**HEAD 2000, November 2000**

*Session 16. Workshops*

Display, Tuesday, November 7, 2000, 8:00am-6:00pm, Bora Bora Ballroom
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## [16.10] Using Bayesian Hierarchical Modeling to Address Pile-Up in the Chandra X-ray Observatory

*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.

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