Theoretical properties of quasi-stationary Monte Carlo methods

Abstract

This paper gives foundational results for the application of quasi-stationarity to Monte Carlo inference problems. We prove natural sufficient conditions for the quasi-limiting distribution of a killed diffusion to coincide with a target density of interest. We also quantify the rate of convergence to quasi-stationarity by relating the killed diffusion to an appropriate Langevin diffusion. As an example, we consider in detail a killed Ornstein--Uhlenbeck process with Gaussian quasi-stationary distribution.

27 pages, 1 figure. Final version of accepted paper. Minor typos corrected

References in corpus (1)

• On Markov chain Monte Carlo methods for tall data

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• An approximation scheme for quasi-stationary distributions of killed diffusions
• No Free Lunch for Approximate MCMC
• Perturbation theory for killed Markov processes and quasi-stationary distributions
• A note on the jump locations of Markov processes