Markov chain Monte Carlowith Gaussian processes for fast parameter estimation and uncertainty quantification in a1Dfluid‐dynamics model of the pulmonary circulation

Abstract

The past few decades have witnessed an explosive synergy between physics and the life sciences. In particular, physical modelling in medicine and physiology is a topical research area. The present work focuses on parameter inference and uncertainty quantification in a 1D fluid‐dynamics model for quantitative physiology: the pulmonary blood circulation. The practical challenge is the estimation of the patient‐specific biophysical model parameters, which cannot be measured directly. In principle this can be achieved based on a comparison between measured and predicted data. However, predicting data requires solving a system of partial differential equations (PDEs), which usually have no closed‐form solution, and repeated numerical integrations as part of an adaptive estimation procedure are computationally expensive. In the present article, we demonstrate how fast parameter estimation combined with sound uncertainty quantification can be achieved by a combination of statistical emulation and Markov chain Monte Carlo (MCMC) sampling. We compare a range of state‐of‐the‐art MCMC algorithms and emulation strategies, and assess their performance in terms of their accuracy and computational efficiency. The long‐term goal is to develop a method for reliable disease prognostication in real time, and our work is an important step towards an automatic clinical decision support system.

Emulation-accelerated Hamiltonian Monte Carlo algorithms for parameter estimation and uncertainty quantification in differential equation models

“…The present study extends our previous work (Paun and Husmeier 2020) by providing a theoretical framework for the emulation algorithms and by investigating the efficiency of the DA scheme in the context of the emulation HMC algorithms. Moreover, we extend the simulation study to provide a broad benchmark set of ODE/PDE models that are representative of the complexity of typical real-world applications, allowing us to carry out a sound method evaluation.…”

“…While an MCMC with DA approach has been taken in previous studies in the literature (Christen and Fox 2005;Golightly et al 2015;Sherlock et al 2017;Higdon et al 2011;Cui et al 2011;Quiroz et al 2018;Banterle et al 2019), to our best knowledge, our current study is the only one to complement our previous study (Paun and Husmeier 2020), and use DA in conjunction with Hamiltonian/Lagrangian Monte Carlo algorithms. Other studies have compared standard random-walk MCMC algorithms to their DA version.…”

“…Methods that correct for the bias and ensure asymptotic exactness use the surrogate for the proposal only (see studies in Rasmussen 2003;Zhang et al 2017;Paun and Husmeier 2020), or incrementally refine the surrogate model as MCMC proceeds (Zhang et al 2017). Other studies employ similar approaches guaranteeing asymptotic convergence to the posterior distribution (Wu and Li 2016;Conrad et al 2016Conrad et al , 2018Gong and Duan 2017), e.g.…”

“…The delayed acceptance (DA) scheme (Christen and Fox 2005;Golightly et al 2015) is another exact method, and it does not depend on any heuristically set terms. This method, employed in Christen and Fox (2005), Golightly et al (2015), Sherlock et al (2017), Higdon et al (2011), Cui et al (2011), Quiroz et al (2018), Banterle et al (2019), Paun and Husmeier (2020), is a two-stage acceptance procedure, with two separate acceptance/rejection decisions. The first decision is a computationally fast pre-filter step based on the surrogate model, which upon rejection of a proposed new parameter avoids carrying out the computationally expensive second step based on the original model.…”

Inference in Cardiovascular Modelling Subject to Medical Interventions

“…Recent methodological advancements in statistical surrogate modelling can be used to overcome this hurdle by training a computationally cheap statistical emulator to replace the original mathematical model (the so-called simulator), as e.g. discussed in [9]. The second challenge is related to a closed-loop effect that arises when making clinical decisions and medical interventions based on predictions from the mathematical model.…”