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Bayesian Inference and Maximum Entropy Methods in Science and Engineering: MaxEnt 37, Jarinu, Brazil, July 09–14, 2017 (Springer Proceedings in Mathematics & Statistics #239)
by Adriano Polpo Julio Stern Francisco Louzada Rafael Izbicki Hellinton TakadaThese proceedings from the 37th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering (MaxEnt 2017), held in São Carlos, Brazil, aim to expand the available research on Bayesian methods and promote their application in the scientific community. They gather research from scholars in many different fields who use inductive statistics methods and focus on the foundations of the Bayesian paradigm, their comparison to objectivistic or frequentist statistics counterparts, and their appropriate applications. Interest in the foundations of inductive statistics has been growing with the increasing availability of Bayesian methodological alternatives, and scientists now face much more difficult choices in finding the optimal methods to apply to their problems. By carefully examining and discussing the relevant foundations, the scientific community can avoid applying Bayesian methods on a merely ad hoc basis. For over 35 years, the MaxEnt workshops have explored the use of Bayesian and Maximum Entropy methods in scientific and engineering application contexts. The workshops welcome contributions on all aspects of probabilistic inference, including novel techniques and applications, and work that sheds new light on the foundations of inference. Areas of application in these workshops include astronomy and astrophysics, chemistry, communications theory, cosmology, climate studies, earth science, fluid mechanics, genetics, geophysics, machine learning, materials science, medical imaging, nanoscience, source separation, thermodynamics (equilibrium and non-equilibrium), particle physics, plasma physics, quantum mechanics, robotics, and the social sciences. Bayesian computational techniques such as Markov chain Monte Carlo sampling are also regular topics, as are approximate inferential methods. Foundational issues involving probability theory and information theory, as well as novel applications of inference to illuminate the foundations of physical theories, are also of keen interest.
Bayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data (Chapman & Hall/CRC Monographs on Statistics and Applied Probability)
by Paul GustafsonBayesian Inference for Partially Identified Models: Exploring the Limits of Limited Data shows how the Bayesian approach to inference is applicable to partially identified models (PIMs) and examines the performance of Bayesian procedures in partially identified contexts. Drawing on his many years of research in this area, the author presents a thorough overview of the statistical theory, properties, and applications of PIMs.The book first describes how reparameterization can assist in computing posterior quantities and providing insight into the properties of Bayesian estimators. It next compares partial identification and model misspecification, discussing which is the lesser of the two evils. The author then works through PIM examples in depth, examining the ramifications of partial identification in terms of how inferences change and the extent to which they sharpen as more data accumulate. He also explains how to characterize the value of information obtained from data in a partially identified context and explores some recent applications of PIMs. In the final chapter, the author shares his thoughts on the past and present state of research on partial identification.This book helps readers understand how to use Bayesian methods for analyzing PIMs. Readers will recognize under what circumstances a posterior distribution on a target parameter will be usefully narrow versus uselessly wide.
Bayesian Inference for Probabilistic Risk Assessment: A Practitioner's Guidebook (Springer Series in Reliability Engineering)
by Dana Kelly Curtis SmithBayesian Inference for Probabilistic Risk Assessment provides a Bayesian foundation for framing probabilistic problems and performing inference on these problems. Inference in the book employs a modern computational approach known as Markov chain Monte Carlo (MCMC). The MCMC approach may be implemented using custom-written routines or existing general purpose commercial or open-source software. This book uses an open-source program called OpenBUGS (commonly referred to as WinBUGS) to solve the inference problems that are described. A powerful feature of OpenBUGS is its automatic selection of an appropriate MCMC sampling scheme for a given problem. The authors provide analysis "building blocks" that can be modified, combined, or used as-is to solve a variety of challenging problems. The MCMC approach used is implemented via textual scripts similar to a macro-type programming language. Accompanying most scripts is a graphical Bayesian network illustrating the elements of the script and the overall inference problem being solved. Bayesian Inference for Probabilistic Risk Assessment also covers the important topics of MCMC convergence and Bayesian model checking. Bayesian Inference for Probabilistic Risk Assessment is aimed at scientists and engineers who perform or review risk analyses. It provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models.
