Monte Carlo on manifolds: sampling densities and integrating functions
| Autor: | Emilio Zappa, Miranda Holmes-Cerfon, Jonathan Goodman |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Surface (mathematics)
FOS: Computer and information sciences General Mathematics Monte Carlo method FOS: Physical sciences 010103 numerical & computational mathematics 01 natural sciences Statistics - Computation symbols.namesake 0103 physical sciences Tangent space FOS: Mathematics Applied mathematics Mathematics - Numerical Analysis 0101 mathematics 010306 general physics Computation (stat.CO) Condensed Matter - Statistical Mechanics Mathematics Statistical Mechanics (cond-mat.stat-mech) Euclidean space Applied Mathematics Orthographic projection Markov chain Monte Carlo Numerical Analysis (math.NA) Manifold symbols Probability distribution |
| Popis: | We describe and analyze some Monte Carlo methods for manifolds in Euclidean space defined by equality and inequality constraints. First, we give an MCMC sampler for probability distributions defined by un-normalized densities on such manifolds. The sampler uses a specific orthogonal projection to the surface that requires only information about the tangent space to the manifold, obtainable from first derivatives of the constraint functions, hence avoiding the need for curvature information or second derivatives. Second, we use the sampler to develop a multi-stage algorithm to compute integrals over such manifolds. We provide single-run error estimates that avoid the need for multiple independent runs. Computational experiments on various test problems show that the algorithms and error estimates work in practice. The method is applied to compute the entropies of different sticky hard sphere systems. These predict the temperature or interaction energy at which loops of hard sticky spheres become preferable to chains. New version. 32 pages, 11 figures |
| Databáze: | OpenAIRE |
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