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

eplications are generally sufficient for the standard error estimation (Efron and
Tibshirani, 1993).
On the identifiability of a mixture model, if the component densities of the mixture
belong to the same parametric family, then the likelihood does not change under a
permutation of the component labels in the parameter Φ and hence neither does its
maximum likelihood estimate Φ . This raises the question of whether the so-called
label-switching problem (for example, what you have as the first cluster now will be the
second cluster in the next sample and so on) occurs in the generation of the bootstrap
replications of the maximum likelihood estimation, as in Monte Carlo Markov chain
computations involving mixture models. McLachlan and Peel (2000) explained that
according to their experience it has not arisen, as they always take the maximum
likelihood estimate Φ
calculated from the original data to be the initial value of
parameter in applying the EM algorithm to each bootstrap sample.
The following steps were used to calculate the bootstrapped standard errors for both
models:
(a) Multivariate Poisson finite mixture model and
(b) Multivariate Poisson hidden Markov model.
Step 1: Using estimated means and transition probabilities/or mixing proportions from
different states/or components simulate the mixture distribution of data.
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