Theory for Reconstruction of an Unknown Number of Contaminant Sources using Probabilistic Inference


  1. Yee, E.
Corporate Authors
Defence R&D Canada - Suffield, Ralston ALTA (CAN)
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 probalistic 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 time and duration) that characterize each source. A mapping (source-receptor relationship) that relates a multiple source distribution to the concentration measurements made by an array of detectors 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 a backward-time Lagrangian stochastic model, is described. An efficient computational algorithm based on a parallel tempered Metropolis-coupled reversible-jump Markov chain Monte Carlo (MCMC) method is formulated and implemented to draw samples from the posterior probability density function of the source parameters. This methodology allows the MCMC method to initiate jumps 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 the parameters for each source to be obtained. The proposed methodology for source reconstruction is tested using synthetic concentrat
Adjoint systems;Bayesian inference;Lagrangian stochastic models;Markov chain Monte Carlo;Source reconstruction
Report Number
DRDC-SUFFIELD-SL-2008-056 — Scientific Literature
Date of publication
20 Mar 2008
Number of Pages
Hardcopy;Document Image stored on Optical Disk

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