Markov-Chain Monte-Carlo methods and non-identifiabilities

• Published in: Monte Carlo methods and applications Vol. 24; no. 3; pp. 203 - 214
• Main Authors: Müller, Christian, Weysser, Fabian, Mrziglod, Thomas, Schuppert, Andreas
• Format: Journal Article
• Language: English
• Published: Berlin De Gruyter 01.09.2018; Walter de Gruyter GmbH
• Subjects: 65C05; Algorithms; Blood coagulation; Chains; Computer simulation; Criteria; Identification methods; Markov chains; Markov-Chain Monte-Carlo; Monte Carlo simulation; non-identifiability; Random walk; Regularization; Regularization methods
• ISSN: 0929-9629; 1569-3961
• DOI: 10.1515/mcma-2018-0018

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.