MCMC methods for inference in a mathematical model of pulmonary circulation

Păun, L. M., Qureshi, M. U., Colebank, M., Hill, N. A. , Olufsen, M. S., Haider, M. A. and Husmeier, D. (2018) MCMC methods for inference in a mathematical model of pulmonary circulation. Statistica Neerlandica, 72(3), pp. 306-338. (doi: 10.1111/stan.12132)

Abstract

This study performs parameter inference in a partial differential equations system of pulmonary circulation. We use a fluid dynamics network model that takes selected parameter values and mimics the behaviour of the pulmonary haemodynamics under normal physiological and pathological conditions. This is of medical interest as it enables tracking the progression of pulmonary hypertension. We show how we make the fluids model tractable by reducing the parameter dimension from a 55D to a 5D problem. The Delayed Rejection Adaptive Metropolis algorithm, coupled with constraint non‐linear optimization, is successfully used to learn the parameter values and quantify the uncertainty in the parameter estimates. To accommodate for different magnitudes of the parameter values, we introduce an improved parameter scaling technique in the Delayed Rejection Adaptive Metropolis algorithm. Formal convergence diagnostics are employed to check for convergence of the Markov chains. Additionally, we perform model selection using different information criteria, including Watanabe Akaike Information Criteria.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Paun, Dr Mihaela and Hill, Professor Nicholas and Qureshi, Mr Umar and Husmeier, Professor Dirk
• Authors: Păun, L. M., Qureshi, M. U., Colebank, M., Hill, N. A., Olufsen, M. S., Haider, M. A., and Husmeier, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics; College of Science and Engineering > School of Mathematics and Statistics > Statistics
• Journal Name: Statistica Neerlandica
• Publisher: Wiley
• ISSN: 0039-0402
• ISSN (Online): 1467-9574
• Published Online: 20 April 2018
• Copyright Holders: Copyright © 2018 The Authors, Statistica Neerlandica and VVS
• First Published: First published in Statistica Neerlandica 72(3): 306-338
• Publisher Policy: Reproduced in accordance with the publisher copyright policy

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
69446	1	EPSRC Centre for Multiscale soft tissue mechanics with application to heart & cancer	Raymond Ogden	Engineering and Physical Sciences Research Council (EPSRC)	EP/N014642/1	M&S - MATHEMATICS