Inference for a Proton Accelerator Using Convolution Models

• Published in: Journal of the American Statistical Association Vol. 103; no. 482; pp. 604 - 613
• Main Authors: Lee, Herbert K. H, Sansó, Bruno, Zhou, Weining, Higdon, David M
• Format: Journal Article
• Language: English
• Published: Alexandria, VA Taylor & Francis 01.06.2008; American Statistical Association; Taylor & Francis Ltd
• Subjects: Applications; Applications and Case Studies; Bayesian analysis; Bayesian method; Bayesian statistics; Computer simulation; Computer simulator; Convolution; Data analysis; Density estimation; Distribution theory; Estimating techniques; Exact sciences and technology; General topics; Inference; Inverse problem; Inverse problems; Magnets; Mathematics; Modeling; Nonparametric models; Parametric inference; Particle accelerators; Particle beams; Physics; Probability and statistics; Probability theory and stochastic processes; Proton accelerators; Proton beams; Protons; Regression analysis; Sciences and techniques of general use; Simulators; Statistical methods; Statistics; Uncertainty; United States > US; Bayes estimation; Statistical method; Computer simulator; Density estimation; Convolution; Bayesian statistics; Distribution function; Limit analysis; Statistical estimation; Application; Inverse problem
• ISSN: 0162-1459; 1537-274X
• DOI: 10.1198/016214507000000833

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.