Abstract:
When modelling univariate count data, the Poisson distribution is a popular choice that is
routinely studied by academics and applied by practitioners. It does not, however, allow for the
modelling of dependencies found in real-world datasets. The Poisson distribution is particulary
insufficient when modelling overdispersed and spatially dependent data. It is for this reason that
extensions of the Poisson distribution that are known to perform well in these two areas are considered.
Poisson mixture regression is effective at modelling overdispersed data and Gaussian
Process/Kriging is a well-known method for capturing spatial dependence. A framework is created
within which exploratory spatial metrics are categorised. Model accuracy is evaluated in
terms of model fit through a residual analysis and Mean-Square Error (MSE) evaluation. The
model’s ability to capture spatial dependence is evaluated with a confusion matrix. This gives us a
range of tools to assess in what manner an extension outperform its counterparts. We then decide
which of the Poisson mixture regression and Gaussian Process/Kriging models achieve the best
performance on a dataset with given spatial characteristics. Expansions to the exploratory spatial
framework, modelling techniques and accuracy measures that are not considered here, are also
suggested for further work.
