Explicit-Duration Markov Switching Models

Time-series are often modelled probabilistically as sequences of segments using first-order Markovian hidden variables representing different dynamics regimes. Such dynamics-regime variables implicitly define a geometric segment-duration distribution. A more flexible distribution requires introducing extra variables into the model with increased computational cost. This can be achieved in different ways, whose properties and categorization are still unclear. This book describes in a simple way different approaches to modelling the segment-duration distribution by categorizing them into three main groups, differing respectively by explicitly encoding information about segment beginning, end and both beginning and end by means of different segment-duration variables and associated distributions. The approaches are described using the framework of belief networks, which makes it possible to visually and therefore easily describe model structure and assess independence among random variables. This description enables a simple and clear understanding of approaches and inference routines in the literature but also to gain new insights especially about models with complex hidden variables.