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Y. Yu, R. Protassov, E. Sourlas, D. van Dyk (Department of Statistics, Harvard University)
Pile-up occurs in X-ray detectors when two or more photons arrive in an event detection cell during the same frame. Such coincident events are counted as a single higher energy event or lost altogether if the total energy goes above the on-board discriminators. Thus, for bright sources pile-up can seriously distort both the count rate and the energy spectrum. Accounting for pile-up is perhaps the most important outstanding data-analytic challenge for Chandra. Conceptually, however, there is no difficulty in addressing pile-up in a hierarchical Bayesian framework. In particular, we can construct a hierarchical model with components accounting for such features as instrument response, background, absorption, and pile-up. A Markov Chain Monte Carlo algorithm dramatically simplifies computational complexity by fitting one component at a time. For pile-up, we need to stochastically separate a subset of the observed counts into multiple counts of lower energy based on the current iteration of the particular spectral/spatial model being fit. The difficulty lies in computation. Simply enumerating the set of photons that could result in a particular observed event, let alone their relative probabilities, is an enormous task. Thus, we believe there is great promise in Monte Carlo techniques which if carefully designed, can automatically exclude numerous possibilities that have minute probability. Although there remains much work to be done, Bayesian hierarchical methods in conjunction with MCMC algorithms may offer a practical and innovative solution.