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

(i) Hidden Markov model with the five components common model (AIC selection)
The estimated covariance matrix and the estimated correlation matrix are given below:
⎡2.2982
⎢
0.0821
⎢
⎢⎣
0.1455
0.0821
0.2739
− 0.0267
0.1455 ⎤
− 0.0267
⎥
⎥
24.6784 ⎥⎦
⎡1
⎢
⎢
⎢⎣
0.1035
1
0.0193 ⎤
− 0.0103
⎥
.
⎥
1 ⎥⎦
From the set of models (f)-(i) for the multivariate Poisson hidden Markov models, the
model with the five components local independence (according to the AIC and the BIC
selection) seem to be the best model.
In both sets of models, (a) the multivariate Poisson finite mixture model and (b) the
multivariate Poisson hidden Markov model, restricted covariance structure does not
seem to be a good indication of the data, even though those models have well separated
components (Chapter 6, section 6.5).
All the information of goodness of fit criteria
• Selection of number of components/ states
• Separation of components/states
• Estimated covariance and correlation matrices,
taken into account, the following conclusions can be made for weed count data. The
multivariate Poisson hidden Markov model with the independent covariance structure
and the five state model was the best representation of data, since this model had a
higher entropy criterion value compared to the finite mixture model and the estimated
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