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Current Trends in Bayesian Methodology with Applications
book

Current Trends in Bayesian Methodology with Applications

by Satyanshu K. Upadhyay, Umesh Singh, Dipak K. Dey, Appaia Loganathan
May 2015
Intermediate to advanced content levelIntermediate to advanced
680 pages
22h 33m
English
Chapman and Hall/CRC
Content preview from Current Trends in Bayesian Methodology with Applications
542 Current Trends in Bayesian Methodology with Applications
The Rao-Blackwell theorem is often use d to s how how the knowledge of
a conditional expec ted value can improve the variance of an estimate, but
this is only a special case of a more general theorem which shows that any
convex cost-function is improved using this technique. For completeness, the
Rao-Blackwell theorem is given in Theorem 26.3.1, [28, p. 51 ].
Theorem 26.3.1 (The Rao-Blackwell theorem [28]). Let x be a random ob-
servable with the distribution P
θ
P = {P
θ
}, and let t be s ufficient
statistics for P
1
. Let
ˆ
θ be an estimator of an estimand g(θ), and let the loss
function L(
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Publisher Resources

ISBN: 9781482235128