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Vernon I, Owen J, Aylett-Bullock J, Cuesta-Lazaro C, Frawley J, Quera-Bofarull A, Sedgewick A, Shi D, Truong H, Turner M, Walker J, Caulfield T, Fong K, Krauss F. Bayesian emulation and history matching of JUNE. Philos Trans A Math Phys Eng Sci 2022; 380:20220039. [PMID: 35965471 PMCID: PMC9376712 DOI: 10.1098/rsta.2022.0039] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2022] [Accepted: 06/07/2022] [Indexed: 05/21/2023]
Abstract
We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.
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Affiliation(s)
- I. Vernon
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J. Owen
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J. Aylett-Bullock
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - C. Cuesta-Lazaro
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - J. Frawley
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - A. Quera-Bofarull
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - A. Sedgewick
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Centre for Extragalactic Astronomy, Durham University, Durham DH13LE, UK
| | - D. Shi
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - H. Truong
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - M. Turner
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - J. Walker
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - T. Caulfield
- Department of Computer Science, Durham University, Durham DH13LE, UK
| | - K. Fong
- Department of Science, Technology, Engineering and Public Policy, University College London, London WC1E6BT, UK
- Department of Anaesthesia, University College London Hospital, London NW12BU, UK
| | - F. Krauss
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
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2
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Vernon I, Owen J, Aylett-Bullock J, Cuesta-Lazaro C, Frawley J, Quera-Bofarull A, Sedgewick A, Shi D, Truong H, Turner M, Walker J, Caulfield T, Fong K, Krauss F. Bayesian emulation and history matching of JUNE. Philos Trans A Math Phys Eng Sci 2022; 380:20210039. [PMID: 35965471 DOI: 10.1098/rsta.2021.0039] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/01/2021] [Accepted: 12/06/2021] [Indexed: 05/21/2023]
Abstract
We analyze JUNE: a detailed model of COVID-19 transmission with high spatial and demographic resolution, developed as part of the RAMP initiative. JUNE requires substantial computational resources to evaluate, making model calibration and general uncertainty analysis extremely challenging. We describe and employ the uncertainty quantification approaches of Bayes linear emulation and history matching to mimic JUNE and to perform a global parameter search, hence identifying regions of parameter space that produce acceptable matches to observed data, and demonstrating the capability of such methods. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.
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Affiliation(s)
- I Vernon
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J Owen
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Department of Mathematical Sciences, Durham University, Durham DH13LE, UK
| | - J Aylett-Bullock
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - C Cuesta-Lazaro
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - J Frawley
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - A Quera-Bofarull
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - A Sedgewick
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Centre for Extragalactic Astronomy, Durham University, Durham DH13LE, UK
| | - D Shi
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Computational Cosmology, Durham University, Durham DH13LE, UK
| | - H Truong
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - M Turner
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Advanced Research Computing, Durham University, Durham DH13LE, UK
| | - J Walker
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
| | - T Caulfield
- Department of Computer Science, Durham University, Durham DH13LE, UK
| | - K Fong
- Department of Science, Technology, Engineering and Public Policy, University College London, London WC1E6BT, UK
- Department of Anaesthesia, University College London Hospital, London NW12BU, UK
| | - F Krauss
- Institute for Data Science, Durham University, Durham DH13LE, UK
- Institute for Particle Physics Phenomenology, Durham University, Durham DH13LE, UK
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Fisher HF, Boys RJ, Gillespie CS, Proctor CJ, Golightly A. Parameter inference for a stochastic kinetic model of expanded polyglutamine proteins. Biometrics 2021; 78:1195-1208. [PMID: 33837525 DOI: 10.1111/biom.13467] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2019] [Revised: 03/21/2021] [Accepted: 03/24/2021] [Indexed: 11/30/2022]
Abstract
The presence of protein aggregates in cells is a known feature of many human age-related diseases, such as Huntington's disease. Simulations using fixed parameter values in a model of the dynamic evolution of expanded polyglutaime (PolyQ) proteins in cells have been used to gain a better understanding of the biological system. However, there is considerable uncertainty about the values of some of the parameters governing the system. Currently, appropriate values are chosen by ad hoc attempts to tune the parameters so that the model output matches experimental data. The problem is further complicated by the fact that the data only offer a partial insight into the underlying biological process: the data consist only of the proportions of cell death and of cells with inclusion bodies at a few time points, corrupted by measurement error. Developing inference procedures to estimate the model parameters in this scenario is a significant task. The model probabilities corresponding to the observed proportions cannot be evaluated exactly, and so they are estimated within the inference algorithm by repeatedly simulating realizations from the model. In general such an approach is computationally very expensive, and we therefore construct Gaussian process emulators for the key quantities and reformulate our algorithm around these fast stochastic approximations. We conclude by highlighting appropriate values of the model parameters leading to new insights into the underlying biological processes.
