Confidence, Likelihood, Probability: Statistical Inference with Confidence Distributions (Cambridge Series in Statistical and Probabilistic Mathematics)
Cambridge University Press, 2/24/2016
EAN 9780521861601, ISBN10: 0521861608
Hardcover, 511 pages, 25.3 x 17.7 x 3.1 cm
Language: English
This lively book 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
14. Applications
15. Finale
summary, and a look into the future.