Thoroughly updated throughout, A First Course in Linear Model Theory, Second Edition is an intermediate-level statistics text that fills an important gap by presenting the theory of linear statistical models at a level appropriate for senior undergraduate or first-year graduate students. With an innovative approach, the authors introduce to students the mathematical and statistical concepts and tools that form a foundation for studying the theory and applications of both univariate and multivariate linear models. In addition to adding R functionality, this second edition features three new chapters and several sections on new topics that are extremely relevant to the current research in statistical methodology. Revised or expanded topics include linear fixed, random and mixed effects models, generalized linear models, Bayesian and hierarchical linear models, model selection, multiple comparisons, and regularized and robust regression. New to the Second Edition: Coverage of inference for linear models has been expanded into two chapters. Expanded coverage of multiple comparisons, random and mixed effects models, model selection, and missing data. A new chapter on generalized linear models (Chapter 12). A new section on multivariate linear models in Chapter 13, and expanded coverage of the Bayesian linear models and longitudinal models. A new section on regularized regression in Chapter 14. Detailed data illustrations using R. The authors' fresh approach, methodical presentation, wealth of examples, use of R, and introduction to topics beyond the classical theory set this book apart from other texts on linear models. It forms a refreshing and invaluable first step in students' study of advanced linear models, generalized linear models, nonlinear models, and dynamic models.

Bayesian Modeling in Bioinformatics discusses the development and application of Bayesian statistical methods for the analysis of high-throughput bioinformatics data arising from problems in molecular and structural biology and disease-related medical research, such as cancer. It presents a broad overview of statistical inference, clustering, and classification problems in two main high-throughput platforms: microarray gene expression and phylogenic analysis. The book explores Bayesian techniques and models for detecting differentially expressed genes, classifying differential gene expression, and identifying biomarkers. It develops novel Bayesian nonparametric approaches for bioinformatics problems, measurement error and survival models for cDNA microarrays, a Bayesian hidden Markov modeling approach for CGH array data, Bayesian approaches for phylogenic analysis, sparsity priors for protein-protein interaction predictions, and Bayesian networks for gene expression data. The text also describes applications of mode-oriented stochastic search algorithms, in vitro to in vivo factor profiling, proportional hazards regression using Bayesian kernel machines, and QTL mapping. Focusing on design, statistical inference, and data analysis from a Bayesian perspective, this volume explores statistical challenges in bioinformatics data analysis and modeling and offers solutions to these problems. It encourages readers to draw on the evolving technologies and promote statistical development in this area of bioinformatics.

Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subject. After reviewing univariate extreme value analysis and multivariate extremes, the book explains univariate extreme value mixture modeling, threshold selection in extreme value analysis, and threshold modeling of non-stationary extremes. It presents new results for block-maxima of vine copulas, develops time series of extremes with applications from climatology, describes max-autoregressive and moving maxima models for extremes, and discusses spatial extremes and max-stable processes. The book then covers simulation and conditional simulation of max-stable processes; inference methodologies, such as composite likelihood, Bayesian inference, and approximate Bayesian computation; and inferences about extreme quantiles and extreme dependence. It also explores novel applications of extreme value modeling, including financial investments, insurance and financial risk management, weather and climate disasters, clinical trials, and sports statistics. Risk analyses related to extreme events require the combined expertise of statisticians and domain experts in climatology, hydrology, finance, insurance, sports, and other fields. This book connects statistical/mathematical research with critical decision and risk assessment/management applications to stimulate more collaboration between these statisticians and specialists.

Extreme Value Modeling and Risk Analysis: Methods and Applications presents a broad overview of statistical modeling of extreme events along with the most recent methodologies and various applications. The book brings together background material and advanced topics, eliminating the need to sort through the massive amount of literature on the subject. After reviewing univariate extreme value analysis and multivariate extremes, the book explains univariate extreme value mixture modeling, threshold selection in extreme value analysis, and threshold modeling of non-stationary extremes. It presents new results for block-maxima of vine copulas, develops time series of extremes with applications from climatology, describes max-autoregressive and moving maxima models for extremes, and discusses spatial extremes and max-stable processes. The book then covers simulation and conditional simulation of max-stable processes; inference methodologies, such as composite likelihood, Bayesian inference, and approximate Bayesian computation; and inferences about extreme quantiles and extreme dependence. It also explores novel applications of extreme value modeling, including financial investments, insurance and financial risk management, weather and climate disasters, clinical trials, and sports statistics. Risk analyses related to extreme events require the combined expertise of statisticians and domain experts in climatology, hydrology, finance, insurance, sports, and other fields. This book connects statistical/mathematical research with critical decision and risk assessment/management applications to stimulate more collaboration between these statisticians and specialists.

Bayesian Modeling in Bioinformatics discusses the development and application of Bayesian statistical methods for the analysis of high-throughput bioinformatics data arising from problems in molecular and structural biology and disease-related medical research, such as cancer. It presents a broad overview of statistical inference, clustering, and classification problems in two main high-throughput platforms: microarray gene expression and phylogenic analysis.

The book explores Bayesian techniques and models for detecting differentially expressed genes, classifying differential gene expression, and identifying biomarkers. It develops novel Bayesian nonparametric approaches for bioinformatics problems, measurement error and survival models for cDNA microarrays, a Bayesian hidden Markov modeling approach for CGH array data, Bayesian approaches for phylogenic analysis, sparsity priors for protein-protein interaction predictions, and Bayesian networks for gene expression data. The text also describes applications of mode-oriented stochastic search algorithms, in vitro to in vivo factor profiling, proportional hazards regression using Bayesian kernel machines, and QTL mapping.

