Bayesian Inference and Markov Chain Monte Carlo Sampling to Reconstruct a Contaminant Source on a Continental Scale

Abstract

A methodology combining Bayesian inference with Markov chain Monte Carlo (MCMC) sampling is applied to a real accidental radioactive release that occurred on a continental scale at the end of May 1998 near Algeciras, Spain. The source parameters (i.e., source location and strength) are reconstructed from a limited set of measurements of the release. Annealing and adaptive procedures are implemented to ensure a robust and effective parameter-space exploration. The simulation setup is similar to an emergency response scenario, with the simplifying assumptions that the source geometry and release time are known. The Bayesian stochastic algorithm provides likely source locations within 100 km from the true source, after exploring a domain covering an area of approximately 1800 km × 3600 km. The source strength is reconstructed with a distribution of values of the same order of magnitude as the upper end of the range reported by the Spanish Nuclear Security Agency. By running the Bayesian MCMC algorithm on a large parallel cluster the inversion results could be obtained in few hours as required for emergency response to continental-scale releases. With additional testing and refinement of the methodology (e.g., tests that also include the source geometry and release time among the unknown source parameters), as well as with the continuous and rapid growth of computational power, the approach can potentially be used for real-world emergency response in the near future.

Model-Free Stochastic Localization of CBRN Releases

“…, B K . Using the observations from sensor B k * , where k * = argmax k d 12k , a decision is made between scenarios L 1 and L 2 via the GLRT with threshold d 12k * , as established in (6) and (12). This scenario is then compared with L 3 by the GLRT, and so on, until N − 1 decisions have been made and only one scenario from L is accepted.…”

“…Since only K sensors are available, the number of positive indicator variables is limited in the constraint (12), ensures that for every release scenario pair in L , there exists a d ijk at least as large as ǫ. Although shown to be NP-hard, (14) can be solved efficiently for large sets B and L using a special purpose algorithm [17].…”

“…Considering the binary nature of the sensor readings, sensor measurement noise is introduced via Bernoulli trials which result in flipping sensor observations. The resulting noisy sensor readings provide a wealth of observations from which probability laws can be established, allowing for solution of (11) and the determination of the d ijk in (12). For evalu-ation of the release detection and source localization methodologies, sensors were sampled once per second for 50 seconds, resulting in an observation window of 50 binary indicators of the presence of a CBRN agent.…”

“…Simulation-aided localization of contaminant releases on a continental scale is presented in [12]. In [13], the inverse problem is replaced by computing the posterior probabilities of a finite set of release locations and selecting the release location with maximal likelihood.…”

Optimization of an Urban Monitoring Network for Retrieving an Unknown Point Source Emission

“…Estimation Theory (Bocquet, 2005;Monache et al, 2008;Yee et al, 2014, etc. ), Monte Carlo algorithms using Markov chains (MCMC) (Gamerman and Lopes, 2006;Keats, 2009, etc.…”