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

5.3.3.1 Properties of the EM algorithm
The EM algorithm is certainly one of the most accepted algorithms to estimate finite
mixture models due to some of its attractive properties listed below:
• The most important advantage of the EM algorithm is surely its convergence
towards the optimum parameter values. This means that, given the recent
mixture model parameters, a single EM iteration provides new parameter
estimates, which are proven to increase the loglikelihood of the model
(Dempster et al., 1977; McLachlan et al., 1997). The convergence of the EM
algorithm is proven by Meilijson (1989) and Wu (1983).
• The EM algorithm ensured that the estimated parameters are within the required
range (admissible range). This means that, for example for the Poisson
distribution, the parameter values are zero or positive and cannot take negative
values.
• The EM algorithm is fairly easy to program.
However, apart from these appealing properties of the EM algorithm, some limitations
have been identified as well:
• The setback with the EM estimation is that the procedure may converge to a
local but not a global optimum (McLachlan et al., 1988; Titterington et al.,
1985). It is generally accepted that the best way to avoid a local solution is to
use multiple sets of starting values for the EM algorithm and to observe the
evolution of final likelihood for the different restarts of the EM algorithm.
84