A Variational Bayesian Estimation Scheme For Parametric Point-Like Pollution Source of Groundwater Layers

Abstract

This paper considers the identification of point-like source of groundwater pollution. The ill-posed character of this problem has recently led to the introduction of a regularization approach that combines source parametrization, and penalization of undesirable solutions based on prior information about the source parameters, thereby ending up with a parametric Bayesian estimation framework. In this framework, a stochastic-type Markov Chain Monte Carlo (MCMC) method has been introduced as an approximate computation tool of the posterior mean estimate of both source parameters and variance of the (assumed homogeneous) observation noise. Being in the more general case of inhomogeneous noise, our main goal is to propose a deterministic-type computation method based on the variational Bayesian approach. Simulation results suggest that the proposed scheme can provide comparable estimation accuracy to MCMC while requiring less computational time.