  The concept of causality has a controversial history. The question of whether
it is possible to represent and address causal problems with probability
theory, or if fundamentally new mathematics such as the do-calculus is required
has been hotly debated, In this paper we demonstrate that, while it is critical
to explicitly model our assumptions on the impact of intervening in a system,
provided we do so, estimating causal effects can be done entirely within the
standard Bayesian paradigm. The invariance assumptions underlying causal
graphical models can be encoded in ordinary Probabilistic graphical models,
allowing causal estimation with Bayesian statistics, equivalent to the
do-calculus.
