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

( y1, y2, y
3)
( y 1, , )
1− y2 y3
y1 y2 y3
( −1, − 1, )
( y1−1, y2, y3−
1)
( y 2, y , y )
( −2, − 1, ) ( y1− 2, y2, y3− 1) ( y1− 2, y2− 2, y3)
( y1− 2, y2−1, y3− 1) ( y1−2, y2, y3−
2)
1− 2 3 y1 y2 y3
Figure 5.1: Flat algorithm (stage 1)
Using the Flat algorithm, one can move along a plane until the minimum coordinate
equal to zero (stage 2). For example, consider the calculation of probability p (2,2,2).
Figure 5.2 and Figure 5.4 illustrate how the Flat algorithm works.
(2,2,2)
(1,2,2) (1,1,2) (1,2,1)
(0,2,2) (0,1,2) (0,2,1) (0,0,2) (0,1,1) (0,2,0)
Figure 5.2: Calculating p (2,2,2) using the Flat algorithm
When you come to this stage, you can use the Flat algorithm for py (
1, y
2)
or py ( 1, y 3)
or py ( 2, y 3)
according to Figure 5.3. Thus, starting from ( y1, y2, y 3)
and applying the
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