Reversible Causal Mechanisms in Bayesian

Causal manipulation theorems proposed by Spirtes et al. in the context of directed probabilistic graphs, such as Bayesian networks, do not model so called reversible causal mechanisms, i.e., mechanisms that are capable of working in several directions, depending on which of their variables are manipulated exogenously. An example involving reversible causal mechanisms is the power train of a car: normally the engine moves the transmission which, in turn, moves the wheels; when the car goes down the hill, however, the driver may want to use the power train to slow down the car, i.e., let the wheels move the transmission, which then moves the engine. Reversible causal mechanisms are modeled quite naturally in the context of equilibrium structural equation models. In this paper, we investigate whether Bayesian networks are capable of representing reversible causal mechanisms. Building on the result of Druzdzel and Si-mon (1993), which shows that conditional probability tables in Bayesian networks can be viewed as descriptions of causal mechanisms, we study the conditions under which a conditional probability table can represent a reversible causal mechanism.