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

the Poisson distribution is well suited to model this kind of data. However, the basic
statistics also demonstrate that the data is clearly overdispersed (Table 6.1), i.e. the
variance is clearly bigger than the mean and this is a problem when modelling the data
with the Poisson distribution. The mean of the Poisson distribution is equal to its
variance, can be denoted by single parameter λ, which is not really accurate for the data.
The solution to the problem of overdispersion (Leroux and Puterman, 1992) is to
assume that the data came from a finite mixture of Poisson distributions, that is, an
unknown number of components with different unknown mean species rates.
(a)
(b)
Frequency
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Counts
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Frequency
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(c)
Frequency
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Counts
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Figure 6.1: Histograms of the species counts: (a) Wild Buckwheat, (b) Dandelion and
(c) Wild Oats
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