Bayesian Inference for Stochastic Processes
by Lyle D. BroemelingThis is the first book designed to introduce Bayesian inference procedures for stochastic processes. There are clear advantages to the Bayesian approach (including the optimal use of prior information). Initially, the book begins with a brief review of Bayesian inference and uses many examples relevant to the analysis of stochastic processes, including the four major types, namely those with discrete time and discrete state space and continuous time and continuous state space. The elements necessary to understanding stochastic processes are then introduced, followed by chapters devoted to the Bayesian analysis of such processes. It is important that a chapter devoted to the fundamental concepts in stochastic processes is included. Bayesian inference (estimation, testing hypotheses, and prediction) for discrete time Markov chains, for Markov jump processes, for normal processes (e.g. Brownian motion and the Ornstein–Uhlenbeck process), for traditional time series, and, lastly, for point and spatial processes are described in detail. Heavy emphasis is placed on many examples taken from biology and other scientific disciplines. In order analyses of stochastic processes, it will use R and WinBUGS. <P><P>Features: <li>Uses the Bayesian approach to make statistical Inferences about stochastic processes <li>The R package is used to simulate realizations from different types of processes <li>Based on realizations from stochastic processes, the WinBUGS package will provide the Bayesian analysis (estimation, testing hypotheses, and prediction) for the unknown parameters of stochastic processes <li>To illustrate the Bayesian inference, many examples taken from biology, economics, and astronomy will reinforce the basic concepts of the subject <li>A practical approach is implemented by considering realistic examples of interest to the scientific community <li>WinBUGS and R code are provided in the text, allowing the reader to easily verify the results of the inferential procedures found in the many examples of the book <P><P>Readers with a good background in two areas, probability theory and statistical inference, should be able to master the essential ideas of this book.
Bayesian Inference in the Social Sciences
by Ivan Jeliazkov Xin-She YangPresents new models, methods, and techniques and considers important real-world applications in political science, sociology, economics, marketing, and financeEmphasizing interdisciplinary coverage, Bayesian Inference in the Social Sciences builds upon the recent growth in Bayesian methodology and examines an array of topics in model formulation, estimation, and applications. The book presents recent and trending developments in a diverse, yet closely integrated, set of research topics within the social sciences and facilitates the transmission of new ideas and methodology across disciplines while maintaining manageability, coherence, and a clear focus.Bayesian Inference in the Social Sciences features innovative methodology and novel applications in addition to new theoretical developments and modeling approaches, including the formulation and analysis of models with partial observability, sample selection, and incomplete data. Additional areas of inquiry include a Bayesian derivation of empirical likelihood and method of moment estimators, and the analysis of treatment effect models with endogeneity. The book emphasizes practical implementation, reviews and extends estimation algorithms, and examines innovative applications in a multitude of fields. Time series techniques and algorithms are discussed for stochastic volatility, dynamic factor, and time-varying parameter models. Additional features include:Real-world applications and case studies that highlight asset pricing under fat-tailed distributions, price indifference modeling and market segmentation, analysis of dynamic networks, ethnic minorities and civil war, school choice effects, and business cycles and macroeconomic performanceState-of-the-art computational tools and Markov chain Monte Carlo algorithms with related materials available via the book's supplemental websiteInterdisciplinary coverage from well-known international scholars and practitionersBayesian Inference in the Social Sciences is an ideal reference for researchers in economics, political science, sociology, and business as well as an excellent resource for academic, government, and regulation agencies. The book is also useful for graduate-level courses in applied econometrics, statistics, mathematical modeling and simulation, numerical methods, computational analysis, and the social sciences.
Bayesian inference with INLA
by Virgilio Gomez-RubioThe 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.
Bayesian Inverse Problems: Fundamentals and Engineering Applications
by Juan Chiachío-RuanoThis book is devoted to a special class of engineering problems called Bayesian inverse problems. These problems comprise not only the probabilistic Bayesian formulation of engineering problems, but also the associated stochastic simulation methods needed to solve them. Through this book, the reader will learn how this class of methods can be useful to rigorously address a range of engineering problems where empirical data and fundamental knowledge come into play. The book is written for a non-expert audience and it is contributed to by many of the most renowned academic experts in this field.
