A high energy/small scale effective spacetime dimension of 3, or even better, 2, is expected to make a quantum theory of gravity more tractable. Thus, evidence for such dimensional reduction has been sought in several approaches, including causal set theory. We propose a Bayesian framework to deal with the difficulties of estimating the dimension of causal sets at the smallest scale. Our results do not show a reduction in dimension to 3 or below when causal sets are well-approximated by Minkowski space at the smallest scales.