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Title: Parameter estimation by implicit sampling

Abstract

© 2015 Mathematical Sciences Publishers. Implicit sampling is a weighted sampling method that is used in data assimilation to sequentially update state estimates of a stochastic model based on noisy and incomplete data. Here we apply implicit sampling to sample the posterior probability density of parameter estimation problems. The posterior probability combines prior information about the parameter with information from a numerical model, e.g., a partial differential equation (PDE), and noisy data. The result of our computations are parameters that lead to simulations that are compatible with the data. We demonstrate the usefulness of our implicit sampling algorithm with an example from subsurface flow. For an efficient implementation, we make use of multiple grids, BFGS optimization coupled to adjoint equations, and Karhunen-Loève expansions for dimensional reduction. Several difficulties of Markov chain Monte Carlo methods, e.g., estimation of burn-in times or correlations among the samples, are avoided because the implicit samples are independent.

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1524002
DOE Contract Number:  
AC02-05CH11231
Resource Type:
Journal Article
Journal Name:
Communications in Applied Mathematics and Computational Science
Additional Journal Information:
Journal Volume: 10; Journal Issue: 2; Journal ID: ISSN 1559-3940
Country of Publication:
United States
Language:
English

Citation Formats

Morzfeld, Matthias, Tu, Xuemin, Wilkening, Jon, and Chorin, Alexandre. Parameter estimation by implicit sampling. United States: N. p., 2015. Web. doi:10.2140/camcos.2015.10.205.
Morzfeld, Matthias, Tu, Xuemin, Wilkening, Jon, & Chorin, Alexandre. Parameter estimation by implicit sampling. United States. doi:10.2140/camcos.2015.10.205.
Morzfeld, Matthias, Tu, Xuemin, Wilkening, Jon, and Chorin, Alexandre. Thu . "Parameter estimation by implicit sampling". United States. doi:10.2140/camcos.2015.10.205.
@article{osti_1524002,
title = {Parameter estimation by implicit sampling},
author = {Morzfeld, Matthias and Tu, Xuemin and Wilkening, Jon and Chorin, Alexandre},
abstractNote = {© 2015 Mathematical Sciences Publishers. Implicit sampling is a weighted sampling method that is used in data assimilation to sequentially update state estimates of a stochastic model based on noisy and incomplete data. Here we apply implicit sampling to sample the posterior probability density of parameter estimation problems. The posterior probability combines prior information about the parameter with information from a numerical model, e.g., a partial differential equation (PDE), and noisy data. The result of our computations are parameters that lead to simulations that are compatible with the data. We demonstrate the usefulness of our implicit sampling algorithm with an example from subsurface flow. For an efficient implementation, we make use of multiple grids, BFGS optimization coupled to adjoint equations, and Karhunen-Loève expansions for dimensional reduction. Several difficulties of Markov chain Monte Carlo methods, e.g., estimation of burn-in times or correlations among the samples, are avoided because the implicit samples are independent.},
doi = {10.2140/camcos.2015.10.205},
journal = {Communications in Applied Mathematics and Computational Science},
issn = {1559-3940},
number = 2,
volume = 10,
place = {United States},
year = {2015},
month = {1}
}

Works referenced in this record:

Ensemble samplers with affine invariance
journal, January 2010

  • Goodman, Jonathan; Weare, Jonathan
  • Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 1
  • DOI: 10.2140/camcos.2010.5.65

Implicit particle filtering for models with partial noise, and an application to geomagnetic data assimilation
journal, January 2012


Small-Noise Analysis and Symmetrization of Implicit Monte Carlo Samplers
journal, July 2015

  • Goodman, Jonathan; Lin, Kevin K.; Morzfeld, Matthias
  • Communications on Pure and Applied Mathematics, Vol. 69, Issue 10
  • DOI: 10.1002/cpa.21592

Bayesian inference with optimal maps
journal, October 2012

  • El Moselhy, Tarek A.; Marzouk, Youssef M.
  • Journal of Computational Physics, Vol. 231, Issue 23
  • DOI: 10.1016/j.jcp.2012.07.022

Recent progress on reservoir history matching: a review
journal, July 2010


A Preconditioner for Substructuring Based on Constrained Energy Minimization
journal, January 2003


Conditions for successful data assimilation: CONDITIONS FOR DATA ASSIMILATION
journal, October 2013

  • Chorin, Alexandre J.; Morzfeld, Matthias
  • Journal of Geophysical Research: Atmospheres, Vol. 118, Issue 20
  • DOI: 10.1002/2013JD019838

