Abstract
This paper presents a theoretical Monte Carlo Markov chain procedure in the framework of graphs. It specifically deals with the construction of a Markov chain whose empirical distribution converges to a given reference one. The Markov chain is constrained over an underlying graph so that states are viewed as vertices, and the transition between two states can have positive probability only in the presence of an edge connecting them. The analysis focuses on the relevant case of support of the target distribution not connected in the graph. Some general arguments on the speed of convergence are also carried out.
Funding Statement
E. D.S. was partially supported by Simmetrie e Disuguaglianze in Modelli Stocastici RM118164035FE854 and by Dipendenza tra Variabili Aleatorie e nei Processi Stocastici RM120172B73EEB91
Acknowledgments
We are deeply grateful to two anonymous referees and to the Editor-in-Chief for the remarkably pertinent suggestions, that greatly improved the article.
Citation
Roy Cerqueti. Emilio De Santis. "Monte Carlo Markov chains constrained on graphs for a target with disconnected support." Electron. J. Statist. 16 (2) 4379 - 4397, 2022. https://doi.org/10.1214/22-EJS2043
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