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

Table 6.8: Parameter estimates (bootstrapped standard errors) of the four component
restricted covariance model
Component
θ
1
θ
2
θ
3
θ
12
θ
13
θ
23
p
j
1 6.4384 0.0152 8.5477 0.0000 0.0000 2.4015 0.0143
(0.3673) (0.0318) (0.3180) (0.0000) (0.0000) (0.1516)
2 0.8485 0.1696 13.5921 0.0000 0.0000 0.0000 0.1213
(0.0277) (0.0070) (0.0778) (0.0000) (0.0000) (0.0000)
3 1.9083 0.4127 2.8167 0.0000 0.0000 0.0000 0.3575
(0.0376)
4 0.8075
(0.0249)
(0.0055)
0.1545
(0.0045)
(0.0285)
0.0819
(0.0049)
(0.0000)
0.0000
(0.0000)
(0.0000)
0.0000
(0.0000)
(0.0000)
0.0000
(0.0000)
0.5069
For the restricted covariance model it is also observed that the components of the model
with small mixing proportions have the large standard errors.
6.4.2 Results for the different multivariate Poisson hidden Markov models
Similar to the multivariate Poisson finite mixture models, for the multivariate Poisson
hidden Markov models all three models, that is, the local independence model, the
common covariance model, and the model with restricted covariance structure were
fitted sequentially for 1 to 7 components ( k =1,…,7). Furthermore, in order to overcome
the well-known drawback of the EM algorithm, i.e. the dependence on the initial
starting values for the model parameters, 10 different sets of starting values were chosen
at random. In fact, the transition probabilities ( P ij
) were uniform random numbers with
constraint ∑
m
P ij
j=
1
= 1 , 1 ≤ i ≤ m . The λ ’s were generated from a uniform distribution
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