Non-asymptotic Error Bounds for Sequential MCMC Methods in Multimodal Settings

2012/05/30 by Nikolaus Schweizer, Schweizer, Nikolaus · 1 citation
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Quantum chaos and dynamical systems #Target Tracking and Data Fusion in Sensor Networks

paper · pdf · doi:10.48550/arxiv.1205.6733

openalex publication_date 2012/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove non-asymptotic error bounds for Sequential MCMC methods in the case of multimodal target distributions. Our bounds depend in an explicit way on upper bounds on relative densities, on constants associated with local mixing properties of the MCMC dynamics, namely, local spectral gaps and local hyperboundedness, and on the amount of probability mass shifted between effectively disconnected components of the state space.

Citations

• Annealed importance sampling
• Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions
• Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference

Cited by

• On the complexity of standard and waste-free SMC samplers

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