A beam of protons is produced by a linear charged particle accelerator, then focused through the use of successive quadrupoles. The initial state of the beam is unknown, in terms of particle position and momentum. Wire scans provide the only available data on the current state of the beam as it passes through and beyond the focusing region; the goal is to infer the initial state from these position histograms. This setup is that of an inverse problem, in which a computer simulator is used to link an initial state configuration to observable values (wire scans), and then inference is performed for the distribution of the initial state. Our Bayesian approach allows estimation of uncertainty in our initial distributions and beam predictions.
"Inferring particle distribution in a proton accelerator experiment." Bayesian Anal. 1 (2) 249 - 264, June 2006. https://doi.org/10.1214/06-BA108