A relaxation method for solving elliptic difference equations
journal, January 1962


A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems Part I: The Linearized Case, with Application to Global Seismic Inversion
journal, January 2013

  • Bui-Thanh, Tan; Ghattas, Omar; Martin, James
  • SIAM Journal on Scientific Computing, Vol. 35, Issue 6
  • DOI: 10.1137/12089586X

Data Assimilation in the Low Noise Regime with Application to the Kuroshio
journal, June 2013


A random map implementation of implicit filters
journal, February 2012

  • Morzfeld, Matthias; Tu, Xuemin; Atkins, Ethan
  • Journal of Computational Physics, Vol. 231, Issue 4
  • DOI: 10.1016/j.jcp.2011.11.022

A Computational Framework for Infinite-Dimensional Bayesian Inverse Problems, Part II: Stochastic Newton MCMC with Application to Ice Sheet Flow Inverse Problems
journal, January 2014

  • Petra, Noemi; Martin, James; Stadler, Georg
  • SIAM Journal on Scientific Computing, Vol. 36, Issue 4
  • DOI: 10.1137/130934805

A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion
journal, January 2012

  • Martin, James; Wilcox, Lucas C.; Burstedde, Carsten
  • SIAM Journal on Scientific Computing, Vol. 34, Issue 3
  • DOI: 10.1137/110845598

Evaluation of Gaussian approximations for data assimilation in reservoir models
journal, July 2013

  • Iglesias, Marco A.; Law, Kody J. H.; Stuart, Andrew M.
  • Computational Geosciences, Vol. 17, Issue 5
  • DOI: 10.1007/s10596-013-9359-x

Minimization for conditional simulation: Relationship to optimal transport
journal, May 2014


Blind Deconvolution via Sequential Imputations
journal, June 1995


Implicit sampling for particle filters
journal, September 2009

  • Chorin, A. J.; Tu, X.
  • Proceedings of the National Academy of Sciences, Vol. 106, Issue 41
  • DOI: 10.1073/pnas.0909196106

A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian tracking
journal, January 2002

  • Arulampalam, M. S.; Maskell, S.; Gordon, N.
  • IEEE Transactions on Signal Processing, Vol. 50, Issue 2
  • DOI: 10.1109/78.978374

Multigrid Monte Carlo method. Conceptual foundations
journal, September 1989


Implicit Estimation of Ecological Model Parameters
journal, January 2013

  • Weir, Brad; Miller, Robert N.; Spitz, Yvette H.
  • Bulletin of Mathematical Biology, Vol. 75, Issue 2
  • DOI: 10.1007/s11538-012-9801-6

Implicit Particle Methods and Their Connection with Variational Data Assimilation
journal, June 2013

  • Atkins, Ethan; Morzfeld, Matthias; Chorin, Alexandre J.
  • Monthly Weather Review, Vol. 141, Issue 6
  • DOI: 10.1175/MWR-D-12-00145.1

Implicit Sampling, with Application to Data Assimilation
journal, January 2013

  • Chorin, Alexandre J.; Morzfeld, Matthias; Tu, Xuemin
  • Chinese Annals of Mathematics, Series B, Vol. 34, Issue 1
  • DOI: 10.1007/s11401-012-0757-5

Uncertainty Quantification and Weak Approximation of an Elliptic Inverse Problem
journal, January 2011

  • Dashti, M.; Stuart, A. M.
  • SIAM Journal on Numerical Analysis, Vol. 49, Issue 6
  • DOI: 10.1137/100814664

Inverse problems: A Bayesian perspective
journal, May 2010


Preconditioning Markov Chain Monte Carlo Simulations Using Coarse-Scale Models
journal, January 2006

  • Efendiev, Y.; Hou, T.; Luo, W.
  • SIAM Journal on Scientific Computing, Vol. 28, Issue 2
  • DOI: 10.1137/050628568

Obstacles to High-Dimensional Particle Filtering
journal, December 2008

  • Snyder, Chris; Bengtsson, Thomas; Bickel, Peter
  • Monthly Weather Review, Vol. 136, Issue 12
  • DOI: 10.1175/2008MWR2529.1

Implicit particle filters for data assimilation
journal, January 2010

  • Chorin, Alexandre; Morzfeld, Matthias; Tu, Xuemin
  • Communications in Applied Mathematics and Computational Science, Vol. 5, Issue 2
  • DOI: 10.2140/camcos.2010.5.221