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

Table 6.11: Parameter estimates (bootstrapped standard errors) of the five states hidden
Markov common covariance model
State λ
1
λ
2
λ
3
λ
123
1 0.2459
(0.1125)
0.0000
(0.0194)
24.5967
(0.8797)
0.0000
(0.0000)
2 1.9775
(0.0343)
0.2086
(0.0089)
8.5108
(0.1715)
0.0000
(0.0000)
3 0.5796
(0.0726)
0.4304
(0.0124)
2.4925
(0.1229)
0.0908
(0.0045)
4 2.0558 0.1685 0.3295 0.0349
(0.0309)
5 0.0323
(0.0180)
(0.0066)
0.1043
(0.0116)
(0.0206)
0.0718
(0.0231)
(0.0014)
0.0036
(0.0006)
Table 6.12: Transition probability matrix of the hidden Markov common covariance
model
⎡0.3765
0.0778 0.1539 0.0151 0.3767⎤
⎢
⎥
⎢
0.0000 0.0000 1.0000 0.0000 0.0000
⎥
⎢0.1572
0.0000 0.5334 0.0802 0.2292⎥
⎢
⎥
⎢0.1027
0.0668 0.0000 0.6119 0.2186⎥
⎢
⎣0.1372
0.0000 0.1223 0.1583 0.5822⎥
⎦
Table 6.11 and Table 6.13 contain the parameter estimates and the bootstrapped
standard errors for the common covariance and the restricted covariance model with
five and four states respectively. Table 6.12 contains the estimated transition probability
matrix for the common covariance model. The ( i, j)
th element of the transition matrix is
the estimated probability P ij
of transition from state state i to state j . This model had
the highest probability of 1 when moving from state two to state three indicating that
the distribution of state two almost surely moved to state three. The next highest
probability was 0.3767 when moving from state one to state five. Table 6.14 contains
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