Continuous time Bayesian networks (CTBN) describe structured stochastic
processes with finitely many states that evolve over continuous time. A CTBN
is a directed (possibly cyclic) dependency graph over a set of variables,
each of which represents a finite state continuous time Markov process whose
transition model is a function of its parents. We address the problem of
learning parameters and structure of a CTBN from fully observed data. We define
a conjugate prior for CTBNs and show how it can be used both for Bayesian
parameter estimation and as the basis of a Bayesian score for structure
learning. Because acyclicity is not a constraint in CTBNs, we can show that
the structure learning problem is significantly easier, both in theory and in
practice, than structure learning for dynamic Bayesian networks
(DBNs). Furthermore, as CTBNs can tailor the parameters and dependency
structure to the different time granularities of the evolution of different
variables, they can provide a better fit to continuous-time processes than
DBNs with a fixed time granularity.