This lively book Confidence, Likelihood and Probability lays out a methodology of confidence distributions and puts them through their paces. Among other merits, they lead to optimal combinations of confidence from different sources of information, and they can make complex models amenable to objective and indeed prior-free analysis for less subjectively inclined statisticians. The generous mixture of theory, illustrations, applications and exercises is suitable for statisticians at all levels of experience, as well as for data-oriented scientists. Some confidence distributions are less dispersed than their competitors.
This concept leads to a theory of risk functions and comparisons for distributions of confidence. Neyman-Pearson type theorems leading to optimal confidence are developed and richly illustrated. Exact and optimal confidence distribution is the gold standard for inferred epistemic distributions. Confidence distributions and likelihood functions are intertwined, allowing prior distributions to be made part of the likelihood. Meta-analysis in likelihood terms is developed and taken beyond traditional methods, suiting it in particular to combining information across diverse data sources.
1. Confidence, likelihood, probability: an invitation
2. Interference in parametric models
3. Confidence distributions
4. Further developments for confidence distribution
5. Invariance, sufficiency and optimality for confidence distributions
6. The fiducial argument
7. Improved approximations for confidence distributions
8. Exponential families and generalised linear models
9. Confidence distributions in higher dimensions
10. Likelihoods and confidence likelihoods
11. Confidence in non- and semiparametric models
12. Predictions and confidence
13. Meta-analysis and combination of information
15. Finale: summary, and a look into the future.
Tore Schweder is a Professor of Statistics in the Department of Economics and at the Centre for Ecology and Evolutionary Synthesis at the University of Oslo. Nils Lid Hjort is Professor of Mathematical Statistics in the Department of Mathematics at the University of Oslo.
"This book presents a detailed and wide-ranging account of an approach to inference that moves the discipline towards increased cohesion, avoiding the artificial distinction between testing and estimation. Innovative and thorough, it is sure to have an impact both in the foundations of inference and in a wide range of practical applications of inference."
– Nancy Reid, University Professor of Statistical Sciences, University of Toronto
"I recommend this book very enthusiastically to any researcher interested in learning more about advanced likelihood theory, based on concepts like confidence distributions and fiducial distributions, and their links with other areas. The book explains in a very didactical way the concepts, their use, their interpretation, etc., illustrated by an impressive number of examples and data sets from a wide range of areas in statistics."
– Ingrid Van Keilegom, Université Catholique de Louvain