Inverse Problems
Source Determination Through Bayesian Inference
A. Keats, M.T. Cheng, E. Yee and F.S. Lien, "Bayesian Treatment of a Chemical Mass Balance Receptor Model with Multiplicative Error Structure", Atmospheric Environment (In press, accepted in 2008)
A. Keats, E. Yee and F.S. Lien, "Reply to the Comments on: Bayesian Inference for Source Determination with Application to a Complex Urban Environment", Atmospheric Environment, 41, 2007, 5547 - 5551.
A. Keats, E. Yee and F.S. Lien, "Efficiently Characterizing the Origin and Decay Rate of a Nonconservative Scalar Using Probability Theory", Ecological Modeling, 205, 2007, 437 - 452.
A. Keats, E. Yee and F.S. Lien , "Bayesian Inference for Source Determination with Applications to a Complex Urban Environment", Atmospheric Environment, 47, 2007, 465 - 479.
E. Yee, F.S. Lien, A. Keats and R. D'Armours, "Bayesian Inversion of Concentration Data: Source Reconstruction in the Adjoint Representation of Atmospheric Diffusion", Special Issue of Journal of Wind Engineering & Industrial Aerodynamics, 96, 2008, 1805 - 1816.
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Determining the source is an ill-posed problem
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The problem can only be solved in a probabilistic sense - there is no unique solution
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Bayesian inference provides a rational framework for the formulation of a solution
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The final solution arrives as a multi-dimensional PDF of the source parameters, conditional upon the measured concentration data.
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The present approach involves 2 major techniques:
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Solving the adjoint advection-diffusion equation to provide efficiency
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Using Markov Chain Monte Carlo (MCMC) to provide a way of rapidly sample the PDF
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Marginal Parameter Distributions and Summary Statistics
