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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
Bayesian Variable Selection for Predictively Optimal Regression 255
An extension of this pr ior used to address the consistency of the es timator is
referred to by [19] as the hyper-g/n prio r and defined as
π(g) =
a 2
2n
1 +
g
n
a/2
,
which yields the marginal likelihood
m
γ
(Y )
g
1 + g
p
γ
/2
1
1 + g
Y
P
γ
Y +
g
1 + g
Y
(I
n
J
n
)Y
n1
2
for which a close d-form expression is found to be
m
γ
(Y ) =
Γ((n 1)/2)
π
(n1)
n
Y
(I
n
J
n
)Y
n1
2
(1 + g)
(np
γ
1)/2
[1 + g(1 R
2
γ
)]
(n1)/2
.
The corresponding Bayes Factor is given by
BF
γ:0
= (1 + g)
(np
γ
1)/2
1 + g(1 R
2
γ
)
(n1)/2
where the multiple coefficient of determination R
2
γ
for M
γ
is g iven by
1 R
2
γ
=
Y
(I
n
H
γ
)Y
Y
(I
n
J
n
)Y
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Publisher Resources

ISBN: 9781482235128