14:00
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 talk I will talk about the problems with the Multilevel Markov Chain Monte Carlo (Dodwell et al. 2015). In so we will prove detailed balance for Adaptive Multilevel Delayed Acceptance, as well as showing that multilevel variance reduction can be achieved without bias, not possible in the original MLMCMC framework.
I will talk about our implementation in the latest version of pymc3, and demonstrate how for classical inverse problem benchmarks the AMLDA sampler offers huge computational savings (> factor of 100 fold speed up).
Finally I will talk heuristically about new / future research, in which we seek to develop parallel strategies for this inherently sequential sampler, as well as point to interesting applied application areas in which the method is proving particular effective.
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This talk will be in person.