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Workshop: Machine Learning for Engineering Modeling, Simulation and Design

Multilevel Delayed Acceptance MCMC with an Adaptive Error Model in PyMC3

Mikkel Lykkegaard · Greg Mingas · Robert Scheichl · Colin Fox · Tim Dodwell


Uncertainty Quantification using Markov Chain Monte Carlo (MCMC) can be prohibitively expensive for target probability densities with expensive likelihood functions, for instance when 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 with the open-source probabilistic programming package PyMC3 and is available in the latest development version. In this paper, we present the algorithm along with an illustrative example.

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