Evans Measuring Statistical Evidence Using Relative Belief

Erscheinungsjahr 2015
ISBN: 978-1-4822-4280-5
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 250 Seiten

Reihe: Chapman & Hall/CRC Monographs on Statistics & Applied Probability

A Sound Basis for the Theory of Statistical Inference

Measuring Statistical Evidence Using Relative Belief provides an overview of recent work on developing a theory of statistical inference based on measuring statistical evidence. It shows that being explicit about how to measure statistical evidence allows you to answer the basic question of when a statistical analysis is correct.

The book attempts to establish a gold standard for how a statistical analysis should proceed. It first introduces basic features of the overall approach, such as the roles of subjectivity, objectivity, infinity, and utility in statistical analyses. It next discusses the meaning of probability and the various positions taken on probability. The author then focuses on the definition of statistical evidence and how it should be measured. He presents a method for measuring statistical evidence and develops a theory of inference based on this method. He also discusses how statisticians should choose the ingredients for a statistical problem and how these choices are to be checked for their relevance in an application.

Zielgruppe

Researchers and postgraduate students in statistics and other fields, notably epidemiology and the social sciences.

Autoren/Hrsg.

Evans, Michael

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

Statistical Problems

Introduction

Statistical Problems

Statistical Models

Infinity and Continuity in Statistics

The Principle of Empirical Criticism

The Concept of Utility

The Principle of Frequentism

Statistical Inferences

Example
Concluding Comments

Probability

Introduction

Principle of Insufficient Reason

Subjective Probability

Relative Frequency Probability

Concluding Comments

Characterizing Statistical Evidence

Introduction

Pure Likelihood Inference

Sufficiency, Ancillarity and Completeness

P-values and Confidence

Bayesian Inferences

Fiducial Inference

Concluding Comments

Measuring Statistical Evidence Using Relative Belief

Introduction

Relative Belief Ratios and Evidence

Other Proposed Measures of Evidence

Measuring the Strength of the Evidence

Inference Based on Relative Belief Ratios

Measuring the Bias in the Evidence

Properties of Relative Belief Inferences

Concluding Comments

Appendix

Choosing and Checking the Model and Prior

Introduction

Choosing the Model

Choosing the Prior

Checking the Ingredients

Checking the Model

Checking the Prior

Modifying the Prior

Concluding Comments

Conclusions

Appendix: The Definition of Density

Bibliography

Index

Über Autor(innen)

Michael Evans is a professor in the Department of Statistics at the University of Toronto. His research focuses on statistical inference, particularly a theory of inference based on the concept of relative belief. He is an associate editor of Bayesian Analysis and a former president of the Statistical Society of Canada.