Convergence Rates for Variable-at-a-Time Metropolis-Hastings Algorithms

• Activity Number: 483
• Type: Contributed
• Date/Time: Thursday, August 7, 2008 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Ronald Neath*+ and Galin Jones
• Companies: Baruch College, City University of New York and The University of Minnesota
• Keywords: Convergence rate ; Geometric ergodicity ; Markov chain Monte Carlo ; Metropolis-Hastings algorithm ; Minorization condition ; Regenerative simulation

Abstract

In a Metropolis-Hastings independence sampler, proposals are drawn from a candidate distribution that does not depend on the current state of the chain. Identifying a suitable candidate density can be a challenging proposition in high-dimensional problems. A popular modification is to update the chain one component at a time, effectively replacing a p-dimensional problem with p one-dimensional problems. Of course the resulting algorithm is no longer an independence sampler, and thus results on uniform ergodicity (Mengersen and Tweedie, 1996) and regeneration times (Mykland, Tierney and Yu, 1995) do not apply. Two main problems are considered in this talk: (i) establishing a bound on the rate of convergence to the stationary distribution, and (ii) the use of regenerative simulation as a means of estimating Monte Carlo standard errors.