Monte Carlo is a very flexible methodology that enables us to analyze these models. As examples, I will discuss two specific hidden Markov models. The first arises in an animal population survey, specifically the manatee population on the eastern coast of United States. The second is a preventive medicine problem, to model a chronic disease for comparison of treatment programs. For each, I will develop the hidden Markov model, develop the MCMC techniques and discuss the data analysis.
Bayesian inference is used to combine the data with the models.
For specific distributions that are difficult to handle with standard MCMC techniques, this update in combination with the Gibbs sampler leads to a more efficient sampling method.