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

In this thesis, three species counts from an agriculture field were selected for analysis.
The main objective was to determine the model for the distribution of these multivariate
counts. The estimation involves finding out the mean and covariance structures of the
distribution. The data are recorded in a grid, and this data can be considered as a twodimensional
Markov random field. At the same time, an agricultural field has a large
neighbourhood system compared to an image. That is, the distance between the
neighbouring points or coordinates in an agricultural field is large compared to the
distance between the neighbouring points or coordinates in an image. A drawback of the
models based on a Markov random field is that they can only be used for small
neighbourhoods in an image, due to the computational complexity and the modeling
problems posed by large neighbourhoods (Aas et al., 1999). These data can be
transformed into a one-dimensional chain. Therefore, as a first step, the grid data were
converted into a sequence or a one-dimensional chain using line scan (Chapter 4).
The analysis of these data involves two methods, (a) the multivariate Poisson finite
mixture model and (b) the multivariate Poisson hidden Markov model. The multivariate
Poisson finite mixture model has been used in many other applications (e.g. marketing
Brijs et al., 2004). However, the multivariate Poisson hidden Markov model is a new
application to this kind of data (agricultural field data) with Poisson counts.
For both models, the computation of the multivariate Poisson probabilities was studied
according to Mahamunulu’s recurrence relations (see section 5.2.2). The preliminary
loglinear analysis suggests that there were no significant two-way interactions. It can be
169