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Affiliation(s)
- H F Fisher
- School of Mathematics, Statistics & Physics, Newcastle University, Newcastle Upon Tyne, UK.,Population Health Sciences Institute, Newcastle University, Newcastle Upon Tyne, UK
| | - R J Boys
- School of Mathematics, Statistics & Physics, Newcastle University, Newcastle Upon Tyne, UK
| | - C S Gillespie
- School of Mathematics, Statistics & Physics, Newcastle University, Newcastle Upon Tyne, UK
| | - C J Proctor
- Institute of Cellular Medicine, Newcastle University, Newcastle Upon Tyne, UK
| | - A Golightly
- School of Mathematics, Statistics & Physics, Newcastle University, Newcastle Upon Tyne, UK
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Jackson SE, Vernon I, Liu J, Lindsey K. Understanding hormonal crosstalk in Arabidopsis root development via emulation and history matching. Stat Appl Genet Mol Biol 2020; 19:sagmb-2018-0053. [PMID: 32649296 DOI: 10.1515/sagmb-2018-0053] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2018] [Accepted: 05/12/2020] [Indexed: 11/15/2022]
Abstract
A major challenge in plant developmental biology is to understand how plant growth is coordinated by interacting hormones and genes. To meet this challenge, it is important to not only use experimental data, but also formulate a mathematical model. For the mathematical model to best describe the true biological system, it is necessary to understand the parameter space of the model, along with the links between the model, the parameter space and experimental observations. We develop sequential history matching methodology, using Bayesian emulation, to gain substantial insight into biological model parameter spaces. This is achieved by finding sets of acceptable parameters in accordance with successive sets of physical observations. These methods are then applied to a complex hormonal crosstalk model for Arabidopsis root growth. In this application, we demonstrate how an initial set of 22 observed trends reduce the volume of the set of acceptable inputs to a proportion of 6.1 × 10-7 of the original space. Additional sets of biologically relevant experimental data, each of size 5, reduce the size of this space by a further three and two orders of magnitude respectively. Hence, we provide insight into the constraints placed upon the model structure by, and the biological consequences of, measuring subsets of observations.
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Affiliation(s)
- Samuel E Jackson
- Southampton Statistical Sciences Research Institute, University of Southampton, Southampton, UK
| | - Ian Vernon
- Department of Mathematical Sciences, Durham University, Durham, UK
| | - Junli Liu
- School of Biological and Biomedical Sciences, Durham University, Durham, UK
| | - Keith Lindsey
- School of Biological and Biomedical Sciences, Durham University, Durham, UK
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Longobardi S, Lewalle A, Coveney S, Sjaastad I, Espe EKS, Louch WE, Musante CJ, Sher A, Niederer SA. Predicting left ventricular contractile function via Gaussian process emulation in aortic-banded rats. Philos Trans A Math Phys Eng Sci 2020; 378:20190334. [PMID: 32448071 PMCID: PMC7287330 DOI: 10.1098/rsta.2019.0334] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/08/2023]
Abstract
Cardiac contraction is the result of integrated cellular, tissue and organ function. Biophysical in silico cardiac models offer a systematic approach for studying these multi-scale interactions. The computational cost of such models is high, due to their multi-parametric and nonlinear nature. This has so far made it difficult to perform model fitting and prevented global sensitivity analysis (GSA) studies. We propose a machine learning approach based on Gaussian process emulation of model simulations using probabilistic surrogate models, which enables model parameter inference via a Bayesian history matching (HM) technique and GSA on whole-organ mechanics. This framework is applied to model healthy and aortic-banded hypertensive rats, a commonly used animal model of heart failure disease. The obtained probabilistic surrogate models accurately predicted the left ventricular pump function (R2 = 0.92 for ejection fraction). The HM technique allowed us to fit both the control and diseased virtual bi-ventricular rat heart models to magnetic resonance imaging and literature data, with model outputs from the constrained parameter space falling within 2 SD of the respective experimental values. The GSA identified Troponin C and cross-bridge kinetics as key parameters in determining both systolic and diastolic ventricular function. This article is part of the theme issue 'Uncertainty quantification in cardiac and cardiovascular modelling and simulation'.
