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Bayesian Data Analysis
Winner of the 2016 De Groot Prize from the International Society for Bayesian AnalysisNow in its third edition, this classic book is widely considered the leading text on Bayesian methods, lauded for its accessible, practical approach to analyzing data and solving research problems. Bayesian Data Analysis, Third Edition continues to take an applied approach to analysis using up-to-date Bayesian methods. The authors—all leaders in the statistics community—introduce basic concepts from a data-analytic perspective before presenting advanced methods. Throughout the text, numerous worked examples drawn from real applications and research emphasize the use of Bayesian inference in practice.New to the Third Edition Four new chapters on nonparametric modelingCoverage of weakly informative priors and boundary-avoiding priorsUpdated discussion of cross-validation and predictive information criteriaImproved convergence monitoring and effective sample size calculations for iterative simulationPresentations of Hamiltonian Monte Carlo, variational Bayes, and expectation propagationNew and revised software codeThe book can be used in three different ways. For undergraduate students, it introduces Bayesian inference starting from first principles. For graduate students, the text presents effective current approaches to Bayesian modeling and computation in statistics and related fields. For researchers, it provides an assortment of Bayesian methods in applied statistics. Additional materials, including data sets used in the examples, solutions to selected exercises, and software instructions, are available on the book’s web page.
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Introduction to Error Analysis, third edition
This remarkable text by John R. Taylor has been a non-stop best-selling international hit since it was first published forty years ago. However, the two-plus decades since the second edition was released have seen two dramatic developments; the huge rise in popularity of Bayesian statistics, and the continued increase in the power and availability of computers and calculators. In response to the former, Taylor has added a full chapter dedicated to Bayesian thinking, introducing conditional probabilities and Bayes’ theorem. The several examples presented in the new third edition are intentionally very simple, designed to give readers a clear understanding of what Bayesian statistics is all about as their first step on a journey to become practicing Bayesians. In response to the second development, Taylor has added a number of chapter-ending problems that will encourage readers to learn how to solve problems using computers. While many of these can be solved using programs such as Matlab or Mathematica, almost all of them are stated to apply to commonly available spreadsheet programs like Microsoft Excel. These programs provide a convenient way to record and process data and to calculate quantities like standard deviations, correlation coefficients, and normal distributions; they also have the wonderful ability – if students construct their own spreadsheets and avoid the temptation to use built-in functions – to teach the meaning of these concepts.
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Hierarchical Modeling and Analysis for Spatial Data
Hierarchical Modeling and Analysis for Spatial Data, Third Edition is the latest edition of this popular and authoritative text on Bayesian modeling and inference for spatial and spatial-temporal data. The text presents a comprehensive and up-to-date treatment of hierarchical and multilevel modeling for spatial and spatio-temporal data within a Bayesian framework. Over the past decade since the second edition, spatial statistics has evolved significantly driven by an explosion in data availability and advances in Bayesian computation. This edition reflects those changes, introducing new methods, expanded applications, and enhanced computational resources to support researchers and practitioners across disciplines, including environmental science, ecology, and public health.Key features of the third edition:A dedicated chapter on state-of-the-art Bayesian modeling of large spatial and spatio-temporal datasetsTwo new chapters on spatial point pattern analysis, covering both foundational and Bayesian perspectivesA new chapter on spatial data fusion, integrating diverse spatial data sources from different probabilistic mechanismsAn accessible introduction to GPS mapping, geodesic distances, and mathematical cartographyAn expanded special topics chapter, including spatial challenges with finite population modeling and spatial directional dataA thoroughly revised chapter on Bayesian inference, featuring an updated review of modern computational techniquesA dedicated GitHub repository providing R programs and solutions to selected exercises, ensuring continued access to evolving software developmentsWith refreshed content throughout, this edition serves as an essential reference for statisticians, data scientists, and researchers working with spatial data. Graduate students and professionals seeking a deep understanding of Bayesian spatial modeling will find this volume an invaluable resource for both theory and practice.
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Multiple Information Source Bayesian Optimization
The book provides a comprehensive review of multiple information sources and multi-fidelity Bayesian optimization, specifically focusing on the novel "Augmented Gaussian Process" methodology. The book is important to clarify the relations and the important differences in using multi-fidelity or multiple information source approaches for solving real-world problems. Choosing the most appropriate strategy, depending on the specific problem features, ensures the success of the final solution. The book also offers an overview of available software tools: in particular it presents two implementations of the Augmented Gaussian Process-based Multiple Information Source Bayesian Optimization, one in Python -- and available as a development branch in BoTorch -- and finally, a comparative analysis against other available multi-fidelity and multiple information sources optimization tools is presented, considering both test problems and real-world applications. The book will be useful to two main audiences: 1. PhD candidates in Computer Science, Artificial Intelligence, Machine Learning, and Optimization 2. Researchers from academia and industry who want to implement effective and efficient procedures for designing experiments and optimizing computationally expensive experiments in domains like engineering design, material science, and biotechnology.
