Randomize-Then-Optimize: A Method for Sampling from Posterior Distributions in Nonlinear Inverse Problems
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Bardsley-2014-RANDOMIZE-THEN-OPTIM.pdf
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Author(s)
Bardsley, Johnathan M.
Solonen, Antti
Haario, Heikki
Laine, Marko
Date Issued
August 2014
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial and Applied Mathematics
Citation
Bardsley, Johnathan M., Antti Solonen, Heikki Haario, and Marko Laine. “Randomize-Then-Optimize: A Method for Sampling from Posterior Distributions in Nonlinear Inverse Problems.” SIAM Journal on Scientific Computing 36, no. 4 (January 2014): A1895–A1910. © 2014 Society for Industrial and Applied Mathematics
Version
Final published version
Abstract
High-dimensional inverse problems present a challenge for Markov chain Monte Carlo (MCMC)-type sampling schemes. Typically, they rely on finding an efficient proposal distribution, which can be difficult for large-scale problems, even with adaptive approaches. Moreover, the autocorrelations of the samples typically increase with dimension, which leads to the need for long sample chains. We present an alternative method for sampling from posterior distributions in nonlinear inverse problems, when the measurement error and prior are both Gaussian. The approach computes a candidate sample by solving a stochastic optimization problem. In the linear case, these samples are directly from the posterior density, but this is not so in the nonlinear case. We derive the form of the sample density in the nonlinear case, and then show how to use it within both a Metropolis--Hastings and importance sampling framework to obtain samples from the posterior distribution of the parameters. We demonstrate, with various small- and medium-scale problems, that randomize-then-optimize can be efficient compared to standard adaptive MCMC algorithms.
MIT Department
Massachusetts Institute of Technology. Department of Aeronautics and Astronautics
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1137/140964023