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Affiliation(s)
- S Longobardi
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - A Lewalle
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
| | - S Coveney
- Insigneo Institute for in-silico Medicine and Department of Computer Science, University of Sheffield, Sheffield, UK
| | - I Sjaastad
- Institute for Experimental Medical Research and KG Jebsen Center for Cardiac Research, University of Oslo, Oslo, Norway
| | - E K S Espe
- Institute for Experimental Medical Research and KG Jebsen Center for Cardiac Research, University of Oslo, Oslo, Norway
| | - W E Louch
- Institute for Experimental Medical Research and KG Jebsen Center for Cardiac Research, University of Oslo, Oslo, Norway
| | - C J Musante
- Pfizer Worldwide Research, Development and Medical, Cambridge, MA, USA
| | - A Sher
- Pfizer Worldwide Research, Development and Medical, Cambridge, MA, USA
| | - S A Niederer
- School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK
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Li T, Cheng Z, Zhang L. Developing a Novel Parameter Estimation Method for Agent-Based Model in Immune System Simulation under the Framework of History Matching: A Case Study on Influenza A Virus Infection. Int J Mol Sci 2017; 18:E2592. [PMID: 29194393 DOI: 10.3390/ijms18122592] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [What about the content of this article? (0)] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/19/2017] [Revised: 11/23/2017] [Accepted: 11/26/2017] [Indexed: 11/16/2022] Open
Abstract
Since they can provide a natural and flexible description of nonlinear dynamic behavior of complex system, Agent-based models (ABM) have been commonly used for immune system simulation. However, it is crucial for ABM to obtain an appropriate estimation for the key parameters of the model by incorporating experimental data. In this paper, a systematic procedure for immune system simulation by integrating the ABM and regression method under the framework of history matching is developed. A novel parameter estimation method by incorporating the experiment data for the simulator ABM during the procedure is proposed. First, we employ ABM as simulator to simulate the immune system. Then, the dimension-reduced type generalized additive model (GAM) is employed to train a statistical regression model by using the input and output data of ABM and play a role as an emulator during history matching. Next, we reduce the input space of parameters by introducing an implausible measure to discard the implausible input values. At last, the estimation of model parameters is obtained using the particle swarm optimization algorithm (PSO) by fitting the experiment data among the non-implausible input values. The real Influeza A Virus (IAV) data set is employed to demonstrate the performance of our proposed method, and the results show that the proposed method not only has good fitting and predicting accuracy, but it also owns favorable computational efficiency.
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Salter JM, Williamson D. A comparison of statistical emulation methodologies for multi-wave calibration of environmental models. Environmetrics 2016; 27:507-523. [PMID: 28042255 PMCID: PMC5157755 DOI: 10.1002/env.2405] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2016] [Revised: 07/01/2016] [Accepted: 07/06/2016] [Indexed: 05/08/2023]
Abstract
Expensive computer codes, particularly those used for simulating environmental or geological processes, such as climate models, require calibration (sometimes called tuning). When calibrating expensive simulators using uncertainty quantification methods, it is usually necessary to use a statistical model called an emulator in place of the computer code when running the calibration algorithm. Though emulators based on Gaussian processes are typically many orders of magnitude faster to evaluate than the simulator they mimic, many applications have sought to speed up the computations by using regression-only emulators within the calculations instead, arguing that the extra sophistication brought using the Gaussian process is not worth the extra computational power. This was the case for the analysis that produced the UK climate projections in 2009. In this paper, we compare the effectiveness of both emulation approaches upon a multi-wave calibration framework that is becoming popular in the climate modeling community called "history matching." We find that Gaussian processes offer significant benefits to the reduction of parametric uncertainty over regression-only approaches. We find that in a multi-wave experiment, a combination of regression-only emulators initially, followed by Gaussian process emulators for refocussing experiments can be nearly as effective as using Gaussian processes throughout for a fraction of the computational cost. We also discover a number of design and emulator-dependent features of the multi-wave history matching approach that can cause apparent, yet premature, convergence of our estimates of parametric uncertainty. We compare these approaches to calibration in idealized examples and apply it to a well-known geological reservoir model.
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Affiliation(s)
- James M. Salter
- College of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterU.K.
| | - Daniel Williamson
- College of Engineering, Mathematics and Physical SciencesUniversity of ExeterExeterU.K.
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