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Bayesian Workflow
Bayesian statistics and statistical practice have evolved over the years, driven by advancements in theory, methods, and computational tools. This book explores the intricate workflows of applied Bayesian statistics, aiming to uncover the tacit knowledge often overlooked in published papers and textbooks. By systematizing the process of Bayesian model development, the book seeks to improve applied analyses and inspire future innovations in theory, methods, and software. It emphasizes the importance of iterative model building, model checking, computational troubleshooting, and simulated-data experimentation, offering a comprehensive perspective on statistical analysis.Through detailed examples and practical guidance, the book bridges the gap between theory and application, empowering practitioners and researchers to navigate the complexities of Bayesian inference. It is not a checklist or cookbook but a flexible framework for understanding and resolving challenges in statistical modeling and decision-making under uncertainty.Features:Covers all aspects of Bayesian statistical workflow, including model building, inference, validation, troubleshooting, and understandingDemonstrates iterative model development and computational problem-solving through real-world case studiesExplores computational challenges, calibration checking, and connections between modeling and computationHighlights the importance of checking models under diverse conditions to understand their limitations and improve their robustnessDiscusses how Bayesian principles apply to non-Bayesian methods in statistics and machine learningIncludes code snippets, exercises, and links to full datasets and code in R and Stan, with applicability to other programming environments like Python and JuliaThis book is designed for practitioners of applied Bayesian statistics, particularly users of probabilistic programming languages such as Stan, as well as developers of methods and software tailored to these users. It also targets researchers in Bayesian theory and methods, offering insights into understudied aspects of statistical workflows. Instructors and students will find adaptable exercises and case studies to enhance their learning experience. Beyond Bayesian inference, the book’s principles are relevant to users of non-Bayesian methods, making it a valuable resource for statisticians, data scientists, and machine learning professionals seeking to improve their modeling and decision-making processes.
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Introduction to Bayesian Inference, Methods and Computation
These lecture notes provide a rapid, accessible introduction to Bayesian statistical methods. The course covers the fundamental philosophy and principles of Bayesian inference, including the reasoning behind the prior/likelihood model construction synonymous with Bayesian methods, through to advanced topics such as nonparametrics, Gaussian processes and latent factor models. These advanced modelling techniques can easily be applied using computer code samples written in Python and Stan which are integrated into the main text. Importantly, the reader will learn methods for assessing model fit, and to choose between rival modelling approaches.
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Bayesian Inference and Computation in Reliability and Survival Analysis
Bayesian analysis is one of the important tools for statistical modelling and inference. Bayesian frameworks and methods have been successfully applied to solve practical problems in reliability and survival analysis, which have a wide range of real world applications in medical and biological sciences, social and economic sciences, and engineering. In the past few decades, significant developments of Bayesian inference have been made by many researchers, and advancements in computational technology and computer performance has laid the groundwork for new opportunities in Bayesian computation for practitioners.Because these theoretical and technological developments introduce new questions and challenges, and increase the complexity of the Bayesian framework, this book brings together experts engaged in groundbreaking research on Bayesian inference and computation to discuss important issues, with emphasis on applications to reliability and survival analysis. Topics covered are timely and have the potential to influence the interacting worlds of biostatistics, engineering, medical sciences, statistics, and more. The included chapters present current methods, theories, and applications in the diverse area of biostatistical analysis. The volume as a whole serves as reference in driving quality global health research.
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Bayesian Essentials with R
This Bayesian modeling book provides a self-contained entry to computational Bayesian statistics. Focusing on the most standard statistical models and backed up by real datasets and an all-inclusive R (CRAN) package called bayess, the book provides an operational methodology for conducting Bayesian inference, rather than focusing on its theoretical and philosophical justifications. Readers are empowered to participate in the real-life data analysis situations depicted here from the beginning. Special attention is paid to the derivation of prior distributions in each case and specific reference solutions are given for each of the models. Similarly, computational details are worked out to lead the reader towards an effective programming of the methods given in the book. In particular, all R codes are discussed with enough detail to make them readily understandable and expandable. Bayesian Essentials with R can be used as a textbook at both undergraduate and graduate levels. It is particularly useful with students in professional degree programs and scientists to analyze data the Bayesian way. The text will also enhance introductory courses on Bayesian statistics. Prerequisites for the book are an undergraduate background in probability and statistics, if not in Bayesian statistics.
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Python Data Analysis
Understand data analysis pipelines using machine learning algorithms and techniques with this practical guideKey FeaturesPrepare and clean your data to use it for exploratory analysis, data manipulation, and data wranglingDiscover supervised, unsupervised, probabilistic, and Bayesian machine learning methodsGet to grips with graph processing and sentiment analysisBook DescriptionData analysis enables you to generate value from small and big data by discovering new patterns and trends, and Python is one of the most popular tools for analyzing a wide variety of data. With this book, you'll get up and running using Python for data analysis by exploring the different phases and methodologies used in data analysis and learning how to use modern libraries from the Python ecosystem to create efficient data pipelines.Starting with the essential statistical and data analysis fundamentals using Python, you'll perform complex data analysis and modeling, data manipulation, data cleaning, and data visualization using easy-to-follow examples. You'll then understand how to conduct time series analysis and signal processing using ARMA models. As you advance, you'll get to grips with smart processing and data analytics using machine learning algorithms such as regression, classification, Principal Component Analysis (PCA), and clustering. In the concluding chapters, you'll work on real-world examples to analyze textual and image data using natural language processing (NLP) and image analytics techniques, respectively. Finally, the book will demonstrate parallel computing using Dask.By the end of this data analysis book, you'll be equipped with the skills you need to prepare data for analysis and create meaningful data visualizations for forecasting values from data.What you will learnExplore data science and its various process modelsPerform data manipulation using NumPy and pandas for aggregating, cleaning, and handling missing valuesCreate interactive visualizations using Matplotlib, Seaborn, and BokehRetrieve, process, and store data in a wide range of formatsUnderstand data preprocessing and feature engineering using pandas and scikit-learnPerform time series analysis and signal processing using sunspot cycle dataAnalyze textual data and image data to perform advanced analysisGet up to speed with parallel computing using DaskWho this book is forThis book is for data analysts, business analysts, statisticians, and data scientists looking to learn how to use Python for data analysis. Students and academic faculties will also find this book useful for learning and teaching Python data analysis using a hands-on approach. A basic understanding of math and working knowledge of the Python programming language will help you get started with this book.
