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

In the applications of the HMMs, likelihood functions and estimates of the model
parameters have been routinely computed. However, not much attention has been paid
to the computation of standard errors and confidence intervals for parameter estimates
of the HMMs (Aittokallio et al., 2000 and Visser et al., 2000). In this thesis, parametric
bootstrap samples were generated according to Efron et al., (1993) and McLachlan et
al., (2000) and the standard errors of parameter estimates were computed (section 5.5,
section 6.3.1 and 6.3.2). These standard errors will be useful for further inferences.
In Chapter 7, we can see that the EM algorithm was performing well for the given
dataset (weed counts), for the lens faults dataset (Aitchison and Ho (1989), p.649) and
for the bacterial count dataset (Aitchison and Ho (1989), p.651) even though it has some
disadvantages (section 5.3.3.1). This analysis also could be done using other
optimization techniques such as simulated annealing. However, there is no guarantee
that this method is suitable for all kinds of data (Brooks and Morgan, 1995). The EM
algorithm has some appealing properties, such as improvement in every iteration and
the parameters are in the ‘admissible range,’ and easy to program (section 5.3.3.1).
9.3 Comparison of different models
There are different ways to handle differences of the fit of the two models. The most
well known test is the likelihood ratio test (LRT). Under the null hypothesis (i.e. the fit
of both models is equal), the LRT is asymptotically distributed as chi-square with
degrees of freedom equal to the difference in the number of parameters if one model is
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