Continuous Time Bayesian Networks

Continuous Time Bayesian NetworksUri Nodelman Christian R. Shelton Daphne KollerStanford University Stanford University Stanford Universitynodelman@cs.stanford.edu cshelton@cs.stanford.edu koller@cs.stanford.eduAbstract others. For example, the distribution over how fast a drugtakes effect might be mediated by how fast it reaches thebloodstream which may itself be affected by how recentlyIn this paper we present a language for nite state con-tinuous time Bayesian networks (CTBNs), which de- the person has eaten.scribe structured stochastic processes that evolve over Bayesian networks (Pearl, 1988) are a standard approachcontinuous time. The state of the system is decom-for modelling structured domains. With such a represen-posed into a set of local variables whose values changeover time. The dynamics of the system are described tation we can be explicit about the direct dependenciesby specifying the behavior of each local variable as a which are present and use the independencies to our ad-function of its parents in a directed (possibly cyclic) vantage computationally. However, Bayesian networks aregraph. The model speci es, at any given point in time, designed to reason about static processes, and cannot bethe distribution over two aspects: when a local variableused directly to answer the types of questions that concernchanges its value and the next value it takes. Thesedistributions are determined by the variable’s current us here.value and the current ...