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Bayesian Data Analysis for the Behavioral and Neural Sciences
This textbook bypasses the need for advanced mathematics by providing in-text computer code, allowing students to explore Bayesian data analysis without the calculus background normally considered a prerequisite for this material. Now, students can use the best methods without needing advanced mathematical techniques. This approach goes beyond “frequentist” concepts of p-values and null hypothesis testing, using the full power of modern probability theory to solve real-world problems. The book offers a fully self-contained course, which demonstrates analysis techniques throughout with worked examples crafted specifically for students in the behavioral and neural sciences. The book presents two general algorithms that help students solve the measurement and model selection (also called “hypothesis testing”) problems most frequently encountered in real-world applications.
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Bayesian Analysis of Stochastic Process Models
Bayesian analysis of complex models based on stochastic processes has in recent years become a growing area. This book provides a unified treatment of Bayesian analysis of models based on stochastic processes, covering the main classes of stochastic processing including modeling, computational, inference, forecasting, decision making and important applied models. Key features: Explores Bayesian analysis of models based on stochastic processes, providing a unified treatment. Provides a thorough introduction for research students. Computational tools to deal with complex problems are illustrated along with real life case studies Looks at inference, prediction and decision making. Researchers, graduate and advanced undergraduate students interested in stochastic processes in fields such as statistics, operations research (OR), engineering, finance, economics, computer science and Bayesian analysis will benefit from reading this book. With numerous applications included, practitioners of OR, stochastic modelling and applied statistics will also find this book useful.
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Foundations of Bayesian Statistics for Data Scientists
This book is an overview of the Bayesian approach to applying the most important inferential methods of statistical science. It is designed as a textbook for advanced undergraduate and master’s students in Data Science, Statistics, or Mathematics who are interested in learning about Bayesian statistics.The reader should be familiar with calculus and should have taken a statistical inference Statistics course covering the basic rules of probability, probability distributions and expectations, as well as the fundamentals of the traditional, frequentist approach to statistics, including sampling distributions, likelihood functions, basic inferential methods such as point estimation, confidence intervals, significance tests, and linear regression models.Key Features:● Uses real world data examples and contains numerous exercises.● Includes software appendices in R and Python.● Offers slides, labs, and other materials on the book’s website.Each chapter begins with a brief review of the primary frequentist methods for its topic before introducing corresponding Bayesian methods. This book presents some substantive theory as well as the methods, and is therefore intended for a reader who wishes to understand Bayesian methods rather than merely apply them. The focus is not just on presenting statistical methodologies but also on demonstrating how to implement them with modern software, emphasizing appropriate simulation methods.
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Bayesian Computation with R
There has been dramatic growth in the development and application of Bayesian inference in statistics. Berger (2000) documents the increase in Bayesian activity by the number of published research articles, the number of books,andtheextensivenumberofapplicationsofBayesianarticlesinapplied disciplines such as science and engineering. One reason for the dramatic growth in Bayesian modeling is the availab- ity of computational algorithms to compute the range of integrals that are necessary in a Bayesian posterior analysis. Due to the speed of modern c- puters, it is now possible to use the Bayesian paradigm to ?t very complex models that cannot be ?t by alternative frequentist methods. To ?t Bayesian models, one needs a statistical computing environment. This environment should be such that one can: write short scripts to de?ne a Bayesian model use or write functions to summarize a posterior distribution use functions to simulate from the posterior distribution construct graphs to illustrate the posterior inference An environment that meets these requirements is the R system. R provides a wide range of functions for data manipulation, calculation, and graphical d- plays. Moreover, it includes a well-developed, simple programming language that users can extend by adding new functions. Many such extensions of the language in the form of packages are easily downloadable from the Comp- hensive R Archive Network (CRAN).
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Bayesian Logical Data Analysis for the Physical Sciences
Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.
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Bayesian Analysis for the Social Sciences
Bayesian methods are increasingly being used in the social sciences, as the problems encountered lend themselves so naturally to the subjective qualities of Bayesian methodology. This book provides an accessible introduction to Bayesian methods, tailored specifically for social science students. It contains lots of real examples from political science, psychology, sociology, and economics, exercises in all chapters, and detailed descriptions of all the key concepts, without assuming any background in statistics beyond a first course. It features examples of how to implement the methods using WinBUGS – the most-widely used Bayesian analysis software in the world – and R – an open-source statistical software. The book is supported by a Website featuring WinBUGS and R code, and data sets.
