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

7.5 Applications
In addition to weed species data, two other data sets (The lens faults dataset p.649 and
the bacterial count data set p.651) presented in Aitchison and Ho (1989) were used to
compare the models among the multivariate Poisson-log normal distribution, the
multivariate Poisson finite mixture and the hidden Markov model (Markov-dependent
finite mixture model). Calculations were carried out for the hidden Markov model,
replacing the mixing proportions in finite mixtures by posterior means of each state.
These posterior means were used to assess the goodness of fit of the hidden Markov
model (HMM). Results are presented and discussed in the next section.
7.5.1 The lens faults data
Table 7.1: Counts ( x 1
, x 2
) of surface and interior faults in 100 lenses
x 0 1 2 3 4 5 6 7 9 10 12 14
1
0 1 1 4 1
1 3 2 6 2 5 2
2 1 2 4 3 2 1 1 1 1 1
3 5 1 2 2 3 2
4 1 2 2 5 3 1 1
5 1 2 1 2 1 2 1
6 2 2 1 1 1
7 1 3 1
8 2
11 1
12 1
x
2
147