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

models would impose a spatial autocorrelation structure where both neighbouring E-W
(East-West) and N-S (North-South) points would exhibit high correlation. A flaw in this
approach is that the last point (December) in each row (year) is assumed to be highly
correlated with the first point (January) in the consecutive row. This is not necessarily
the case, however the effect of this assumption would be minimal. Thus the line scan
method can transform the data into a 1-D sequence that is capable of approximating the
spatial autocorrelation structure. If a periodic 1-D model is not used this would
correspond to a spatial model where the neighbourhood system would only include E-W
neighbours.
The weed species counts in the agriculture field also spatially correlated. The twodimensional
grid data can be transformed horizontally to a one-dimensional chain, by
sweeping the a x b grid line by line. There will be slight irregularities in region borders
with this approach rather than with the corresponding scheme based on Markov random
field. However, the line scan transformation has less effect on irregularities since the
agricultural field has a large neighbourhood system. That is, the distance between the
neighbourhood points or coordinates in the agricultural field is large. In the literature
review (section 1.2.3), it is given that the classification accuracy of the hidden Markov
random field and the hidden Markov model will provide similar results and the hidden
Markov model is much faster and simpler than the one based on Markov random fields
(Fjφrtoft et al., 2003 and Aas et al., 1999). Therefore, in this thesis, a novel multivariate
Poisson hidden Markov model, which is a stochastic process, generated by a Markov
chain whose state sequence cannot be observed directly but which can be indirectly
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