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

(c) Finite mixture with the five components common model (AIC and BIC
selection)
The estimated covariance matrix and the estimated correlation matrix are given below:
⎡2.4377
⎢
0.0512
⎢
⎢⎣
0.2293
0.0512
0.2669
− 0.0922
0.2293 ⎤
− 0.0922
⎥
⎥
25.3294 ⎥⎦
⎡1
⎢
⎢
⎢⎣
0.0635
1
0.0292 ⎤
− 0.0355
⎥
.
⎥
1 ⎥⎦
(d) Finite mixture with the five components independent model (BIC selection)
The estimated covariance matrix and the estimated correlation matrix are given below:
⎡2.2517
⎢
0.0750
⎢
⎢⎣
0.1133
0.0750
0.2878
− 0.0662
0.1133 ⎤
− 0.0662
⎥
⎥
25.0697 ⎥⎦
⎡1
⎢
⎢
⎢⎣
0.0932
1
0.0151 ⎤
− 0.0246
⎥
.
⎥
1 ⎥⎦
(e) Finite mixture with the six components independent model (AIC selection)
The estimated covariance matrix and the estimated correlation matrix are given below:
⎡2.4517
⎢
0.0563
⎢
⎢⎣
0.2162
0.0563
0.3562
− 0.0659
0.2162 ⎤
− 0.0659
⎥
⎥
25.3373⎥⎦
⎡1
⎢
⎢
⎢⎣
0.0602
1
0.0274 ⎤
− 0.0219
⎥
.
⎥
1 ⎥⎦
From the set of models (a)-(e) for the multivariate Poisson finite mixtures, the model
with the five components and the local independence which select by the BIC criterion
seem to be the best model compared to all the parameters estimates in the observed and
the estimated covariance and correlation matrices.
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