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We consider sampling and enumeration problems for Markov equivalence classes. We create and analyze a Markov chain for uniform random sampling on the DAGs inside a Markov equivalence class. Though the worst case is exponentially slow mixing, we find a condition on the Markov equivalence class for polynomial time mixing. We also investigate the ratio of Markov equivalence classes to DAGs and a Markov chain of He, Jia, and Yu for random sampling of sparse Markov equivalence classes.
The hardcore model on a graph $G$ with parameter $lambda>0$ is a probability measure on the collection of all independent sets of $G$, that assigns to each independent set $I$ a probability proportional to $lambda^{|I|}$. In this paper we consider th
Recent work has introduced sparse exchangeable graphs and the associated graphex framework, as a generalization of dense exchangeable graphs and the associated graphon framework. The development of this subject involves the interplay between the stat
We analyze random walks on a class of semigroups called ``left-regular bands. These walks include the hyperplane chamber walks of Bidigare, Hanlon, and Rockmore. Using methods of ring theory, we show that the transition matrices are diagonalizable an
RNA motifs typically consist of short, modular patterns that include base pairs formed within and between modules. Estimating the abundance of these patterns is of fundamental importance for assessing the statistical significance of matches in genome
In this paper we develop a general framework for constructing and analysing coupled Markov chain Monte Carlo samplers, allowing for both (possibly degenerate) diffusion and piecewise deterministic Markov processes. For many performance criteria of in