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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
552 Current Trends in Bayesian Methodology with Applications
26.5.4 Partially observed finite HMM
Consider the following model described probabilistically as
r
k
Π(r
k
|r
k1
), y
k
p(y
k
|r
k
), z
k
p(z
k
|y
k
), (26.34)
where the dynamics of r
k
is given by a homogeneous first order finite state
Markov cha in. Here r
k
and y
k
together describe a partially observed finite
HMM (POfHMM). However instead of y
k
, z
k
is actually observed. The graph-
ical representation of the model is shown in Figure 2 6.3(b).
Similar to (26.5.3), the joint density can be decomposed as
p(r
k
, y
0:k
|z
0:k
) = p(r
k
|y
0:k
, z
0:k
) p(y
0:k
|z
0:k
). (26.35)
Again, the density p(y
0:k
|z
0:k
) can be targeted using a PF in the form of N
weighted particles as p(y
0:k
|z
0:k
)
P
N
i=1
ω
(i)
k
δ(y
0:k
y
(i)
0:k
). Then for each ...
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Publisher Resources

ISBN: 9781482235128