Methods and Algorithms for Scientific Computing

A Nonparametric Ensemble Transform Method for Bayesian Inference

Abstract

Many applications, such as intermittent data assimilation, lead to a recursive application of Bayesian inference within a Monte Carlo context. Popular data assimilation algorithms include sequential Monte Carlo methods and ensemble Kalman filters (EnKFs). These methods differ in the way Bayesian inference is implemented. Sequential Monte Carlo methods rely on importance sampling combined with a resampling step, while EnKFs utilize a linear transformation of Monte Carlo samples based on the classic Kalman filter. While EnKFs have proven to be quite robust even for small ensemble sizes, they are not consistent since their derivation relies on a linear regression ansatz. In this paper, we propose another transform method, which does not rely on any a priori assumptions on the underlying prior and posterior distributions. The new method is based on solving an optimal transportation problem for discrete random variables.

Keywords

  1. Bayesian inference
  2. Monte Carlo method
  3. sequential data assimilation
  4. linear programming
  5. resampling

MSC codes

  1. 65C05
  2. 62M20
  3. 93E11
  4. 62F15
  5. 86A22

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Information & Authors

Information

Published In

cover image SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Pages: A2013 - A2024
ISSN (online): 1095-7197

History

Submitted: 25 January 2013
Accepted: 13 May 2013
Published online: 6 August 2013

Keywords

  1. Bayesian inference
  2. Monte Carlo method
  3. sequential data assimilation
  4. linear programming
  5. resampling

MSC codes

  1. 65C05
  2. 62M20
  3. 93E11
  4. 62F15
  5. 86A22

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