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Activity Number: 421 - Advances in Bayesian Modeling and Inferential Methods
Type: Contributed
Date/Time: Tuesday, July 31, 2018 : 2:00 PM to 3:50 PM
Sponsor: International Society for Bayesian Analysis (ISBA)
Abstract #329207
Title: Complexity Results for MCMC Derived from Quantitative Bounds
Author(s): Jun Yang* and Jeffrey S Rosenthal
Companies: University of Toronto and University of Toronto
Keywords: MCMC; Convergence Complexity; Quantitative Bounds; High-dimensional Markov Chain; Computational Statistics; Bayesian Inference

This paper considers how to obtain MCMC quantitative convergence bounds which can be translated into tight complexity bounds in high-dimensional setting. We propose a modified drift-and-minorization approach, which establishes a generalized drift condition defined in a subset of the state space. The subset is called the ``large set'', and is chosen to rule out some ``bad'' states which have poor drift property when the dimension gets large. Using the ``large set'' together with a ``centered'' drift function, a quantitative bound can be obtained which can be translated into a tight complexity bound. As a demonstration, we analyze a certain realistic Gibbs sampler algorithm and obtain a complexity upper bound for the mixing time, which shows that the number of iterations required for the Gibbs sampler to converge is constant. It is our hope that this modified drift-and-minorization approach can be employed in many other specific examples to obtain complexity bounds for high-dimensional Markov chains.

Authors who are presenting talks have a * after their name.

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