A dynamic Bayesian network to represent discrete duration models

Originally devoted to specific applications such as biology, medicine and demography, duration models are now widely used in economy, finance or reliability. Recent works in various fields of application have shown the relevancy of using Bayesian networks to model complex systems, namely stochastic systems with an underlying distribution that does not fit to a well-known parametric form. In this paper, the description of a specific dynamic Bayesian network, referred to as Graphical Duration Model (GDM), is given. A GDM aims to represent a wide range of duration models. Its structure allows especially to fit multi-state systems featuring complex sojourn-time distributions and contextual dependencies. To that end, a duration variable is explicitly introduced to the state transition model which is classically represented by a Markov chain. A recursive algorithm efficiently perform inference in this model is derived along with its proof of correctness and space and time complexity studies. Finally, this approach is illustrated with an application in survival analysis in which the proposed model is compared with the commonly used Markov chain modelling.