Markov-Chain Monte-Carlo methods and non-identifiabilities

Müller Christian (), Weysser Fabian, Mrziglod Thomas and Schuppert Andreas
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Müller Christian: RwtH Aachen Joint Research Center for Computational Biomedicine, Aachen, Germany
Weysser Fabian: Bayer AG, Applied Mathematics, Leverkusen, Germany
Mrziglod Thomas: Bayer AG, Applied Mathematics, Leverkusen, Germany
Schuppert Andreas: RwtH Aachen Joint Research Center for Computational Biomedicine, Aachen, Germany

Monte Carlo Methods and Applications, 2018, vol. 24, issue 3, 203-214

Abstract: We consider the problem of sampling from high-dimensional likelihood functions with large amounts of non-identifiabilities via Markov-Chain Monte-Carlo algorithms. Non-identifiabilities are problematic for commonly used proposal densities, leading to a low effective sample size. To address this problem, we introduce a regularization method using an artificial prior, which restricts non-identifiable parts of the likelihood function. This enables us to sample the posterior using common MCMC methods more efficiently. We demonstrate this with three MCMC methods on a likelihood based on a complex, high-dimensional blood coagulation model and a single series of measurements. By using the approximation of the artificial prior for the non-identifiable directions, we obtain a sample quality criterion. Unlike other sample quality criteria, it is valid even for short chain lengths. We use the criterion to compare the following three MCMC variants: The Random Walk Metropolis Hastings, the Adaptive Metropolis Hastings and the Metropolis adjusted Langevin algorithm.

Keywords: Markov-Chain Monte-Carlo; non-identifiability (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1515/mcma-2018-0018

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