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Bayesian Applications in Environmental and Ecological Studies with R and Stan
Modern ecological and environmental sciences are dominated by observational data. As a result, traditional statistical training often leaves scientists ill-prepared for the data analysis tasks they encounter in their work. Bayesian methods provide a more robust and flexible tool for data analysis, as they enable information from different sources to be brought into the modelling process. Bayesian Applications in Evnironmental and Ecological Studies with R and Stan provides a Bayesian framework for model formulation, parameter estimation, and model evaluation in the context of analyzing environmental and ecological data.Features:An accessible overview of Bayesian methods in environmental and ecological studiesEmphasizes the hypothetical deductive process, particularly model formulationNecessary background material on Bayesian inference and Monte Carlo simulationDetailed case studies, covering water quality monitoring and assessment, ecosystem response to urbanization, fisheries ecology, and moreAdvanced chapter on Bayesian applications, including Bayesian networks and a change point modelComplete code for all examples, along with the data used in the book, are available via GitHubThe book is primarily aimed at graduate students and researchers in the environmental and ecological sciences, as well as environmental management professionals. This is a group of people representing diverse subject matter fields, who could benefit from the potential power and flexibility of Bayesian methods.
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Bayesian Logical Data Analysis for the Physical Sciences
Bayesian inference provides a simple and unified approach to data analysis, allowing experimenters to assign probabilities to competing hypotheses of interest, on the basis of the current state of knowledge. By incorporating relevant prior information, it can sometimes improve model parameter estimates by many orders of magnitude. This book provides a clear exposition of the underlying concepts with many worked examples and problem sets. It also discusses implementation, including an introduction to Markov chain Monte-Carlo integration and linear and nonlinear model fitting. Particularly extensive coverage of spectral analysis (detecting and measuring periodic signals) includes a self-contained introduction to Fourier and discrete Fourier methods. There is a chapter devoted to Bayesian inference with Poisson sampling, and three chapters on frequentist methods help to bridge the gap between the frequentist and Bayesian approaches. Supporting Mathematica® notebooks with solutions to selected problems, additional worked examples, and a Mathematica tutorial are available at www.cambridge.org/9780521150125.
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Contemporary Bayesian Econometrics and Statistics
Tools to improve decision making in an imperfect world This publication provides readers with a thorough understanding of Bayesian analysis that is grounded in the theory of inference and optimal decision making. Contemporary Bayesian Econometrics and Statistics provides readers with state-of-the-art simulation methods and models that are used to solve complex real-world problems. Armed with a strong foundation in both theory and practical problem-solving tools, readers discover how to optimize decision making when faced with problems that involve limited or imperfect data. The book begins by examining the theoretical and mathematical foundations of Bayesian statistics to help readers understand how and why it is used in problem solving. The author then describes how modern simulation methods make Bayesian approaches practical using widely available mathematical applications software. In addition, the author details how models can be applied to specific problems, including: * Linear models and policy choices * Modeling with latent variables and missing data * Time series models and prediction * Comparison and evaluation of models The publication has been developed and fine- tuned through a decade of classroom experience, and readers will find the author's approach very engaging and accessible. There are nearly 200 examples and exercises to help readers see how effective use of Bayesian statistics enables them to make optimal decisions. MATLAB? and R computer programs are integrated throughout the book. An accompanying Web site provides readers with computer code for many examples and datasets. This publication is tailored for research professionals who use econometrics and similar statistical methods in their work. With its emphasis on practical problem solving and extensive use of examples and exercises, this is also an excellent textbook for graduate-level students in a broad range of fields, including economics, statistics, the social sciences, business, and public policy.
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Foundations of Bayesian Statistics for Data Scientists
This book is an overview of the Bayesian approach to applying the most important inferential methods of statistical science. It is designed as a textbook for advanced undergraduate and master’s students in Data Science, Statistics, or Mathematics who are interested in learning about Bayesian statistics.The reader should be familiar with calculus and should have taken a statistical inference Statistics course covering the basic rules of probability, probability distributions and expectations, as well as the fundamentals of the traditional, frequentist approach to statistics, including sampling distributions, likelihood functions, basic inferential methods such as point estimation, confidence intervals, significance tests, and linear regression models.Key Features:● Uses real world data examples and contains numerous exercises.● Includes software appendices in R and Python.● Offers slides, labs, and other materials on the book’s website.Each chapter begins with a brief review of the primary frequentist methods for its topic before introducing corresponding Bayesian methods. This book presents some substantive theory as well as the methods, and is therefore intended for a reader who wishes to understand Bayesian methods rather than merely apply them. The focus is not just on presenting statistical methodologies but also on demonstrating how to implement them with modern software, emphasizing appropriate simulation methods.
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Bayesian Probability Theory
From the basics to the forefront of modern research, this book presents all aspects of probability theory, statistics and data analysis from a Bayesian perspective for physicists and engineers. The book presents the roots, applications and numerical implementation of probability theory, and covers advanced topics such as maximum entropy distributions, stochastic processes, parameter estimation, model selection, hypothesis testing and experimental design. In addition, it explores state-of-the art numerical techniques required to solve demanding real-world problems. The book is ideal for students and researchers in physical sciences and engineering.
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Data Analysis
Statistics lectures have been a source of much bewilderment and frustration for generations of students. This book attempts to remedy the situation by expounding a logical and unified approach to the whole subject of data analysis.This text is intended as a tutorial guide for senior undergraduates and research students in science and engineering. After explaining the basic principles of Bayesian probability theory, their use is illustrated with a variety of examples ranging from elementary parameter estimation to image processing. Other topics covered include reliability analysis, multivariate optimization, least-squares and maximum likelihood, error-propagation, hypothesis testing, maximum entropy and experimentaldesign.The Second Edition of this successful tutorial book contains a new chapter on extensions to the ubiquitous least-squares procedure, allowing for the straightforward handling of outliers and unknown correlated noise, and a cutting-edge contribution from John Skilling on a novel numerical technique for Bayesian computation called 'nested sampling'.
