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

Raftery, 1998); identification of textile flaws from images (Campbell et al., 1997);
classification of astronomical data (Celeux and Govaert, 1995); and classification of
radar images (Fjørtoft et al., 2003).
The next section will provide an overview of the general formulation of the finite
mixture model and is mainly drawn from books and review articles (McLachlan and
Basford, 1988; McLachlan and Peel, 2000; Titterington et al., 1985 and Titterington,
1990).
5.3.1 Description of model-based clustering
In general, in model-based clustering, the observed data are assumed to come from
several unknown components (segments, components, latent classes or clusters are
synonyms and will sometimes be used interchangeably) that are mixed in unknown
proportions. The objective is then to ‘unmix’ the observations and to estimate the
parameters of the underlying density distributions within each component. The idea is
the observations belong to the same class are alike with respect to the observed
variables in the sense that their observed values are considered as coming from a
mixture of the same density distributions, whose parameters are unknown quantities to
be estimated (McLachlan and Basford, 1988). The density distribution is used to
estimate the probability of the observed values of the component variables, conditional
on knowing the mixture component from which those values were drawn.
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