Bayesian Inversion of Concentration Data for an Unknown Number of Contaminant Sources


  1. Yee, E.
Corporate Authors
Defence R&D Canada - Suffield, Ralston ALTA (CAN)
In this paper, we address the inverse problem of source reconstruction for the difficult case of multiple sources when the number of sources is unknown a priori. The problem is solved using a Bayesian probabilistic inferential framework in which Bayesian probability theory is used to derive the posterior probability density function for the number of sources and for the parameters (e.g., location, emission rate, release duration) that characterize each source. A mapping (or, source–receptor relationship) that relates a multiple source distribution to the concentration data measured by the array of sensors is formulated based on a forward-time Lagrangian stochastic model. A computationally efficient methodology for determination of the likelihood function for the problem, based on an adjoint representation of the source–receptor relationship and realized in terms of a backward-time Lagrangian stochastic model, is described. An efficient computational algorithm based on a reversible jump Markov chain Monte Carlo (MCMC) method is formulated and implemented to draw samples from the posterior density function of the source parameters. This methodology allows the MCMC method to jump between the hypothesis spaces corresponding to different numbers of sources in the source distribution and, thereby, allows a sample from the full joint posterior distribution of the number of sources and source parameters to be obtained. The proposed methodology for source reconstruction is tested

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Source reconstruction;Multiple sources;Bayesian inference;Markov chain Monte Carlo;Lagrangian stochastic models;adjoint systems
Report Number
DRDC-SUFFIELD-TR-2007-085 — Technical Report
Date of publication
01 Jun 2007
Number of Pages

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