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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
186 Current Trends in Bayesian Methodology with Applications
An interval that will contain an obser ved value of y
i
with virtual certainty,
given that we know µ
i
and δ
i
, is µ
i
± δ
1/2
i
z
(1+p)/2
. L e t s
1i
and s
2i
be lower
and upper bounds respectively on the half-length of this interval. The values
s
1i
and s
2i
represent what we know about the scaling of y
i
and we choose
these so that s
1i
is not excessively small or s
2i
excessively large. These choices
imply that
s
2
2i
z
2
(1+p)/2
δ
1
i
s
2
1i
z
2
(1+p)/2
. (9.7)
Therefore, σ
0
= max{(m
2i
m
1i
)/2s
2i
: i = 1, . . . , p} is compatible with (9.6)
and (9.7), which specifies another hyperparameter. It is perhaps logical for
(m
2i
m
1i
)/2s
2i
to be constant but this is not necessary.
Let G (α
0i
, β
0i
, ·) denote the gamma(α
0i
, β
0i
) cdf, ...
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Publisher Resources

ISBN: 9781482235128