Hidden Markov models (HMMs) are a popular class of models used in the analysis of sequential data, particularly time series data. A discrete-time, finite-state HMM is a doubly stochastic process composed of a state process, S, and a state-dependent observation process Y, with the observations taken to be conditionally independent given the states. The state process is assumed to be generated according to an underlying Markov chain, while the observations are generated according to a set of state-dependent distributions. Much of their appeal, however, is due to the immense flexibility provided by their framework and the many ways in which their architecture can be structured and extended.

Application of HMMs to ecological and environmental data are usually driven by the simple notion that parts of the observed process behave, in some manner, different than others. In movement ecology, the HMM states may serve as proxies for distinct animal behaviors of interest, while for wind time series data, we may want to differentiate periods of high wind speeds from those of low wind speeds. In the model building journey of fitting HMMs to complex ecological and environmental time series, we typically navigate through multi-modal posterior distributions, issues with identifiability and lack-of-fit due to unaccounted heterogeneity. Through various data examples, including: diving with a tiger shark, cruising with white sharks in Mexico and the personalities of neonate garter snakes, I will discuss how we can learn from multi-modal posterior distributions, address common model-fitting issues, as well as cover the HMM extensions and architectures that will serve useful in the analysis of general ecological and environmental data. I will also touch upon work in-progress in the general areas of movement ecology and environmental statistics, along with additional HMM architectures, that will provide many avenues for future research.