Bayesian Mediation Analysis using R
by Atanu BhattacharjeeDelve into the realm of statistical methodology for mediation analysis with a Bayesian perspective in high dimensional data through this comprehensive guide. Focused on various forms of time-to-event data methodologies, this book helps readers master the application of Bayesian mediation analysis using R. Across ten chapters, this book explores concepts of mediation analysis, survival analysis, accelerated failure time modeling, longitudinal data analysis, and competing risk modeling. Each chapter progressively unravels intricate topics, from the foundations of Bayesian approaches to advanced techniques like variable selection, bivariate survival models, and Dirichlet process priors. With practical examples and step-by-step guidance, this book empowers readers to navigate the intricate landscape of high-dimensional data analysis, fostering a deep understanding of its applications and significance in diverse fields.
Bayesian Methods: A Social and Behavioral Sciences Approach, Third Edition (Chapman & Hall/CRC Statistics in the Social and Behavioral Sciences)
by Jeff GillAn Update of the Most Popular Graduate-Level Introductions to Bayesian Statistics for Social ScientistsNow that Bayesian modeling has become standard, MCMC is well understood and trusted, and computing power continues to increase, Bayesian Methods: A Social and Behavioral Sciences Approach, Third Edition focuses more on implementation details of th
Bayesian Methods for Data Analysis (Chapman & Hall/CRC Texts in Statistical Science)
by Bradley P. Carlin Thomas A. LouisBroadening its scope to nonstatisticians, Bayesian Methods for Data Analysis, Third Edition provides an accessible introduction to the foundations and applications of Bayesian analysis. Along with a complete reorganization of the material, this edition concentrates more on hierarchical Bayesian modeling as implemented via Markov chain Monte Carlo (
Bayesian Methods for Ecology
by Michael A. MccarthyThe interest in using Bayesian methods in ecology is increasing, however many ecologists have difficulty with conducting the required analyses. McCarthy bridges that gap, using a clear and accessible style. The text also incorporates case studies to demonstrate mark-recapture analysis, development of population models and the use of subjective judgement. The advantages of Bayesian methods, are also described here, for example, the incorporation of any relevant prior information and the ability to assess the evidence in favour of competing hypotheses. Free software is available as well as an accompanying web-site containing the data files and WinBUGS codes. Bayesian Methods for Ecology will appeal to academic researchers, upper undergraduate and graduate students of Ecology.
Bayesian Methods for Finite Population Sampling
by Malay GhoshAssuming a basic knowledge of the frequentist approach to finite population sampling, Bayesian Methods for Finite Population Sampling describes Bayesian and predictive approaches to inferential problems with an emphasis on the likelihood principle. The authors demonstrate that a variety of levels of prior information can be used in survey sampling in a Bayesian manner. Situations considered range from a noninformative Bayesian justification of standard frequentist methods when the only prior information available is the belief in the exchangeability of the units to a full-fledged Bayesian model. Intended primarily for graduate students and researchers in finite population sampling, this book will also be of interest to statisticians who use sampling and lecturers and researchers in general statistics and biostatistics.
Bayesian Methods for Management and Business
by Eugene D. HahnHIGHLIGHTS THE USE OF BAYESIAN STATISTICS TO GAIN INSIGHTS FROM EMPIRICAL DATAFeaturing an accessible approach, Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems demonstrates how Bayesian statistics can help to provide insights into important issues facing business and management. The book draws on multidisciplinary applications and examples and utilizes the freely available software WinBUGS and R to illustrate the integration of Bayesian statistics within data-rich environments.Computational issues are discussed and integrated with coverage of linear models, sensitivity analysis, Markov Chain Monte Carlo (MCMC), and model comparison. In addition, more advanced models including hierarchal models, generalized linear models, and latent variable models are presented to further bridge the theory and application in real-world usage.Bayesian Methods for Management and Business: Pragmatic Solutions for Real Problems also features:Numerous real-world examples drawn from multiple management disciplines such as strategy, international business, accounting, and information systemsAn incremental skill-building presentation based on analyzing data sets with widely applicable models of increasing complexityAn accessible treatment of Bayesian statistics that is integrated with a broad range of business and management issues and problemsA practical problem-solving approach to illustrate how Bayesian statistics can help to provide insight into important issues facing business and managementBayesian Methods for Management and Business: Pragmatic Solutions for Real Problems is an important textbook for Bayesian statistics courses at the advanced MBA-level and also for business and management PhD candidates as a first course in methodology. In addition, the book is a useful resource for management scholars and practitioners as well as business academics and practitioners who seek to broaden their methodological skill sets.
