Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

Mikkel B. Lykkegaard; Grigorios Mingas; Robert Scheichl; Colin Fox; Tim J. Dodwell

Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

Mikkel B. Lykkegaard, Grigorios Mingas, Robert Scheichl, Colin Fox, Tim J. Dodwell

Research output: Contribution to conference › Paper › peer-review

44 Downloads (Pure)

Abstract

Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, the algorithm is presented along with an illustrative example.

Original language	English
Number of pages	8
Publication status	Published - 10 Dec 2020
Event	Machine Learning for Engineering Modeling, Simulation, and Design Workshop at Neural Information Processing Systems 2020 - Duration: 10 Dec 2020 → 10 Dec 2020 https://ml4eng.github.io/

Workshop

Workshop	Machine Learning for Engineering Modeling, Simulation, and Design Workshop at Neural Information Processing Systems 2020
Period	10/12/20 → 10/12/20
Internet address	https://ml4eng.github.io/

Bibliographical note

8 pages, 4 figures, accepted for Machine Learning for Engineering Modeling, Simulation, and Design Workshop at Neural Information Processing Systems 2020

Keywords

stat.CO

Access to Document

2012.05668v1.pdfAccepted author manuscript, 1.71 MB

https://ml4eng.github.io/

Re-shaping the Test Pyramid
Butler, R. (PI), Anaya-Izquierdo, K. (CoI), Rhead, A. (CoI) & Scheichl, R. (CoI)
Engineering and Physical Sciences Research Council
1/08/19 → 31/08/25
Project: Research council
Multiscale Modelling of Aerospace Composites
Butler, R. (PI) & Scheichl, R. (CoI)
Engineering and Physical Sciences Research Council
6/01/14 → 5/02/18
Project: Research council

Cite this

@conference{5b65710ae66b42a7bf91c656896066f6,

title = "Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3",

abstract = "Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, the algorithm is presented along with an illustrative example. ",

keywords = "stat.CO",

author = "Lykkegaard, \{Mikkel B.\} and Grigorios Mingas and Robert Scheichl and Colin Fox and Dodwell, \{Tim J.\}",

note = "8 pages, 4 figures, accepted for Machine Learning for Engineering Modeling, Simulation, and Design Workshop at Neural Information Processing Systems 2020; Machine Learning for Engineering Modeling, Simulation, and Design<br/>Workshop at Neural Information Processing Systems 2020 ; Conference date: 10-12-2020 Through 10-12-2020",

year = "2020",

month = dec,

day = "10",

language = "English",

url = "https://ml4eng.github.io/",

}

TY - CONF

T1 - Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

AU - Lykkegaard, Mikkel B.

AU - Mingas, Grigorios

AU - Scheichl, Robert

AU - Fox, Colin

AU - Dodwell, Tim J.

N1 - 8 pages, 4 figures, accepted for Machine Learning for Engineering Modeling, Simulation, and Design Workshop at Neural Information Processing Systems 2020

PY - 2020/12/10

Y1 - 2020/12/10

N2 - Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, the algorithm is presented along with an illustrative example.

AB - Uncertainty Quantification through Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when the evaluation it involves solving a Partial Differential Equation (PDE), as is the case in a wide range of engineering applications. Multilevel Delayed Acceptance (MLDA) with an Adaptive Error Model (AEM) is a novel approach, which alleviates this problem by exploiting a hierarchy of models, with increasing complexity and cost, and correcting the inexpensive models on-the-fly. The method has been integrated within the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, the algorithm is presented along with an illustrative example.

KW - stat.CO

M3 - Paper

T2 - Machine Learning for Engineering Modeling, Simulation, and Design<br/>Workshop at Neural Information Processing Systems 2020

Y2 - 10 December 2020 through 10 December 2020

ER -

Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

Abstract

Workshop

Bibliographical note

Keywords

Access to Document

Fingerprint

Projects

Re-shaping the Test Pyramid

Multiscale Modelling of Aerospace Composites

Cite this