Highly Structured Models for Spectral Analysis in High-Energy Astrophysics

The Chandra X-Ray Observatory, launched by the space shuttle Columbia in July 1999, has taken its place with the Hubble Space Telescope, the Compton Gamma Ray Observatory and the Spitzer Infrared Space Telescope in NASA’s fleet of state of the art space-based Great Observatories. As the world’s premier X-ray observatory, Chandra gives astronomers a powerful tool to investigate black holes, exploding stars and colliding galaxies in the hot turbulent regions of the universe. Chandra uses four pairs of ultra-smooth high-resolution mirrors and efficient X-ray photon counters to produce images at least 30 times sharper than any previous X-ray telescope. Unlocking the information in these images, however, requires subtle statistical analysis; currently popular statistical methods typically involve Gaussian approximations (e.g., minimum χ2 fitting), which are not justifiable for the high-resolution low-count data. In this article, we employ modern Bayesian computational techniques (e.g., expectation–maximization-type algorithms, the Gibbs sampler and Metropolis–Hastings) to fit new highly structured models that account for the Poisson nature of photon counts, background contamination, image blurring due to instrumental constraints, photon absorption, photon pileup and source features such as spectral emission lines and absorption features. This application demonstrates the flexibility and power of modern Bayesian methodology and algorithms to handle highly structured models that are convolved with complex data collection mechanisms involving nonignorable missing data.