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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
526 Current Trends in Bayesian Methodology with Applications
the complete posterior density π
γ
(ψ, w|y) we get the target posterior density
π
γ
(ψ|y), that is,
Z
R
n
π
γ
(ψ, w|y)dw = π
γ
(ψ|y).
So if we can generate a Markov chain {ψ
(i)
, w
(i)
}
N
i=1
with stationary den-
sity π
γ
(ψ, w|y), then the marginal chain {ψ
(i)
}
N
i=1
has the stationary density
π
γ
(ψ|y) defined in (25 .7). This is the standard technique of data augmenta-
tion and here w is playing the r ole of “latent” va riables (or “missing data”)
[21].
Since we are using conjugate priors for (β, σ
2
) in (25.6), integ rating
π
γ
(ψ, w|y) with respect β we have
π
γ
(σ
2
, τ
2
, w|y) (στ)
n
exp{−
1
2τ
2
n
X
i=1
(y
i
h
λ
(w
i
))
2
}
τ
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Publisher Resources

ISBN: 9781482235128