Bayesian Methods for Measures of Agreement (Chapman & Hall/CRC Biostatistics Series)
by Lyle D. BroemelingUsing WinBUGS to implement Bayesian inferences of estimation and testing hypotheses, Bayesian Methods for Measures of Agreement presents useful methods for the design and analysis of agreement studies. It focuses on agreement among the various players in the diagnostic process.The author employs a Bayesian approach to provide statistical inferences
Bayesian Methods for Repeated Measures (Chapman & Hall/CRC Biostatistics Series)
by Lyle D. BroemelingAnalyze Repeated Measures Studies Using Bayesian TechniquesGoing beyond standard non-Bayesian books, Bayesian Methods for Repeated Measures presents the main ideas for the analysis of repeated measures and associated designs from a Bayesian viewpoint. It describes many inferential methods for analyzing repeated measures in various scientific areas,
Bayesian Methods for the Physical Sciences: Learning from Examples in Astronomy and Physics (Springer Series in Astrostatistics #4)
by Stefano Andreon Brian WeaverStatistical literacy is critical for the modern researcher in Physics and Astronomy. This book empowers researchers in these disciplines by providing the tools they will need to analyze their own data. Chapters in this book provide a statistical base from which to approach new problems, including numerical advice and a profusion of examples. The examples are engaging analyses of real-world problems taken from modern astronomical research. The examples are intended to be starting points for readers as they learn to approach their own data and research questions. Acknowledging that scientific progress now hinges on the availability of data and the possibility to improve previous analyses, data and code are distributed throughout the book. The JAGS symbolic language used throughout the book makes it easy to perform Bayesian analysis and is particularly valuable as readers may use it in a myriad of scenarios through slight modifications. This book is comprehensive, well written, and will surely be regarded as a standard text in both astrostatistics and physical statistics. Joseph M. Hilbe, President, International Astrostatistics Association, Professor Emeritus, University of Hawaii, and Adjunct Professor of Statistics, Arizona State University
Bayesian Methods in Epidemiology (Chapman & Hall/CRC Biostatistics Series)
by Lyle D. BroemelingWritten by a biostatistics expert with over 20 years of experience in the field, Bayesian Methods in Epidemiology presents statistical methods used in epidemiology from a Bayesian viewpoint. It employs the software package WinBUGS to carry out the analyses and offers the code in the text and for download online.The book examines study designs that
Bayesian Methods in Health Economics (Chapman & Hall/CRC Biostatistics Series)
by Gianluca BaioHealth economics is concerned with the study of the cost-effectiveness of health care interventions. This book provides an overview of Bayesian methods for the analysis of health economic data. After an introduction to the basic economic concepts and methods of evaluation, it presents Bayesian statistics using accessible mathematics. The next chapters describe the theory and practice of cost-effectiveness analysis from a statistical viewpoint, and Bayesian computation, notably MCMC. The final chapter presents three detailed case studies covering cost-effectiveness analyses using individual data from clinical trials, evidence synthesis and hierarchical models and Markov models. The text uses WinBUGS and JAGS with datasets and code available online.
Bayesian Methods in Pharmaceutical Research (Chapman & Hall/CRC Biostatistics Series)
by Emmanuel Lesaffre, Gianluca Baio and Bruno BoulangerSince the early 2000s, there has been increasing interest within the pharmaceutical industry in the application of Bayesian methods at various stages of the research, development, manufacturing, and health economic evaluation of new health care interventions. In 2010, the first Applied Bayesian Biostatistics conference was held, with the primary objective to stimulate the practical implementation of Bayesian statistics, and to promote the added-value for accelerating the discovery and the delivery of new cures to patients. This book is a synthesis of the conferences and debates, providing an overview of Bayesian methods applied to nearly all stages of research and development, from early discovery to portfolio management. It highlights the value associated with sharing a vision with the regulatory authorities, academia, and pharmaceutical industry, with a view to setting up a common strategy for the appropriate use of Bayesian statistics for the benefit of patients. The book covers: Theory, methods, applications, and computing Bayesian biostatistics for clinical innovative designs Adding value with Real World Evidence Opportunities for rare, orphan diseases, and pediatric development Applied Bayesian biostatistics in manufacturing Decision making and Portfolio management Regulatory perspective and public health policies Statisticians and data scientists involved in the research, development, and approval of new cures will be inspired by the possible applications of Bayesian methods covered in the book. The methods, applications, and computational guidance will enable the reader to apply Bayesian methods in their own pharmaceutical research.
