multivariate poisson hidden markov models for analysis of spatial ...

0.8 0.6
0.2
1
0.4
2
(1) P [H]=2/3 (2) P [H]=1/6
P [T]=1/3
P [T]=5/6
Figure 2.4: 2-biased coins model
0.8 0.8 0.2 0.6 0.4 0.8
1 1 1 2 2 1 1
H H T T T T H
The probabilities for the following events can be calculated as follows:
1. The probability of the above state transition sequence:
P[1112211]= π (1)
P 11 P 11 P 12 P 22 P 21 P 11 =1× 0.8× 0.8× 0.2× 0.6× 0.4× 0.8 = 0.025.
2. The probabilities of the above output sequence given the above transition
sequence:
P[(HHTTTTH)|( 1112211)]= 2 × 2 × 1 × 5 × 5 × 1 × 2 =0.023.
3 3 3 6 6 3 3
3. The probability of the above output sequence and the above transition sequence:
P[(HHTTTTH)∩( 1112211)]= 0.025× 0.023 = 5.7× 10 −4 .
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