A Bayesian approach for neutral particles source estimation

In this work, the adjoint to the transport operator is used to estimate the spatial distribution of an energy dependent neutral particles source in a homogeneous one-dimensional medium, from measurements of internal detectors. An analytical discrete ordinates formulation, the ADO method, is applied to derive a spatially explicit solution for the adjoint flux. A Bayesian approach is considered to relate the measurements with prior information and then the Metropolis-Hastings algorithm is used do draw samples of the posterior distributions. Explicit expressions for the measurements are derived, allowing relevant reduction in computational time. Simulations are performed for successfully estimating polynomial and piecewise constant localized energy dependent sources. Two and six energy group problems are considered.