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

CHAPTER 1
GENERAL INTRODUCTION
1.1 Introduction
The analysis of multivariate count data (e.g. weed counts for different species in a field)
that are overdispersed relative to the Poisson distribution (i.e. variance > mean) has
recently received considerable attention (Karlis and Meligkotsidou, 2006; Chib and
Winkelmann, 2001). Such data might arise in an agricultural field study where
overdispersion is caused by the individual variability of experimental units, soil types or
fertilizer levels. Therefore, these data (e.g. weed counts) are not homogenous within the
field. The Poisson mixture model is a flexible alternative model which can represent the
inhomogeneous population. Finite Poisson mixtures are very popular for clustering
since they lead to a simple and natural interpretation, as models describing a population
consisting of a finite number of subpopulations.
These types of count data can be modelled using model-based clustering methods, such
as multivariate Poisson finite mixture models (or independent finite mixture models)
and multivariate Poisson hidden Markov models (or Markov-dependent finite mixture
models). It is assumed that the counts follow independent Poisson distributions
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