Handbook of Bayesian, Fiducial, and Frequentist Inference

James Berger, Xiao-Li Meng, Nancy Reid, Min-ge Xie

• Publisher: Chapman and Hall/CRC
• Year: 2024
• Print ISBN: 9780367321987
• eBook ISBN: 9781003837695
• Edition: 1
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

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

Table of contents

• Cover
• Half Title Page
• Series Page
• Title Page
• Copyright Page
• Table of Contents
• Preface
• About the editors
• Contributors
• 1 Risky Business
• 2 Empirical Bayes: Concepts and Methods
• 3 Distributions for Parameters
• 4 Objective Bayesian Inference and Its Relationship to Frequentism
• 5 Fiducial Inference, Then and Now
• 6 Bridging Bayesian, Frequentist and Fiducial Inferences Using Confidence Distributions
• 7 Objective Bayesian Testing and Model Uncertainty
• 8 A BFFer’s Exploration with Nuisance Constructs: Bayesian p-value, H -likelihood, and Cauchyanity
• 9 Bayesian Neural Networks and Dimensionality Reduction
• 10 The Tangent Exponential Model
• 11 Data Integration and Model Fusion in the Bayesian and Frequentist Frameworks
• 12 How the Game-Theoretic Foundation for Probability Resolves the Bayesian vs. Frequentist Standoff
• 13 Introduction to Generalized Fiducial Inference
• 14 Dempster-Shafer Theory for Statistical Inference
• 15 Slicing and Dicing a Path Through the Fiducial Forest
• 16 Inferential Models and Possibility Measures
• 17 Conformal Predictive Distributions: An Approach to Nonparametric Fiducial Prediction
• 18 Fiducial Inference and Decision Theory
• Index