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Statistical Decision Theory and Bayesian Analysis
In this new edition the author has added substantial material on Bayesian analysis, including lengthy new sections on such important topics as empirical and hierarchical Bayes analysis, Bayesian calculation, Bayesian communication, and group decision making. With these changes, the book can be used as a self-contained introduction to Bayesian analysis. In addition, much of the decision-theoretic portion of the text was updated, including new sections covering such modern topics as minimax multivariate (Stein) estimation.
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Oxford Handbook of Applied Bayesian Analysis
Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry. This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & SocialSciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
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Introduction to Bayesian Data Analysis for Cognitive Science
This book introduces Bayesian data analysis and Bayesian cognitive modeling to students and researchers in cognitive science (e.g., linguistics, psycholinguistics, psychology, computer science), with a particular focus on modeling data from planned experiments. The book relies on the probabilistic programming language Stan and the R package brms, which is a front-end to Stan. The book only assumes that the reader is familiar with the statistical programming language R, and has basic high school exposure to pre-calculus mathematics; some of the important mathematical constructs needed for the book are introduced in the first chapter.Through this book, the reader will be able to develop a practical ability to apply Bayesian modeling within their own field. The book begins with an informal introduction to foundational topics such as probability theory, and univariate and bi-/multivariate discrete and continuous random variables. Then, the application of Bayes' rule for statistical inference is introduced with several simple analytical examples that require no computing software; the main insight here is that the posterior distribution of a parameter is a compromise between the prior and the likelihood functions. The book then gradually builds up the regression framework using the brms package in R, ultimately leading to hierarchical regression modeling (aka the linear mixed model). Along the way, there is detailed discussion about the topic of prior selection, and developing a well-defined workflow. Later chapters introduce the Stan programming language, and cover advanced topics using practical examples: contrast coding, model comparison using Bayes factors and cross-validation, hierarchical models and reparameterization, defining custom distributions, measurement error models and meta-analysis, and finally, some examples of cognitive models: multinomial processing trees, finite mixture models, and accumulator models. Additional chapters, appendices, and exercises are provided as online materials and can be accessed here: https://github.com/bnicenboim/bayescogsci.
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Design and Analysis of Cross-Over Trials
Design and Analysis of Cross-Over Trials is concerned with a specific kind of comparative trial known as the cross-over trial, in which subjects receive different sequences of treatments. Such trials are widely used in clinical and medical research, and in other diverse areas such as veterinary science, psychology, sports science, and agriculture.The first edition of this book was the first to be wholly devoted to the subject. The second edition was revised to mirror growth and development in areas where the design remained in widespread use and new areas where it had grown in importance. This new Third Edition:Contains seven new chapters written in the form of short case studies that address re-estimating sample size when testing for average bioequivalence, fitting a nonlinear dose response function, estimating a dose to take forward from phase two to phase three, establishing proof of concept, and recalculating the sample size using conditional powerEmploys the R package Crossover, specially created to accompany the book and provide a graphical user interface for locating designs in a large catalog and for searching for new designsIncludes updates regarding the use of period baselines and the analysis of data from very small trialsReflects the availability of new procedures in SAS, particularly proc glimmix Presents the SAS procedure proc mcmc as an alternative to WinBUGS for Bayesian analysisComplete with real data and downloadable SAS code, Design and Analysis of Cross-Over Trials, Third Edition provides a practical understanding of the latest methods along with the necessary tools for implementation.
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Oxford Handbook of Applied Bayesian Analysis
Bayesian analysis has developed rapidly in applications in the last two decades and research in Bayesian methods remains dynamic and fast-growing. Dramatic advances in modelling concepts and computational technologies now enable routine application of Bayesian analysis using increasingly realistic stochastic models, and this drives the adoption of Bayesian approaches in many areas of science, technology, commerce, and industry.This Handbook explores contemporary Bayesian analysis across a variety of application areas. Chapters written by leading exponents of applied Bayesian analysis showcase the scientific ease and natural application of Bayesian modelling, and present solutions to real, engaging, societally important and demanding problems. The chapters are grouped into five general areas: Biomedical & Health Sciences; Industry, Economics & Finance; Environment & Ecology; Policy, Political & SocialSciences; and Natural & Engineering Sciences, and Appendix material in each touches on key concepts, models, and techniques of the chapter that are also of broader pedagogic and applied interest.