Focusing on design, statistical inference, and data analysis from a Bayesian perspective, this volume explores statistical challenges in bioinformatics data analysis and modeling and offers solutions to these problems. It encourages readers to draw on the evolving technologies and promote statistical development in this area of bioinformatics.

This volume describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. Introducing dynamic modeling for GLMs and containing over 1000 references and equations, Generalized Linear Models considers parametric and semiparametric approaches to overdispersed GLMs, presents methods of analyzing correlated binary data using latent variables. It also proposes a semiparametric method to model link functions for binary response data, and identifies areas of important future research and new applications of GLMs.

This volume describes how to conceptualize, perform, and critique traditional generalized linear models (GLMs) from a Bayesian perspective and how to use modern computational methods to summarize inferences using simulation. Introducing dynamic modeling for GLMs and containing over 1000 references and equations, Generalized Linear Models considers parametric and semiparametric approaches to overdispersed GLMs, presents methods of analyzing correlated binary data using latent variables. It also proposes a semiparametric method to model link functions for binary response data, and identifies areas of important future research and new applications of GLMs.

Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics. Each chapter is self-contained and focuses on a Bayesian methodology. It gives an overview of the area, presents theoretical insights, and emphasizes applications through motivating examples. This book reflects the diversity of Bayesian analysis, from novel Bayesian methodology, such as nonignorable response and factor analysis, to state-of-the-art applications in economics, astrophysics, biomedicine, oceanography, and other areas. It guides readers in using Bayesian techniques for a range of statistical analyses.

Collecting Bayesian material scattered throughout the literature, Current Trends in Bayesian Methodology with Applications examines the latest methodological and applied aspects of Bayesian statistics. The book covers biostatistics, econometrics, reliability and risk analysis, spatial statistics, image analysis, shape analysis, Bayesian computation, clustering, uncertainty assessment, high-energy astrophysics, neural networking, fuzzy information, objective Bayesian methodologies, empirical Bayes methods, small area estimation, and many more topics. Each chapter is self-contained and focuses on a Bayesian methodology. It gives an overview of the area, presents theoretical insights, and emphasizes applications through motivating examples. This book reflects the diversity of Bayesian analysis, from novel Bayesian methodology, such as nonignorable response and factor analysis, to state-of-the-art applications in economics, astrophysics, biomedicine, oceanography, and other areas. It guides readers in using Bayesian techniques for a range of statistical analyses.

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

This accessible reference includes selected contributions from Bayesian Thinking - Modeling and Computation, Volume 25 in the Handbook of Statistics Series, with a focus on key methodologies and applications for Bayesian models and computation. It describes parametric and nonparametric Bayesian methods for modeling, and how to use modern computational methods to summarize inferences using simulation. The book covers a wide range of topics including objective and subjective Bayesian inferences, with a variety of applications in modeling categorical, survival, spatial, spatiotemporal, Epidemiological, small area and micro array data.

Aids critical thinking on causal effects
Provides simulation based computing techniques
Covers Bioinformatics and Biostatistics

Research in Bayesian analysis and statistical decision theory is rapidly expanding and diversifying, making it increasingly more difficult for any single researcher to stay up to date on all current research frontiers. This book provides a review of current research challenges and opportunities. While the book can not exhaustively cover all current research areas, it does include some exemplary discussion of most research frontiers. Topics include objective Bayesian inference, shrinkage estimation and other decision based estimation, model selection and testing, nonparametric Bayes, the interface of Bayesian and frequentist inference, data mining and machine learning, methods for categorical and spatio-temporal data analysis and posterior simulation methods. Several major application areas are covered: computer models, Bayesian clinical trial design, epidemiology, phylogenetics, bioinformatics, climate modeling and applications in political science, finance and marketing. As a review of current research in Bayesian analysis the book presents a balance between theory and applications. The lack of a clear demarcation between theoretical and applied research is a reflection of the highly interdisciplinary and often applied nature of research in Bayesian statistics. The book is intended as an update for researchers in Bayesian statistics, including non-statisticians who make use of Bayesian inference to address substantive research questions in other fields. It would also be useful for graduate students and research scholars in statistics or biostatistics who wish to acquaint themselves with current research frontiers.

This volume describes how to develop Bayesian thinking, modelling and computation both from philosophical, methodological and application point of view. It further describes parametric and nonparametric Bayesian methods for modelling and how to use modern computational methods to summarize inferences using simulation. The book covers wide range of topics including objective and subjective Bayesian inferences with a variety of applications in modelling categorical, survival, spatial, spatiotemporal, Epidemiological, software reliability, small area and micro array data. The book concludes with a chapter on how to teach Bayesian thoughts to nonstatisticians.

Key Features:

-Critical thinking on causal effects
-Objective Bayesian philosophy
-Nonparametric Bayesian methodology
-Simulation based computing techniques
-Bioinformatics and Biostatistics
Key Features:

-Critical thinking on causal effects
-Objective Bayesian philosophy
-Nonparametric Bayesian methodology
-Simulation based computing techniques
-Bioinformatics and Biostatistics