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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.
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