Handbook of Bayesian, Fiducial, and Frequentist Inference

Handbook of Bayesian, Fiducial, and Frequentist Inference PDF

Author: James Berger

Publisher: CRC Press

Published: 2024-02-26

Total Pages: 564

ISBN-13: 1003837697

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The emergence of data science, in recent decades, has magnified the need for efficient methodology for analyzing data and highlighted the importance of statistical inference. Despite the tremendous progress that has been made, statistical science is still a young discipline and continues to have several different and competing paths in its approaches and its foundations. While the emergence of competing approaches is a natural progression of any scientific discipline, differences in the foundations of statistical inference can sometimes lead to different interpretations and conclusions from the same dataset. The increased interest in the foundations of statistical inference has led to many publications, and recent vibrant research activities in statistics, applied mathematics, philosophy and other fields of science reflect the importance of this development. The BFF approaches not only bridge foundations and scientific learning, but also facilitate objective and replicable scientific research, and provide scalable computing methodologies for the analysis of big data. Most of the published work typically focusses on a single topic or theme, and the body of work is scattered in different journals. This handbook provides a comprehensive introduction and broad overview of the key developments in the BFF schools of inference. It is intended for researchers and students who wish for an overview of foundations of inference from the BFF perspective and provides a general reference for BFF inference. Key Features: Provides a comprehensive introduction to the key developments in the BFF schools of inference Gives an overview of modern inferential methods, allowing scientists in other fields to expand their knowledge Is accessible for readers with different perspectives and backgrounds

Handbook of Bayesian Variable Selection

Handbook of Bayesian Variable Selection PDF

Author: Mahlet G. Tadesse

Publisher: CRC Press

Published: 2021-12-24

Total Pages: 762

ISBN-13: 1000510255

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Bayesian variable selection has experienced substantial developments over the past 30 years with the proliferation of large data sets. Identifying relevant variables to include in a model allows simpler interpretation, avoids overfitting and multicollinearity, and can provide insights into the mechanisms underlying an observed phenomenon. Variable selection is especially important when the number of potential predictors is substantially larger than the sample size and sparsity can reasonably be assumed. The Handbook of Bayesian Variable Selection provides a comprehensive review of theoretical, methodological and computational aspects of Bayesian methods for variable selection. The topics covered include spike-and-slab priors, continuous shrinkage priors, Bayes factors, Bayesian model averaging, partitioning methods, as well as variable selection in decision trees and edge selection in graphical models. The handbook targets graduate students and established researchers who seek to understand the latest developments in the field. It also provides a valuable reference for all interested in applying existing methods and/or pursuing methodological extensions. Features: Provides a comprehensive review of methods and applications of Bayesian variable selection. Divided into four parts: Spike-and-Slab Priors; Continuous Shrinkage Priors; Extensions to various Modeling; Other Approaches to Bayesian Variable Selection. Covers theoretical and methodological aspects, as well as worked out examples with R code provided in the online supplement. Includes contributions by experts in the field. Supported by a website with code, data, and other supplementary material

Bayesian Methods for Finite Population Sampling

Bayesian Methods for Finite Population Sampling PDF

Author: Malay Ghosh

Publisher: Routledge

Published: 2021-12-17

Total Pages: 296

ISBN-13: 1351464426

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Assuming 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.

Handbook of Approximate Bayesian Computation

Handbook of Approximate Bayesian Computation PDF

Author: Scott A. Sisson

Publisher: CRC Press

Published: 2018-09-03

Total Pages: 679

ISBN-13: 1439881510

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As the world becomes increasingly complex, so do the statistical models required to analyse the challenging problems ahead. For the very first time in a single volume, the Handbook of Approximate Bayesian Computation (ABC) presents an extensive overview of the theory, practice and application of ABC methods. These simple, but powerful statistical techniques, take Bayesian statistics beyond the need to specify overly simplified models, to the setting where the model is defined only as a process that generates data. This process can be arbitrarily complex, to the point where standard Bayesian techniques based on working with tractable likelihood functions would not be viable. ABC methods finesse the problem of model complexity within the Bayesian framework by exploiting modern computational power, thereby permitting approximate Bayesian analyses of models that would otherwise be impossible to implement. The Handbook of ABC provides illuminating insight into the world of Bayesian modelling for intractable models for both experts and newcomers alike. It is an essential reference book for anyone interested in learning about and implementing ABC techniques to analyse complex models in the modern world.