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Bayesian Models
A fully updated and expanded edition of the essential primer on Bayesian modeling for ecologistsUniquely suited to deal with complexity in a statistically coherent way, Bayesian modeling has become an indispensable tool for ecological research. This book teaches the basic principles of mathematics and statistics needed to apply Bayesian models to the analysis of ecological data, using language non-statisticians can understand. Deemphasizing computer coding in favor of a clear treatment of model building, it starts with a definition of probability and proceeds step-by-step through distribution theory, likelihood, simple Bayesian models, and hierarchical Bayesian models. Now revised and expanded, Bayesian Models enables students and practitioners to gain new insights from ecological models and data properly tempered by uncertainty.Covers the basic rules of probability needed to model diverse types of ecological data in the Bayesian frameworkShows how to write proper mathematical expressions for posterior distributions using directed acyclic graphs as templatesExplains how to use the powerful Markov chain Monte Carlo algorithm to find posterior distributions of model parameters, latent states, and missing dataTeaches how to check models to assure they meet the assumptions of model-based inferenceDemonstrates how to make inferences from single and multiple Bayesian modelsProvides worked problems for practicing and strengthening modeling skillsFeatures new chapters on spatial models and modeling missing data
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Bayesian Full Information Structrual Analysis
1 1. Statement of the problem. Bayes' theorem provides a very powerful tool for statistical inference, especially when pooling information from different sources is appropriate. Thus, prior information resulting from economic theory and/or from previous (real or hypothetical) samples can be combined with the information embodied in new observations; and this operation can be performed formally, within a rigorous mathematical framework. To introduce the Bayesian analysis of the simultaneous equations model, we shall base our presentation in the very convenient exposition given by Dreze in his presidential adress to the . S' 2 C f Second World ongress 0 the Econometr1c oC1ety. The Bayesian method in statistics is usually presented as follows Consider the joint probability density function f(x.e) defined on the product space X x9, where X = {x} denotes the sample space, and e = {e} denotes the parameter space, If we decompose the joint density f(x,e) in a conditional density f(x/e) and a marginal lThe beginning of this section reviews some very well known proposi- tions of Bayesian analysis. Those who are familiar with the subject can skip this part, and start with p.5. 2J.H.Dreze."Econometrics and Decision Theory". Presidential adress delivered at the Second World Congress of the Econometric Society.
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WAIC and WBIC with Python Stan
Master the art of machine learning and data science by diving into the essence of mathematical logic with this comprehensive textbook. This book focuses on the widely applicable information criterion (WAIC), also described as the Watanabe-Akaike information criterion, and the widely applicable Bayesian information criterion (WBIC), also described as the Watanabe Bayesian information criterion. The book expertly guides you through relevant mathematical problems while also providing hands-on experience with programming in Python and Stan. Whether you’re a data scientist looking to refine your model selection process or a researcher who wants to explore the latest developments in Bayesian statistics, this accessible guide will give you a firm grasp of Watanabe Bayesian Theory.The key features of this indispensable book include:A clear and self-contained writing style, ensuring ease of understanding for readers at various levels of expertise.100 carefully selected exercises accompanied by solutions in the main text, enabling readers to effectively gauge their progress and comprehension.A comprehensive guide to Sumio Watanabe’s groundbreaking Bayes theory, demystifying a subject once considered too challenging even for seasoned statisticians.Detailed source programs and Stan codes that will enhance readers’ grasp of the mathematical concepts presented.A streamlined approach to algebraic geometry topics in Chapter 6, making Bayes theory more accessible and less daunting.Embark on your machine learning and data science journey with this essential textbook and unlock the full potential of WAIC and WBIC today!
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Bayesian Analysis in Natural Language Processing, Second Edition
Natural language processing (NLP) went through a profound transformation in the mid-1980s when it shifted to make heavy use of corpora and data-driven techniques to analyze language. Since then, the use of statistical techniques in NLP has evolved in several ways. One such example of evolution took place in the late 1990s or early 2000s, when full-fledged Bayesian machinery was introduced to NLP. This Bayesian approach to NLP has come to accommodate various shortcomings in the frequentist approach and to enrich it, especially in the unsupervised setting, where statistical learning is done without target prediction examples.In this book, we cover the methods and algorithms that are needed to fluently read Bayesian learning papers in NLP and to do research in the area. These methods and algorithms are partially borrowed from both machine learning and statistics and are partially developed "in-house" in NLP. We cover inference techniques such as Markov chain Monte Carlo sampling and variational inference, Bayesian estimation, and nonparametric modeling. In response to rapid changes in the field, this second edition of the book includes a new chapter on representation learning and neural networks in the Bayesian context. We also cover fundamental concepts in Bayesian statistics such as prior distributions, conjugacy, and generative modeling. Finally, we review some of the fundamental modeling techniques in NLP, such as grammar modeling, neural networks and representation learning, and their use with Bayesian analysis.
R 2,868.08
Frontiers of Statistical Decision Making and Bayesian Analysis
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.
R 3,094.47
Frontiers of Statistical Decision Making and Bayesian Analysis
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.
R 3,095.37
Statistical and Econometric Methods for Transportation Data Analysis
The book's website (with databases and other support materials) can be accessed here.Praise for the Second Edition:The second edition introduces an especially broad set of statistical methods … As a lecturer in both transportation and marketing research, I find this book an excellent textbook for advanced undergraduate, Master’s and Ph.D. students, covering topics from simple descriptive statistics to complex Bayesian models. … It is one of the few books that cover an extensive set of statistical methods needed for data analysis in transportation. The book offers a wealth of examples from the transportation field. —The American Statistician Statistical and Econometric Methods for Transportation Data Analysis, Third Edition offers an expansion over the first and second editions in response to the recent methodological advancements in the fields of econometrics and statistics and to provide an increasing range of examples and corresponding data sets. It describes and illustrates some of the statistical and econometric tools commonly used in transportation data analysis. It provides a wide breadth of examples and case studies, covering applications in various aspects of transportation planning, engineering, safety, and economics. Ample analytical rigor is provided in each chapter so that fundamental concepts and principles are clear and numerous references are provided for those seeking additional technical details and applications. New to the Third Edition Updated references and improved examples throughout. New sections on random parameters linear regression and ordered probability models including the hierarchical ordered probit model. A new section on random parameters models with heterogeneity in the means and variances of parameter estimates. Multiple new sections on correlated random parameters and correlated grouped random parameters in probit, logit and hazard-based models. A new section discussing the practical aspects of random parameters model estimation. A new chapter on Latent Class Models. A new chapter on Bivariate and Multivariate Dependent Variable Models. Statistical and Econometric Methods for Transportation Data Analysis, Third Edition can serve as a textbook for advanced undergraduate, Masters, and Ph.D. students in transportation-related disciplines including engineering, economics, urban and regional planning, and sociology. The book also serves as a technical reference for researchers and practitioners wishing to examine and understand a broad range of statistical and econometric tools required to study transportation problems.
