Efficient exact PDE solutions for MCMC

Colin Fox; Mathias Palm; Geoff K. Nicholls

doi:10.1117/12.351327

25 June 1999 Efficient exact PDE solutions for MCMC

Colin Fox, Mathias Palm, Geoff K. Nicholls

Proceedings Volume 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems; (1999) https://doi.org/10.1117/12.351327
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Non-invasive imaging based on wave scattering remain sa difficult problem in those cases where the forward map can only be adequately simulated by solving the appropriate partial-differential equation. We develop a method for solving linear PDEs which is efficient and exact, trading off computation time against storage requirements. The method is based on using the present solution within the Woodbury formula for updating solutions away from changes in the trial image, or state. Hence the method merges well with typical Metropolis-Hastings algorithms using localized update. The scaling of the method as a function of image size and measurement set size is given. We conclude that this method is considerably more efficient than earlier algorithms that we have used to demonstrate sampling for inverse problems in this class.

Citation Download Citation

Colin Fox, Mathias Palm, and Geoff K. Nicholls "Efficient exact PDE solutions for MCMC", Proc. SPIE 3816, Mathematical Modeling, Bayesian Estimation, and Inverse Problems, (25 June 1999); https://doi.org/10.1117/12.351327

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