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

underlying data. The advantage of the hidden Markov model is that it takes serial
correlation into account and by introducing suitable covariance structure the idea of the
spatial information can be found. Although I have applied this model to “weed counts”
it could easily be applied to other datasets. For example, consider an outbreak of a viral
infection from a health dataset. A health region is covered by a grid and one can observe
the number of cases infecting within a small neighbourhood of each grid point in the
health region. The data could also be multivariate if there were several viral infections
occurring across the region.
The model suggested in this thesis, the multivariate Poisson hidden Markov model,
provides the pattern of the weed distribution. It also gives rates and positive covariance
or relationships for weed species within the state. Unconditional covariance matrix for
the independent covariance structure shows that there is a negative correlation between
Dandelion and Wild Oats. Also, the independent model provides the probability of
moving from state i to state j, called transition probabilities. This model could
demonstrate how species switch from one component to another, that is, move from one
position to another over time.
Our model, the multivariate Poisson hidden Markov model, can deal with both the
overdispersion and the spatial information of the data. Therefore this model together
with the GIS (geographic information systems) generated weed density maps, will help
researchers and farmers to get an insight of weed distributions for herbicide
applications. The benefits of this technology include a reduction in spray volume and
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