R 7,666.85
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis
Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis, Second Edition, provides a comprehensive guide for practitioners who wish to understand, construct, and analyze intelligent systems for decision support based on probabilistic networks. This new edition contains six new sections, in addition to fully-updated examples, tables, figures, and a revised appendix. Intended primarily for practitioners, this book does not require sophisticated mathematical skills or deep understanding of the underlying theory and methods nor does it discuss alternative technologies for reasoning under uncertainty. The theory and methods presented are illustrated through more than 140 examples, and exercises are included for the reader to check his or her level of understanding. The techniques and methods presented for knowledge elicitation, model construction and verification, modeling techniques and tricks, learning models from data, and analyses of models have all been developed and refined on the basis of numerous courses that the authors have held for practitioners worldwide.
R 3,592.13
Design and Analysis of Cross-Over Trials
Design and Analysis of Cross-Over Trials is concerned with a specific kind of comparative trial known as the cross-over trial, in which subjects receive different sequences of treatments. Such trials are widely used in clinical and medical research, and in other diverse areas such as veterinary science, psychology, sports science, and agriculture.The first edition of this book was the first to be wholly devoted to the subject. The second edition was revised to mirror growth and development in areas where the design remained in widespread use and new areas where it had grown in importance. This new Third Edition:Contains seven new chapters written in the form of short case studies that address re-estimating sample size when testing for average bioequivalence, fitting a nonlinear dose response function, estimating a dose to take forward from phase two to phase three, establishing proof of concept, and recalculating the sample size using conditional powerEmploys the R package Crossover, specially created to accompany the book and provide a graphical user interface for locating designs in a large catalog and for searching for new designsIncludes updates regarding the use of period baselines and the analysis of data from very small trialsReflects the availability of new procedures in SAS, particularly proc glimmix Presents the SAS procedure proc mcmc as an alternative to WinBUGS for Bayesian analysisComplete with real data and downloadable SAS code, Design and Analysis of Cross-Over Trials, Third Edition provides a practical understanding of the latest methods along with the necessary tools for implementation.
R 2,454.00
Bayesian Thinking
Apply Bayesian analysis to real engineering, science, and business problems Professionals facing uncertain data need a complete workflow from problem framing to defensible decisions. Bayesian Thinking: Case Studies and AI Tools to Support Data-Driven Decisions in Engineering, Science, and Business delivers that workflow through case studies in reliability engineering, medical diagnostics, economics, and product quality. Readers master every stage: framing real-world questions as probabilistic models, eliciting domain-informed priors, selecting models via Bayes factors and WAIC, running inference in R and Stan, and applying statistical decision theory to optimize actions. The book shows how to partner with AI for prompt engineering, model exploration, and sensitivity analysis while preserving human judgment and rigor. Clear code snippets, visual diagnostics, and posterior predictive checks build intuition fast. You will learn to optimize maintenance schedules, evaluate diagnostic tests, model system performance, and extract actionable insights from noisy data under uncertainty. Integrate artificial intelligence as a collaborative partner in Bayesian workflows for smarter prior elicitation, model exploration, and sensitivity analysis. Elicit and calibrate informative priors from domain knowledge across engineering, medicine, and business with transparency and mathematical rigor. Interpret posterior distributions confidently using visual diagnostics, trace plots, and posterior predictive checks during iterative model building. Transform ambiguous real-world problems into formal Bayesian models ready for rigorous inference and statistical decision analysis. Apply Bayesian methods to reliability challenges including failure analysis, maintenance optimization, and performance modeling of complex systems. Reliability engineers, data analysts in manufacturing and aerospace, and analytics professionals will find immediate, practical value. Graduate students and researchers in statistics, industrial engineering, bioengineering, and economics gain a structured, code-driven approach to Bayesian modeling and decision-making under real-world uncertainty.
R 4,885.00
Student’s Guide to Bayesian Statistics
Supported by a wealth of learning features, exercises, and visual elements as well as online video tutorials and interactive simulations, this book is the first student-focused introduction to Bayesian statistics. Without sacrificing technical integrity for the sake of simplicity, the author draws upon accessible, student-friendly language to provide approachable instruction perfectly aimed at statistics and Bayesian newcomers. Through a logical structure that introduces and builds upon key concepts in a gradual way and slowly acclimatizes students to using R and Stan software, the book covers: An introduction to probability and Bayesian inferenceUnderstanding Bayes′ rule Nuts and bolts of Bayesian analytic methodsComputational Bayes and real-world Bayesian analysisRegression analysis and hierarchical methods This unique guide will help students develop the statistical confidence and skills to put the Bayesian formula into practice, from the basic concepts of statistical inference to complex applications of analyses.
