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arXiv · 2012.05668

Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

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

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Mikkel B. Lykkegaard, Grigorios Mingas, Robert Scheichl, Colin Fox, Tim J. Dodwell. 2020-12-10. Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3. https://arxiv.org/abs/2012.05668

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