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

The multivariate Poisson hidden Markov model has some improvements over the
existing the multivariate finite mixture model. The computation time of the model is
less in the hidden Markov model compared to the finite mixture model for large sample
sizes (section 8.3). Another feature of the multivariate Poisson hidden Markov model is
that it can take into account the serial correlation among observations and provide the
transition probabilities from one state to another.
9.4 Model application to different datasets
The multivariate Poisson finite mixture and the multivariate Poisson hidden Markov
models provided a better fit than the multivariate Poisson-log normal model of
Aitchison and Ho (1989). The Newton-Raphson method is used to calculate the
parameters of the multivariate Poisson-log normal model (section 7.5).
9.5 Real world applications
In general, the multivariate count data occur in different fields of study. In this thesis,
we focused on counts for three weed species found in an agricultural field. Even though
we selected: Wild Buckwheat, Dandelion and Wild Oats as examples, we can generalize
this method to other weed counts as well. The main objective was to find out the
distribution of these species. The multivariate Poisson finite mixture models and the
multivariate Poisson hidden Markov models are two clustering methods to unmix the
distribution and to find parameters and the number of components or states given the
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