Hidden Markov models (HMMs) have been originally developed for engineering applications in speech and hand-writing recognition and image segmentation. Then, HMMs became popular within the statistical community as efficient tools for the classification of dynamic data (HMMs are dynamic extension of finite mixture models), with applications in a many different areas, ranging from economics and finance to ecology and environmental sciences, medicine, genetics, epidemiology.
The course will present the basic concepts for dealing with Bayesian inference in HMMs, i.e. parameter estimation, model choice, and variable selection. Inference will be performed numerically, by using Markov chain Monte Carlo methods.
Models related to HMMs will be also presented: finite mixture models at the beginning of the course, and Markov switching autoregressive models, spatial hidden Markov models, hidden Markov mixed models at the end.
All methodological topics will be discussed jointly with applications to real data case studies.
Sessions where trainees can directly apply HMMs via the use of the R package will be part of the course.