Bayesian Methods in Statistics: From Concepts to Practice
by Mel SlaterThis book walks you through learning probability and statistics from a Bayesian point of view. From an introduction to probability theory through to frameworks for doing rigorous calculations of probability, it discusses Bayes’ Theorem before illustrating how to use it in a variety of different situations with data addressing social and psychological issues. The book also: Equips you with coding skills in the statistical modelling language Stan and programming language R. Discusses how Bayesian approaches to statistics compare to classical approaches. Introduces Markov Chain Monte Carlo methods for doing Bayesian statistics through computer simulations, so you understand how Bayesian solutions are implemented. Features include an introduction to each chapter and a chapter summary to help you check your learning. All the examples and data used in the book are also available in the online resources so you can practice at your own pace. For readers with some understanding of basic mathematical functions and notation, this book will get you up and running so you can do Bayesian statistics with confidence.
Bayesian Methods in Statistics: From Concepts to Practice
by Mel SlaterThis book walks you through learning probability and statistics from a Bayesian point of view. From an introduction to probability theory through to frameworks for doing rigorous calculations of probability, it discusses Bayes’ Theorem before illustrating how to use it in a variety of different situations with data addressing social and psychological issues. The book also: Equips you with coding skills in the statistical modelling language Stan and programming language R. Discusses how Bayesian approaches to statistics compare to classical approaches. Introduces Markov Chain Monte Carlo methods for doing Bayesian statistics through computer simulations, so you understand how Bayesian solutions are implemented. Features include an introduction to each chapter and a chapter summary to help you check your learning. All the examples and data used in the book are also available in the online resources so you can practice at your own pace. For readers with some understanding of basic mathematical functions and notation, this book will get you up and running so you can do Bayesian statistics with confidence.
Bayesian Methods in the Search for MH370 (SpringerBriefs in Electrical and Computer Engineering)
by Neil Gordon Jason Williams Sam Davey Ian Holland Mark RuttenThis book demonstrates how nonlinear/non-Gaussian Bayesian time series estimation methods were used to produce a probability distribution of potential MH370 flight paths. It provides details of how the probabilistic models of aircraft flight dynamics, satellite communication system measurements, environmental effects and radar data were constructed and calibrated. The probability distribution was used to define the search zone in the southern Indian Ocean.The book describes particle-filter based numerical calculation of the aircraft flight-path probability distribution and validates the method using data from several of the involved aircraft’s previous flights. Finally it is shown how the Reunion Island flaperon debris find affects the search probability distribution.
Bayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation
by Ming T. Tan Guo-Liang Tian Kai Wang NgBayesian Missing Data Problems: EM, Data Augmentation and Noniterative Computation presents solutions to missing data problems through explicit or noniterative sampling calculation of Bayesian posteriors. The methods are based on the inverse Bayes formulae discovered by one of the author in 1995. Applying the Bayesian approach to important real-wor
Bayesian Model Selection and Statistical Modeling
by Tomohiro AndoAlong with many practical applications, Bayesian Model Selection and Statistical Modeling presents an array of Bayesian inference and model selection procedures. It thoroughly explains the concepts, illustrates the derivations of various Bayesian model selection criteria through examples, and provides R code for implementation. The author shows how
Bayesian Modeling and Computation in Python (Chapman & Hall/CRC Texts in Statistical Science)
by Osvaldo A. Martin Ravin Kumar Junpeng LaoBayesian Modeling and Computation in Python aims to help beginner Bayesian practitioners to become intermediate modelers. It uses a hands on approach with PyMC3, Tensorflow Probability, ArviZ and other libraries focusing on the practice of applied statistics with references to the underlying mathematical theory. The book starts with a refresher of the Bayesian Inference concepts. The second chapter introduces modern methods for Exploratory Analysis of Bayesian Models. With an understanding of these two fundamentals the subsequent chapters talk through various models including linear regressions, splines, time series, Bayesian additive regression trees. The final chapters include Approximate Bayesian Computation, end to end case studies showing how to apply Bayesian modelling in different settings, and a chapter about the internals of probabilistic programming languages. Finally the last chapter serves as a reference for the rest of the book by getting closer into mathematical aspects or by extending the discussion of certain topics. This book is written by contributors of PyMC3, ArviZ, Bambi, and Tensorflow Probability among other libraries.