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.