Minimization for conditional simulation: Relationship to optimal transport

In this paper, we consider the problem of generating independent samples from a conditional distribution when independent samples from the prior distribution are available. Although there are exact methods for sampling from the posterior (e.g. Markov chain Monte Carlo or acceptance/rejection), these...

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Vydané v:Journal of computational physics Ročník 265; s. 1 - 15
Hlavný autor: Oliver, Dean S.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Elsevier Inc 15.05.2014
Predmet:
Algorithms
Computer simulation
Conditional simulation
Cost function
Ensemble Kalman filter
Ensemble smoother
Iterative EnKF
Mapping
Mathematical analysis
Mathematical models
Minimization
Optimal transport
Optimization
Quasi-linear
Randomized maximum likelihood
Ensemble smoother
Ensemble Kalman filter
Quasi-linear
Randomized maximum likelihood
Conditional simulation
Optimal transport
Iterative EnKF
ISSN:0021-9991, 1090-2716
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Shrnutí:In this paper, we consider the problem of generating independent samples from a conditional distribution when independent samples from the prior distribution are available. Although there are exact methods for sampling from the posterior (e.g. Markov chain Monte Carlo or acceptance/rejection), these methods tend to be computationally demanding when evaluation of the likelihood function is expensive, as it is for most geoscience applications. As an alternative, in this paper we discuss deterministic mappings of variables distributed according to the prior to variables distributed according to the posterior. Although any deterministic mappings might be equally useful, we will focus our discussion on a class of algorithms that obtain implicit mappings by minimization of a cost function that includes measures of data mismatch and model variable mismatch. Algorithms of this type include quasi-linear estimation, randomized maximum likelihood, perturbed observation ensemble Kalman filter, and ensemble of perturbed analyses (4D-Var). When the prior pdf is Gaussian and the observation operators are linear, we show that these minimization-based simulation methods solve an optimal transport problem with a nonstandard cost function. When the observation operators are nonlinear, however, the mapping of variables from the prior to the posterior obtained from those methods is only approximate. Errors arise from neglect of the Jacobian determinant of the transformation and from the possibility of discontinuous mappings.
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content type line 23
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2014.01.048