## Continuous Time Bayesian Networks

[PDF] (Corrected)

### Abstract

In this paper we present a language for finite state continuous time
Bayesian networks (CTBNs), which describe structured stochastic
processes that evolve over continuous time. The state of the system is
decomposed into a set of local variables whose values change over
time. The dynamics of the system are described by specifying the
behavior of each local variable as a function of its parents in a
directed (possibly cyclic) graph. The model specifies, at any given
point in time, the distribution over two aspects: when a local
variable changes its value and the next value it takes. These
distributions are determined by the variable's current value and the
current values of its parents in the graph. More formally, each
variable is modeled as a finite state continuous time Markov process
whose transition intensities are functions of its parents. We present
a probabilistic semantics for the language in terms of the generative
model a CTBN defines over sequences of events. We list types of
queries one might ask of a CTBN, discuss the conceptual and
computational difficulties associated with exact inference, and
provide an algorithm for approximate inference which takes advantage
of the structure within the process.

### Full Citation

U. Nodelman, C.R. Shelton, and D. Koller (2002). "Continuous Time
Bayesian Networks." Proceedings of the Eighteenth Conference on
Uncertainty in Artificial Intelligence (UAI) (pp. 378-387).

### Bibtex

@inproceedings{Nodelman+al:UAI02,
author = "U. Nodelman and C.R. Shelton and D. Koller",
booktitle = "Proceedings of the Eighteenth Conference on
Uncertainty in Artificial Intelligence (UAI)",
title = "Continuous Time {B}ayesian Networks",
pages = "378--387",
year = "2002",
}