This dissertation presents a novel contribution to scientific knowledge in the form of the development of statistical methodology for integrating diverse, genomic data sets, and by contributing to the understanding of the conservation of post- reproductive brain aging in mammals. Broadly speaking, this work is divided into two complimentary sections. The first section describes the development of a mixed effects modeling approach for integrating high-dimensional, genomic data sets. Microarray-based technologies allow researchers to monitor gene expression, transcription factor binding and alternative splicing on a genome-wide scale. The current challenge is to develop methods that analyze and integrate these vast data sets in a manner that produces biologically meaningful results, which can then be experimentally followed-up in the lab. The approach is described in terms of analyzing array data in the context of biologically-related groups of genes. A key component to this approach is the development of a novel model selection strategy that utilizes the biological information contained in the Gene Ontology graph in order to balance between biological specificity and model parsimony.

As the cost of high-throughput sequencing goes down, huge volumes of biological and medical data have been produced from various sequencing platforms at multiple molecular levels including genome, transcriptome, proteome, epigenome, metabolome, and so on. For a long time, data analysis on single molecular levels has paved the way to answer many important research questions. However, many Aging-Related Neuronal Diseases (ARNDs) and Central Nervous System (CNS) aging involve interactions of molecules from multiple molecular levels, in which conclusions based on single molecular levels are usually incomplete and sometimes misleading. In these scenarios, multi-omics data analysis has unprecedentedly helped capture much more useful information for the diagnosis, treatment, prognosis, and drug discovery of ARNDs. The first step towards a multi-omics analysis is to establish reliable and robust multi-omics datasets. In the past years, a few important ARNDs-associated multi-omics databases like Allen Brain have been constructed, which raised immediate needs like data curation, normalization, interpretation, and visualization for integrative multi-omics explorations. Though there have been several well-established multi-omics databases for ARNDs like Alzheimer’s disease, similar databases for other ARNDs are still in urgent need. After the databases establish, many computational tools and experiential strategies should be developed specifically for them. First, the multi-omics data are usually extremely noisy, complex, heterogeneous and in high dimension, which presents the need for appropriate denoising and dimension reduction methods. Second, since the multi-omics and non-omics data like pathological and clinical data are usually in different data spaces, a useful algorithm to mapping them into the same data space and integrate them is nontrivial. In the multi-omics era, there are numerous data-centric tools for the integration of multi-omics datasets, which could be generally divided into three categories: unsupervised, supervised, and semi-supervised methods. Commonly used algorithms include but not limited to Bayesian-based methods, Network-based methods, multi-step analysis methods, and multiple kernel learning methods. Third, methods are needed in studying and verifying the association between two or more levels of multi-omics data and non-omics data. For example, expression quantitative trait loci (eQTL) analysis is widely used to infer the association between a single nucleotide polymorphism (SNP) and the expression of a gene. Recently, the association between omics data and more complex data like pathological and clinical imaging data has been a hot research topic. The outcomes may reveal the underlying molecular mechanism and promote de novo drug design as well as drug repurposing for ARNDs. Here, we welcome investigators to share their Original Research, Review, Mini Review, Hypothesis and Theory, Perspective, Conceptual Analysis, Data Report, Brief Research Report, Code related to multi-omics studies of ARNDs, which can be applied for better diagnosis, treatment, prognosis and drug discovery of human diseases in the future era of precision medicine. Potential contents include but are not limited to the following: ▪ Methods for integrating, interpreting, or visualizing two or more omics data. ▪ Methods for identifying interactions between different data modalities. ▪ Methods for disease subtyping, biomarker prediction. ▪ Machine learning or deep learning methods on dimensional reduction and feature selection for big noisy data. ▪ Methods for studying the association among different omics data or between omics and non-omics data like clinical, pathological, and imaging data. ▪ Review of multi-omics resource about ARNDs and/or CNS aging. ▪ Experimental validation of biomarkers identified from multi-omics data analysis. ▪ Disease diagnosis and prognosis prediction from imaging and non-imaging data analysis, or both. ▪ Clinical applications or validations of findings from multi-omics data analysis.

The only single-source——now completely updated and revised——to offer a unified treatment of the theory, methodology, and applications of the EM algorithm Complete with updates that capture developments from the past decade, The EM Algorithm and Extensions, Second Edition successfully provides a basic understanding of the EM algorithm by describing its inception, implementation, and applicability in numerous statistical contexts. In conjunction with the fundamentals of the topic, the authors discuss convergence issues and computation of standard errors, and, in addition, unveil many parallels and connections between the EM algorithm and Markov chain Monte Carlo algorithms. Thorough discussions on the complexities and drawbacks that arise from the basic EM algorithm, such as slow convergence and lack of an in-built procedure to compute the covariance matrix of parameter estimates, are also presented. While the general philosophy of the First Edition has been maintained, this timely new edition has been updated, revised, and expanded to include: New chapters on Monte Carlo versions of the EM algorithm and generalizations of the EM algorithm New results on convergence, including convergence of the EM algorithm in constrained parameter spaces Expanded discussion of standard error computation methods, such as methods for categorical data and methods based on numerical differentiation Coverage of the interval EM, which locates all stationary points in a designated region of the parameter space Exploration of the EM algorithm's relationship with the Gibbs sampler and other Markov chain Monte Carlo methods Plentiful pedagogical elements—chapter introductions, lists of examples, author and subject indices, computer-drawn graphics, and a related Web site The EM Algorithm and Extensions, Second Edition serves as an excellent text for graduate-level statistics students and is also a comprehensive resource for theoreticians, practitioners, and researchers in the social and physical sciences who would like to extend their knowledge of the EM algorithm.

Recognition that aging is not the accumulation of disease, but rather comprises fundamental biological processes that are amenable to experimental study, is the basis for the recent growth of experimental biogerontology. As increasingly sophisticated studies provide greater understanding of what occurs in the aging brain and how these changes occur

Big Data in Omics and Imaging: Association Analysis addresses the recent development of association analysis and machine learning for both population and family genomic data in sequencing era. It is unique in that it presents both hypothesis testing and a data mining approach to holistically dissecting the genetic structure of complex traits and to designing efficient strategies for precision medicine. The general frameworks for association analysis and machine learning, developed in the text, can be applied to genomic, epigenomic and imaging data. FEATURES Bridges the gap between the traditional statistical methods and computational tools for small genetic and epigenetic data analysis and the modern advanced statistical methods for big data Provides tools for high dimensional data reduction Discusses searching algorithms for model and variable selection including randomization algorithms, Proximal methods and matrix subset selection Provides real-world examples and case studies Will have an accompanying website with R code The book is designed for graduate students and researchers in genomics, bioinformatics, and data science. It represents the paradigm shift of genetic studies of complex diseases– from shallow to deep genomic analysis, from low-dimensional to high dimensional, multivariate to functional data analysis with next-generation sequencing (NGS) data, and from homogeneous populations to heterogeneous population and pedigree data analysis. Topics covered are: advanced matrix theory, convex optimization algorithms, generalized low rank models, functional data analysis techniques, deep learning principle and machine learning methods for modern association, interaction, pathway and network analysis of rare and common variants, biomarker identification, disease risk and drug response prediction.