field study in the Mud River, WV to understand how AlkMD influences patterns in aquatic insect production. This work revealed roughly 3-fold declines in annual production of sensitive taxa throughout the year in reaches affected by AlkMD. These declines were more severe during summer base flow when pollutant concentrations were higher, thereby preventing sensitive organisms from completing their life cycles. Finally, in Chapter Four I described the idea of chemical fragmentation in river networks by performing a geospatial analysis of chemical pollution in Central Appalachia. In this work I showed that the ~30% of headwaters that remain after MTM intensification over the last four decades support ~10% of macroinvertebrates not found in mined reaches. Collectively my work moves beyond the simple tools used to understand the static, local consequences of chemical pollution in freshwater ecosystems.</p> / Dissertation

Pollution studies have sought to understand the relationships between adverse health effects and harmful exposures. Many environmental health studies are predicated on the idea that each exposure has both acute and long term health effects that need to be accurately mapped. Considerable work has been done linking air pollution to deleterious health outcomes but the underlying biological pathways and contributing sources remain difficult to identify. There are many statistical issues that arise in the exploration of these longitudinal study designs such as understanding pathways of effects, addressing missing data, and assessing the health effects of multipollutant mixtures. To this end this dissertation aims to address the afore mentioned statistical issues. Our first contribution investigates the mechanistic pathways between air pollutants and measures of cardiac electrical instability. The methods from chapter 1 propose a path analysis that would allow for the estimation of health effects according to multiple paths using structural equation models. Our second contribution recognizes that panel studies suffer from attrition over time and the loss of data can affect the analysis. Methods from Chapter 2 extend current regression calibration approaches by imputing missing data through the use of moving averages and assumed correlation structures. Our last contribution explores the use of factor analysis and two-stage hierarchical regression which are two commonly used approaches in the analysis of multipollutant mixtures. The methods from Chapter 3 attempt to compare the performance of these two existing methodologies for estimating health effects from multipollutant sources.

Many prior distributions are suggested for variance parameters in the hierarchical model. The “Non-informative” interval of the conjugate inverse-gamma prior might cause problems. I consider three priors – conjugate inverse-gamma, log-normal and truncated normal for the variance parameters and do the numerical analysis on Gelman’s 8-schools data. Then with the posterior draws, I compare the Bayesian credible intervals of parameters using the three priors. I use predictive distributions to do predictions and then discuss the differences of the three priors suggested. / text

Hierarchical models provide a flexible way of modeling complex behavior. However, the complicated interdependencies among the parameters in the hierarchy make training such models difficult. MCMC methods have been widely used for this purpose, but can often only approximate the necessary distributions. Acceptance-rejection sampling allows for perfect simulation from these often unnormalized distributions by drawing from another distribution over the same support. The efficacy of acceptance-rejection sampling is explored through application to a small dataset which has been widely used for evaluating different methods for inference on hierarchical models. A particular algorithm is developed to draw variates from the posterior distribution. The algorithm is both verified and validated, and then finally applied to the given data, with comparisons to the results of different methods.

The planet is experiencing a dramatic loss of species. The majority of species are unknown to science, and it is usually infeasible to conduct a census of a region to acquire a complete inventory of all life forms. Therefore, it is important to estimate and conduct statistical inference on the total number of species in a region based on samples obtained from field observations. Such estimates may suggest the number of species new to science and at potential risk of extinction. In this thesis, we develop novel methodology to conduct statistical inference, based on abundance-based data collected from multiple sampling locations, on the number of species within a taxonomic group residing in a region. The primary contribution of this work is the formulation of novel statistical methodology for analysis in this setting, where abundances of species are recorded at multiple sampling units across a region. This particular area has received relatively little attention in the literature. In the first chapter, the problem of estimating the number of species is formulated in a broad context, one that occurs in several seemingly unrelated fields of study. Estimators are commonly developed from statistical sampling models. Depending on the organisms or objects under study, different sampling techniques are used, and consequently, a variety of statistical models have been developed for this problem. A review of existing estimation methods, categorized by the associated sampling model, is presented in the second chapter. The third chapter develops a new negative binomial mixture model. The negative binomial model is employed to account for the common tendency of individuals of a particular species to occur in clusters. An exponential mixing distribution permits inference on the number of species that exist in the region, but were in fact absent from the sampling units. Adopting a classical approach for statistical inference, we develop the maximum likelihood estimator, and a corresponding profile-log-likelihood interval estimate of species richness. In addition, a Gaussian-based confidence interval based on large-sample theory is presented. The fourth chapter further extends the hierarchical model developed in Chapter 3 into a Bayesian framework. The motivation for the Bayesian paradigm is explained, and a hierarchical model based on random effects and discrete latent variables is presented. Computing the posterior distribution in this case is not straight-forward. A data augmentation technique that indirectly places priors on species richness is employed to compute the model using a Metropolis-Hastings algorithm. The fifth chapter examines the performance of our new methodology. Simulation studies are used to examine the mean-squared error of our proposed estimators. Comparisons to several commonly-used non-parametric estimators are made. Several conclusions emerge, and settings where our approaches can yield superior performance are clarified. In the sixth chapter, we present a case study. The methodology is applied to a real data set of oribatid mites (a taxonomic order of micro-arthropods) collected from multiple sites in a tropical rainforest in Panama. We adjust our statistical sampling models to account for the varying masses of material sampled from the sites. The resulting estimates of species richness for the oribatid mites are useful, and contribute to a wider investigation, currently underway, examining the species richness of all arthropods in the rainforest. Our approaches are the only existing methods that can make full use of the abundance-based data from multiple sampling units located in a single region. The seventh and final chapter concludes the thesis with a discussion of key considerations related to implementation and modeling assumptions, and describes potential avenues for further investigation. / Graduate

Master of Science / Department of Psychological Sciences / Richard J. Harris / The revised hierarchical model assumes a strong lexical link from L2 to L1 and a strong conceptual link from L1 to L2, with both links being contingent on L2 fluency. The bilingual memory literature has discussed the role of L2 fluency in bilingual lexical and semantic retrieval; however, little is known on how priming for a target language (L1 or L2) may affect lexical and semantic access or how it is affected by L2 proficiency. The present study utilized the revised hierarchical model to examine how language priming and intermediate levels of L2 fluency affects bilingual lexical and semantic retrieval in a yes/no image/word task. 181 participants read four paragraphs of discourse to prime for a specific target language (English or Spanish) and performed a modified picture-word interference task (MPWI), in which they had to determine if image/word pairs were congruent (matched) or incongruent (did not match). The main dependent variables were accuracy and RT on the MPWI task. Additional DVs were accuracy and RT on comprehension questions over the content of the priming discourse and question type (explicit, factual, and pragmatic). Across intermediate levels of L2 fluency, those more fluent performed faster and were more accurate on the MPWI task than those less fluent. No differences were observed when the image/word pairs were congruent for English or Spanish, yet there was a language difference when incongruent for Spanish. Readers had highest percent correct for explicit questions and lowest for pragmatic questions, took longer on factual than pragmatic question, and took longer to respond when priming discourse and questions were in Spanish than when in English. The results are interpreted and discussed in terms of the revised hierarchical model, in that fluency, at least at the intermediate level, affects processing time more than accuracy. Limitations of the study, future directions, and implications for L2 educators are also discussed.

This work deals with communication in multiagent systems. The protocols for negotiation and argumentation are shown, and model example of their usage is described. We describe hierarchical model of trust in contexts, that is used for representation of agent's believes. The argumentation protocol for those agents is designed, and is used for solving conflicts.

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