**HEAD Division Meeting 1999, April 1999**

*Session 33. Other*

Poster, Wednesday, April 14, 1999, 8:30am Wed. - 2:00pm Thurs., Gold Room
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## [33.05] Simultaneous Analysis of Elliptical Images and Energy Spectra with Low Photon Counts via Bayesian Posterior Simulation

*David Esch, David A. van Dyk (Harvard University), Vinay L. Kashyap, Aneta Siemiginowska (Harvard-Smithsonian Center for Astrophysics), Alanna Connors (Wellesley College)*

In this paper we attack the outstanding problem of the
analysis of spatial-spectral data by developing models for
low count high resolution images that allow the energy
spectrum to vary across the image. We begin with simple
elliptic images (e.g., for a dispersed point source, a
globular cluster, or a cluster of galaxies) that are modeled
with bivariate Gaussian or Lorentzian distributions. The
point spread function is approximated by an analytic form
based on conditional bivariate normal distributions with
means and variance-covariance matrices (parameterized via a
eigen decomposition) that depend on the location of the
incoming photon on the detector. Although an approximation
to the actual point spread function, this solution will
greatly accelerate the computationally expensive algorithms
that we use for Bayesian model fitting.

We incorporate spectral information using the model
developed in van Dyk et al. (1999, this publication)
conditional on the location of the photon on the detector.
The shape of the continuum and the absorption rate in this
conditional distribution are allowed to vary smoothly across
the image. This is accomplished via a Generalized Liner
Model for the Poisson photon intensity parameters in each
spectral cross spatial cell. The Generalized Linear Model
parameterizes the log intensity parameters as a linear
function of some transformation of the associated Energy
(e.g., as in a power law) and location on the detector. The
Poisson nature of the model easily allows for the low count
high resolution data of the several new generation
space-based telescopes which are expected over the next ten
years. The model also allows for in-space and telescope
absorption of photons and background emissions in a manner
analogous to van Dyk et al. (1999). This highly structured
hierarchical model can be fit in the Bayesian paradigm using
Markov Chain Monte Carlo methods (e.g., the Gibbs sampler
and the Metropolis-Hastings algorithm).

If the author provided an email address or URL for general inquiries,
it is as follows:

esch@stat.harvard.edu

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