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Activity Number:
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38
- Inference, Optimization, and Computation on Discrete Structures
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Type:
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Invited
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Date/Time:
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Sunday, August 8, 2021 : 3:30 PM to 5:20 PM
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Sponsor:
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IMS
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Abstract #316769
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Title:
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Spectral gaps and error estimates for infinite-dimensional Metropolis-Hastings with non-Gaussian priors
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Author(s):
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James Johndrow* and Bamdad Hosseini
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Companies:
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University of Pennsylvania and California Institute of Technology
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Keywords:
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MCMC;
Metropolis-Hastings;
Bayesian;
Inverse problems
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Abstract:
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We study a class of Metropolis-Hastings algorithms for target measures that are absolutely continuous with respect to a large class of non-Gaussian prior measures on Banach spaces. The algorithm is shown to have a spectral gap in a Wasserstein-like semimetric weighted by a Lyapunov function. A number of error bounds are given for computationally tractable approximations of the algorithm including bounds on the closeness of Ces\'{a}ro averages and other pathwise quantities via perturbation theory. Several applications illustrate the breadth of problems to which the results apply such as likelihood approximation by Galerkin-type projections and approximate simulation of proposals.
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Authors who are presenting talks have a * after their name.
