Handbook Of Bayesian Fiducial And Frequentist Inference

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

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 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.

This book constitutes the refereed proceedings of the 7th International Conference on Belief Functions, BELIEF 2022, held in Paris, France, in October 2022. The theory of belief functions is now well established as a general framework for reasoning with uncertainty, and has well-understood connections to other frameworks such as probability, possibility, and imprecise probability theories. It has been applied in diverse areas such as machine learning, information fusion, and pattern recognition. The 29 full papers presented in this book were carefully selected and reviewed from 31 submissions. The papers cover a wide range on theoretical aspects on mathematical foundations, statistical inference as well as on applications in various areas including classification, clustering, data fusion, image processing, and much more.

In today’s global and highly competitive environment, continuous improvement in the processes and products of any field of engineering is essential for survival. This book gathers together the full range of statistical techniques required by engineers from all fields. It will assist them to gain sensible statistical feedback on how their processes or products are functioning and to give them realistic predictions of how these could be improved. The handbook will be essential reading for all engineers and engineering-connected managers who are serious about keeping their methods and products at the cutting edge of quality and competitiveness.

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 analysis is today understood to be an extremely powerful method of statistical analysis, as well an approach to statistics that is particularly transparent and intuitive. It is thus being extensively and increasingly utilized in virtually every area of science and society that involves analysis of data.A widespread misconception is that Bayesian analysis is a more subjective theory of statistical inference than what is now called classical statistics. This is true neither historically nor in practice. Indeed, objective Bayesian analysis dominated the statistical landscape from roughly 1780 to 1930, long before 'classical' statistics or subjective Bayesian analysis were developed. It has been a subject of intense interest to a multitude of statisticians, mathematicians, philosophers, and scientists. The book, while primarily focusing on the latest and most prominent objective Bayesian methodology, does present much of this fascinating history.The book is written for four different audiences. First, it provides an introduction to objective Bayesian inference for non-statisticians; no previous exposure to Bayesian analysis is needed. Second, the book provides an overview of the development and current state of objective Bayesian analysis and its relationship to other statistical approaches, for those with interest in the philosophy of learning from data. Third, the book presents a careful development of the particular objective Bayesian approach that we recommend, the reference prior approach. Finally, the book presents as much practical objective Bayesian methodology as possible for statisticians and scientists primarily interested in practical applications.

The main theme of this monograph is “comparative statistical inference. ” While the topics covered have been carefully selected (they are, for example, restricted to pr- lems of statistical estimation), my aim is to provide ideas and examples which will assist a statistician, or a statistical practitioner, in comparing the performance one can expect from using either Bayesian or classical (aka, frequentist) solutions in - timation problems. Before investing the hours it will take to read this monograph, one might well want to know what sets it apart from other treatises on comparative inference. The two books that are closest to the present work are the well-known tomes by Barnett (1999) and Cox (2006). These books do indeed consider the c- ceptual and methodological differences between Bayesian and frequentist methods. What is largely absent from them, however, are answers to the question: “which - proach should one use in a given problem?” It is this latter issue that this monograph is intended to investigate. There are many books on Bayesian inference, including, for example, the widely used texts by Carlin and Louis (2008) and Gelman, Carlin, Stern and Rubin (2004). These books differ from the present work in that they begin with the premise that a Bayesian treatment is called for and then provide guidance on how a Bayesian an- ysis should be executed. Similarly, there are many books written from a classical perspective.