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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
Comparing Proportions: A Modern Solution to a Classical Problem 69
The corresponding reference posterior expected loss fr om using σ
0
as a
proxy for σ, given a random sample of size n, is
d(σ
0
|z) =
Z
0
n δ
z
{σ
0
|σ, µ}π(σ |z)
=
n
2
ψ
n 1
2
1 +
ns
2
(n 3)σ
2
0
+ log
2σ
2
0
ns
2
.
By definition, the Bayes point estimator with respect to this loss function,
the intrinsic reference estimato r of σ is that value of σ
0
which minimizes
d(σ
0
|z); this is found to be σ
(z) =
ns/
n 3. Thus, the intrinsic reference
estimator of the va riance is
σ
2
(z) =
n s
2
n 3
,
an estimator already suggested by Stein [16], which is always larger than
both the MLE and the conventiona l unbiased ...
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Publisher Resources

ISBN: 9781482235128