Approximate Bayesian Computation for Source Term Estimation

Bayesian inference is a vital tool for consistent manipulation of the uncertainty that is present in many military scenarios. However, in some highly complex environments, it is hard to write down an analytic form for the likelihood function that underlies Bayesian inference. Approximate Bayesian computation (ABC) algorithms address this difficulty by enabling one to proceed without analytically specifying or evaluating the likelihood distribution. This is achieved through the use of computer simulation models that stochastically simulate measurements for a given set of parameter values. This paper gives an overview of standard ABC methods such as rejection and Markov chain Monte Carlo (MCMC) sampling. It then goes on to discuss ABC versions of sequential Monte Carlo (SMC) samplers, which are the recently-developed next-generation particle filters for Bayesian sampling. SMC Samplers have properties that make them highly suitable for complex estimation and inference problems in the presence of uncertainty. This includes an ability to efficiently explore multi-modal distributions. One application of SMC-ABC algorithms is source term estimation for chemical, biological, radiological and nuclear (CBRN) defence when the number of releases is unknown. A proof-of-principle study has been conducted using a bar-sensor model and a Gaussian dispersion model for agent behaviour, including the effect of wind. The outcome is that the algorithms are able to estimate model parameters to a reasonable degree of accuracy, but there is some ambiguity between the location and time of releases due to wind effects.