In recent years, there has been a quantum leap in the quality and quantity of new data in observational high-energy astrophysics. Recently launched or soon-to-be launched space-based telescopes that are designed to detect and map ultra-violet, X-ray, and gamma-ray electromagnetic emission are opening a whole new window to study the hot and turbulent regions of the cosmos. The new instrumentation allows for very high resolution imaging, spectral analysis, and time series analysis. The Chandra X-ray Observatory, for example, produces images at least thirty times sharper than any previous X-ray telescope.
The complexity of these instruments, the complexity of the astronomical sources, and the complexity of the scientific questions leads to a subtle inference problem that requires sophisticated statistical tools. In this talk we discuss the use of highly structured statistical models that are designed to capture the complexity of both the data collection process and the cosmic sources themselves. To fit these models, we use Bayesian statistical methods that are well suited to answer relevant scientific questions. Bayesian techniques allow us to combine information in the data with scientific data outside the data such as smoothness constraints on extended emission. Thus, we propose combining a Poisson likelihood that accounts for the low-count nature of the data with a multi-scale prior distribution that encourages smooth reconstructions and allows for structure on multiple scales in the emission. Although such prior distributions are generally formulated in terms of a number of user specified tuning parameters, we show that these parameters can also be fit to the data. In principle these methods can be used to jointly model the spectral and spatial characteristics of the data.
The statistical computation that is necessary to fit such highly structured models can be formidable. We propose both EM algorithms for mode finding and Markov chain Monte Carlo methods to fully explore the posterior distribution. Because the computational efficiency of such methods can be highly sensitive to the choice of Markov chain, they must be designed and implemented with care. Thus, we discuss both our choice of implementation and convergence criterion.
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