The Annals of Statistics
- Ann. Statist.
- Volume 39, Number 6 (2011), 3262-3289.
Convergence of adaptive and interacting Markov chain Monte Carlo algorithms
Adaptive and interacting Markov chain Monte Carlo algorithms (MCMC) have been recently introduced in the literature. These novel simulation algorithms are designed to increase the simulation efficiency to sample complex distributions. Motivated by some recently introduced algorithms (such as the adaptive Metropolis algorithm and the interacting tempering algorithm), we develop a general methodological and theoretical framework to establish both the convergence of the marginal distribution and a strong law of large numbers. This framework weakens the conditions introduced in the pioneering paper by Roberts and Rosenthal [J. Appl. Probab. 44 (2007) 458–475]. It also covers the case when the target distribution π is sampled by using Markov transition kernels with a stationary distribution that differs from π.
Ann. Statist., Volume 39, Number 6 (2011), 3262-3289.
First available in Project Euclid: 5 March 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 65C05: Monte Carlo methods 60F05: Central limit and other weak theorems 62L10: Sequential analysis 65C05: Monte Carlo methods
Secondary: 65C40: Computational Markov chains 60J05: Discrete-time Markov processes on general state spaces 93E35: Stochastic learning and adaptive control
Fort, G.; Moulines, E.; Priouret, P. Convergence of adaptive and interacting Markov chain Monte Carlo algorithms. Ann. Statist. 39 (2011), no. 6, 3262--3289. doi:10.1214/11-AOS938. https://projecteuclid.org/euclid.aos/1330958679
- Supplementary material: Supplement to paper “Convergence of adaptive and interacting Markov chain Monte Carlo algorithms”. This supplement provides a detailed proof of Lemma 4.2 and Propositions 3.1, 4.3 and 5.2. It also contains a discussion on the setwise convergence of transition kernels.