Weak convergence of Metropolis algorithms for non-i.i.d. target distributions

2007/08/01 by Mylène Bédard · 64 citations
Decision Sciences · Mathematics · Physics and Astronomy · #Component (thermodynamics) #Convergence (economics) #Diffusion #Distribution (mathematics) #Function (biology) #Markov Chains and Monte Carlo Methods #Rate of convergence #Scaling #Simulation Techniques and Applications #Term (time) #Theoretical and Computational Physics #math.PR #msc:60F05 #msc:65C40

paper · pdf · doi:10.1214/105051607000000096

published in The Annals of Applied Probability 17(4) (Institute of Mathematical Statistics) · Published in at http://dx.doi.org/10.1214/105051607000000096 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

openalex publication_date 2007/08/01 · arxiv created 2007/10/19 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

In this paper, we shall optimize the efficiency of Metropolis algorithms for multidimensional target distributions with scaling terms possibly depending on the dimension. We propose a method for determining the appropriate form for the scaling of the proposal distribution as a function of the dimension, which leads to the proof of an asymptotic diffusion theorem. We show that when there does not exist any component with a scaling term significantly smaller than the others, the asymptotically optimal acceptance rate is the well-known 0.234.

Citations

• Optimal scaling of MaLa for nonlinear regression
• Equation of State Calculations by Fast Computing Machines
• Monte Carlo sampling methods using Markov chains and their applications
• General state space Markov chains and MCMC algorithms

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