R 3,119.00
Bayesian Analysis in Statistics and Econometrics
This volume is based on the invited and the contributed presentations given at the Indo-U.S. Workshop on Bayesian Analysis in Statistics and Econometrics (BASE), Dec. 19-23, 1988, held at the Hotel Taj Residency, Bangalore, India. The workshop was jointly sponsored by The Ohio State University, The Indian Statistical Institute, The Indian Econometrics So ciety, U.S. National Science Foundation and the NSF-NBER Seminar on Bayesian Inference in Econometrics. Profs. Morrie DeGroot, Prem Goel, and Arnold Zellner were the program organizers. Unfortunately, Morrie became seriously ill just before the workshop was to start and could not participate in the workshop. Almost a year later, Morrie passed away after fighting valiantly with the illness. Not to find Morrie among ourselves was a shock for most of us. He was a continuous source of inspiration and ideas. Even while Morrie was fighting for his life, we had a lot of discussions about the contents of this volume and the Bangalore Workshop. He even talked about organizing a Second Indo-U.S. workshop some time in the near future. We are dedicating this volume to the memory of Prof. Morris H. DeGroot. We have taken a conscious decision not to include any biography of Morrie in this volume. An excellent biography of Morrie has appeared in Statistical Science [(1991), vol. 6, 1-14], and we could not have done a better job than that.
R 4,293.51
Bayesian inference with INLA
The integrated nested Laplace approximation (INLA) is a recent computational method that can fit Bayesian models in a fraction of the time required by typical Markov chain Monte Carlo (MCMC) methods. INLA focuses on marginal inference on the model parameters of latent Gaussian Markov random fields models and exploits conditional independence properties in the model for computational speed.Bayesian Inference with INLA provides a description of INLA and its associated R package for model fitting. This book describes the underlying methodology as well as how to fit a wide range of models with R. Topics covered include generalized linear mixed-effects models, multilevel models, spatial and spatio-temporal models, smoothing methods, survival analysis, imputation of missing values, and mixture models. Advanced features of the INLA package and how to extend the number of priors and latent models available in the package are discussed. All examples in the book are fully reproducible and datasets and R code are available from the book website.This book will be helpful to researchers from different areas with some background in Bayesian inference that want to apply the INLA method in their work. The examples cover topics on biostatistics, econometrics, education, environmental science, epidemiology, public health, and the social sciences.
R 2,601.00
Bayesian Approaches to Clinical Trials and Health-Care Evaluation
READ ALL ABOUT IT! David Spiegelhalter has recently joined the ranks of Isaac Newton, Charles Darwin and Stephen Hawking by becoming a fellow of the Royal Society. Originating from the Medical Research Council’s biostatistics unit, David has played a leading role in the Bristol heart surgery and Harold Shipman inquiries. Order a copy of this author’s comprehensive text TODAY! The Bayesian approach involves synthesising data and judgement in order to reach conclusions about unknown quantities and make predictions. Bayesian methods have become increasingly popular in recent years, notably in medical research, and although there are a number of books on Bayesian analysis, few cover clinical trials and biostatistical applications in any detail. Bayesian Approaches to Clinical Trials and Health-Care Evaluation provides a valuable overview of this rapidly evolving field, including basic Bayesian ideas, prior distributions, clinical trials, observational studies, evidence synthesis and cost-effectiveness analysis. Covers a broad array of essential topics, building from the basics to more advanced techniques. Illustrated throughout by detailed case studies and worked examples Includes exercises in all chapters Accessible to anyone with a basic knowledge of statistics Authors are at the forefront of research into Bayesian methods in medical research Accompanied by a Web site featuring data sets and worked examples using Excel and WinBUGS - the most widely used Bayesian modelling package Bayesian Approaches to Clinical Trials and Health-Care Evaluation is suitable for students and researchers in medical statistics, statisticians in the pharmaceutical industry, and anyone involved in conducting clinical trials and assessment of health-care technology.
R 3,483.00
Spatial and Spatio-temporal Bayesian Models with R - INLA
Spatial and Spatio-Temporal Bayesian Models with R-INLA provides a much needed, practically oriented & innovative presentation of the combination of Bayesian methodology and spatial statistics. The authors combine an introduction to Bayesian theory and methodology with a focus on the spatial and spatio-temporal models used within the Bayesian framework and a series of practical examples which allow the reader to link the statistical theory presented to real data problems. The numerous examples from the fields of epidemiology, biostatistics and social science all are coded in the R package R-INLA, which has proven to be a valid alternative to the commonly used Markov Chain Monte Carlo simulations
R 3,222.00
Introduction to Python in Earth Science Data Analysis
This textbook introduces the use of Python programming for exploring and modelling data in the field of Earth Sciences. It drives the reader from his very first steps with Python, like setting up the environment and starting writing the first lines of codes, to proficient use in visualizing, analyzing, and modelling data in the field of Earth Science. Each chapter contains explicative examples of code, and each script is commented in detail. The book is minded for very beginners in Python programming, and it can be used in teaching courses at master or PhD levels. Also, Early careers and experienced researchers who would like to start learning Python programming for the solution of geological problems will benefit the reading of the book.
R 2,624.51
Bayesian Survival Analysis
Survival analysis arises in many fields of study including medicine, biology, engineering, public health, epidemiology, and economics. This book provides a comprehensive treatment of Bayesian survival analysis. It presents a balance between theory and applications, and for each class of models discussed, detailed examples and analyses from case studies are presented whenever possible. The applications are all from the health sciences, including cancer, AIDS, and the environment.
R 5,468.18
