Indirect Causes in Dynamic Bayesian Networks Revisited

Modeling causal dependencies often demands cycles at a coarse-grained temporal scale. If Bayesian networks are to be used for modeling uncertainties, cycles are eliminated with dynamic Bayesian networks, spreading indirect dependencies over time and enforcing an infinitesimal resolution of time. Without a "causal design," i.e., without anticipating indirect influences appropriately in time, we argue that such networks return spurious results. By introducing activator random variables, we propose template fragments for modeling dynamic Bayesian networks under a causal use of time, anticipating indirect influences on a solid mathematical basis, obeying the laws of Bayesian networks.