Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers
Abstract
Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved implicit sampling schemes at a relatively small additional cost. Here, computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.
- Authors:
-
- Courant Institute, New York, NY (United States)
- Univ. of Arizona, Tucson, AZ (United States)
- Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
- OSTI Identifier:
- 1418471
- Grant/Contract Number:
- AC02-05CH11231; DMS-1217065; DMS-1418775; DMS-1419044
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Communications on Pure and Applied Mathematics
- Additional Journal Information:
- Journal Volume: 69; Journal Issue: 10; Journal ID: ISSN 0010-3640
- Publisher:
- Wiley
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING
Citation Formats
Goodman, Jonathan, Lin, Kevin K., and Morzfeld, Matthias. Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers. United States: N. p., 2015.
Web. doi:10.1002/cpa.21592.
Goodman, Jonathan, Lin, Kevin K., & Morzfeld, Matthias. Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers. United States. https://doi.org/10.1002/cpa.21592
Goodman, Jonathan, Lin, Kevin K., and Morzfeld, Matthias. Mon .
"Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers". United States. https://doi.org/10.1002/cpa.21592. https://www.osti.gov/servlets/purl/1418471.
@article{osti_1418471,
title = {Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers},
author = {Goodman, Jonathan and Lin, Kevin K. and Morzfeld, Matthias},
abstractNote = {Implicit samplers are algorithms for producing independent, weighted samples from multivariate probability distributions. These are often applied in Bayesian data assimilation algorithms. We use Laplace asymptotic expansions to analyze two implicit samplers in the small noise regime. Our analysis suggests a symmetrization of the algorithms that leads to improved implicit sampling schemes at a relatively small additional cost. Here, computational experiments confirm the theory and show that symmetrization is effective for small noise sampling problems.},
doi = {10.1002/cpa.21592},
journal = {Communications on Pure and Applied Mathematics},
number = 10,
volume = 69,
place = {United States},
year = {Mon Jul 06 00:00:00 EDT 2015},
month = {Mon Jul 06 00:00:00 EDT 2015}
}
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- Marzouk, Youssef; Moselhy, Tarek; Parno, Matthew
- Handbook of Uncertainty Quantification
Sampling via Measure Transport: An Introduction
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