André Inge: Hidden Markov Models Theory and Simulation

Markov chains describe stochastic transitions between states over time and the observations are the sequence of states. The assumption is that the state at the next step is dependent only on the current state. In many applications these states are not observable and the observations are instead outputs from another stochastic process which is dependent on the state of the unobservable process. These models are called hidden markov models (HMMs). This paper will provide a theoretical background for discrete-time, finite-state HMMs starting in ordinary markov chains. It will also answer questions on how to infer information about the hidden process and how to predict future distributions. It ends with simulations and a real data example where the covered material is put into use. Examples are also provided throughout the paper. The simulations showed that local maxima of the likelihood can be detected through assigning implausible starting values for estimation algorithms and that the precision of global decoding increase with smaller overlapping of the density/mass of the state dependent variables.