Inference for a Proton Accelerator Using Convolution Models

Proton beams present difficulties in analysis because of the limited data that can be collected. The study of such beams must depend on complex computer simulators that incorporate detailed physical equations. The statistical problem of interest is to infer the initial state of the beam from the limited data collected as the beam passes through a series of focusing magnets. We are thus faced with a classic inverse problem where the computer simulator links the initial state to the observables. We propose a new model for the initial distribution that is derived from the discretized process convolution approach. This model provides a computationally tractable method for this highly challenging problem. Taking a Bayesian perspective allows better estimation of the uncertainty and propagation of this uncertainty.