dsmmR: Estimation and Simulation of Drifting Semi-Markov Models

Markov models are a common approach in the researcher's toolbox for aiding with the modeling of many real-life phenomena, often presented as a sequence of states in discrete time, known as a Markov chain.However, this assumes that the sequence under inspection is time-homogeneous and that the sojourn times always follow a geometric distribution.Notice that this is not always true in practice, for example when modeling DNA sequences.Drifting semi-Markov models (DSMM) aim to be a discrete-time pairing of semi-Markov models with drifting Markov models.Semi-Markov models allow an arbitrary choice for the distribution of the sojourn times.The drifting Markov models describe the non-homogeneity of a sequence through a smooth, known shape that is gradually evolving, expressed through a polynomial function.As a result, DSMM are best suited to capture non-homogeneities which occur from the intrinsic evolution of the system or from the interactions between the system and the environment.For a detailed introduction to semi-Markov models see Barbu & Limnios (2009).Drifting Markov models were first introduced in Vergne (2008).