Making continuous time Bayesian networks more flexible

The time duration in continuous time Bayesian networks, i.e., the time that a variable stays in a state until it transitions to another state, follows an exponential distribution. The exponential distribution is widely applied to describe the waiting time between events in a Poisson process, which describes the distribution of the number of events in one unit of time. This distribution is parameterized by a single rate and has mode zero, implying that the highest probability mass for events to happen is attributed to the earliest times. To describe biological processes, the exponential distribution is not always natural. For example, if the immune system has not encountered a pathogen before, it most likely responds to a viral infection after a few days, rather than immediately. In this paper, we generalize our recently proposed hypoexponential continuous time Bayesian networks, by allowing any number of hypoexponential variables, i.e., variables having a hypoexponential time duration distribution. In addition, we propose and compare two learning methods to estimate parameters for the generalized models. Finally, the practical value of the generalized models is demonstrated by means of a realistic medical problem.