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

is reached. The result of this procedure gives us the maximum likelihood estimator of
the hidden Markov model (Baum et al., 1970).
It should be noted that the Baum-Welch method leads to a local maximum of λ only. In
practice, to get a good solution, the initial guess λ
0
is very important. Usually several
sets of starting guesses of λ 0
are used and one with the greatest likelihood value is
chosen. Laird (1978) suggested a grid search method, which divides the searching
domain into equally spaced small grids and starts from each of the intersections. Leroux
and Puterman (1992) argue that the grid method would generate too many initial points
when high dimensional spaces are involved and as such, they suggested a clustering
algorithm.
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