Multilevel Delayed Acceptance MCMC
| Autor: | M. B. Lykkegaard, T. J. Dodwell, C. Fox, G. Mingas, R. Scheichl |
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| Jazyk: | angličtina |
| Rok vydání: | 2022 |
| Předmět: |
Statistics and Probability
Methodology (stat.ME) FOS: Computer and information sciences Applied Mathematics Modeling and Simulation 62F15 62M05 65C05 65C40 Discrete Mathematics and Combinatorics Statistics Probability and Uncertainty Statistics - Computation Computation (stat.CO) Statistics - Methodology |
| Popis: | We develop a novel Markov chain Monte Carlo (MCMC) method that exploits a hierarchy of models of increasing complexity to efficiently generate samples from an unnormalized target distribution. Broadly, the method rewrites the Multilevel MCMC approach of Dodwell et al. (2015) in terms of the Delayed Acceptance (DA) MCMC of Christen & Fox (2005). In particular, DA is extended to use a hierarchy of models of arbitrary depth, and allow subchains of arbitrary length. We show that the algorithm satisfies detailed balance, hence is ergodic for the target distribution. Furthermore, multilevel variance reduction is derived that exploits the multiple levels and subchains, and an adaptive multilevel correction to coarse-level biases is developed. Three numerical examples of Bayesian inverse problems are presented that demonstrate the advantages of these novel methods. The software and examples are available in PyMC3. 29 pages, 12 figures |
| Databáze: | OpenAIRE |
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