Supplement to "Reversible MCMC on Markov equivalence classes of sparse directed acyclic graphs"

This supplementary material includes three parts: some preliminary results, four examples, an experiment, three new algorithms, and all proofs of the results in the paper [4]. In this Section, we provide algorithms introduced by Dor and Tarsi [3], and Chickering [1, 2] respectively. These results are necessary to implement our proposed approach technically. Some definitions and notation are introduced first. A directed edge of a DAG is compelled if it occurs in the corresponding completed PDAG, otherwise, the directed edge is reversible and the corresponding parents are reversible parents.