On the application of improved symplectic integrators in Hamiltonian Monte Carlo |
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Authors: | Janne Mannseth Tore S. Kleppe Hans J. Skaug |
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Affiliation: | 1. Department of Mathematics, University of Bergen, Allégaten, Bergen, Norway;2. Department of Mathematics and Natural Sciences, University of Stavanger, Stavanger, Norway |
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Abstract: | We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Integration schemes from Blanes et al., and a new scheme are considered as candidates to the commonly used leapfrog method. All integration schemes are tested within the framework of the No-U-Turn sampler (NUTS), both for a logistic regression model and a student t-model. The results show that the leapfrog method is inferior to all the new methods both in terms of asymptotic expected acceptance probability for a model problem and the efficient sample size per computing time for the realistic models. |
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Keywords: | Efficient Sample Size Hamiltonian Monte Carlo Integration scheme Leapfrog method No-U-Turn Sampler Parameterized numerical scheme |
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