Year: 2025
Type: preprint
Abstract: We investigate the use of the Metropolis-Hastings algorithm to sample posterior distribution in a Bayesian inverse problem, where the likelihood function is random. Concretely, we consider the case where one has full field observations of a PDE solution, in case a one-dimensional diffusion equation, subject to a Gaussian observation error. Assuming one uses a particle-based Monte Carlo simulation when approximating the likelihood function, one gets an approximate likelihood with additive Gaussian noise in the log-likelihood. We study how these two Gaussian distributions affect the distribution of ratios of approximate likelihood evaluations, as required when evaluating acceptance probabilities in the Metropolis-Hastings algorithm. We do so through both theoretical analysis and numerical experiments.
Source: arXiv (Cornell University)
Authors: Løvbak, Emil, Krumscheid, Sebastian
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979342983
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