Number-Theoretic Methods in Statistics

Number-Theoretic Methods in Statistics PDF

Author: Kai-Tai Fang

Publisher: CRC Press

Published: 1993-12-01

Total Pages: 356

ISBN-13: 9780412465208

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This book is a survey of recent work on the application of number theory in statistics. The essence of number-theoretic methods is to find a set of points that are universally scattered over an s-dimensional unit cube. In certain circumstances this set can be used instead of random numbers in the Monte Carlo method. The idea can also be applied to other problems such as in experimental design. This book will illustrate the idea of number-theoretic methods and their application in statistics. The emphasis is on applying the methods to practical problems so only part-proofs of theorems are given.

Statistical Inference

Statistical Inference PDF

Author: Helio S. Migon

Publisher: CRC Press

Published: 2014-09-03

Total Pages: 388

ISBN-13: 1439878803

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A Balanced Treatment of Bayesian and Frequentist Inference Statistical Inference: An Integrated Approach, Second Edition presents an account of the Bayesian and frequentist approaches to statistical inference. Now with an additional author, this second edition places a more balanced emphasis on both perspectives than the first edition. New to the Second Edition New material on empirical Bayes and penalized likelihoods and their impact on regression models Expanded material on hypothesis testing, method of moments, bias correction, and hierarchical models More examples and exercises More comparison between the approaches, including their similarities and differences Designed for advanced undergraduate and graduate courses, the text thoroughly covers statistical inference without delving too deep into technical details. It compares the Bayesian and frequentist schools of thought and explores procedures that lie on the border between the two. Many examples illustrate the methods and models, and exercises are included at the end of each chapter.

Statistical Inference

Statistical Inference PDF

Author: Murray Aitkin

Publisher: CRC Press

Published: 2010-06-02

Total Pages: 256

ISBN-13: 1420093444

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Filling a gap in current Bayesian theory, Statistical Inference: An Integrated Bayesian/Likelihood Approach presents a unified Bayesian treatment of parameter inference and model comparisons that can be used with simple diffuse prior specifications. This novel approach provides new solutions to difficult model comparison problems and offers direct

Handbook of Forensic Statistics

Handbook of Forensic Statistics PDF

Author: David L. Banks

Publisher: CRC Press

Published: 2020-11-05

Total Pages: 571

ISBN-13: 1000096068

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Handbook of Forensic Statistics is a collection of chapters by leading authorities in forensic statistics. Written for statisticians, scientists, and legal professionals having a broad range of statistical expertise, it summarizes and compares basic methods of statistical inference (frequentist, likelihoodist, and Bayesian) for trace and other evidence that links individuals to crimes, the modern history and key controversies in the field, and the psychological and legal aspects of such scientific evidence. Specific topics include uncertainty in measurements and conclusions; statistically valid statements of weight of evidence or source conclusions; admissibility and presentation of statistical findings; and the state of the art of methods (including problems and pitfalls) for collecting, analyzing, and interpreting data in such areas as forensic biology, chemistry, and pattern and impression evidence. The particular types of evidence that are discussed include DNA, latent fingerprints, firearms and toolmarks, glass, handwriting, shoeprints, and voice exemplars.

Statistical Inference Based on the likelihood

Statistical Inference Based on the likelihood PDF

Author: Adelchi Azzalini

Publisher: CRC Press

Published: 1996-06-01

Total Pages: 356

ISBN-13: 9780412606502

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The Likelihood plays a key role in both introducing general notions of statistical theory, and in developing specific methods. This book introduces likelihood-based statistical theory and related methods from a classical viewpoint, and demonstrates how the main body of currently used statistical techniques can be generated from a few key concepts, in particular the likelihood. Focusing on those methods, which have both a solid theoretical background and practical relevance, the author gives formal justification of the methods used and provides numerical examples with real data.