Advanced tools for astronomical time series and image analysis

The algorithms described here, which I have developed for applications in X-ray and gamma-ray astronomy, will hopefully be of use in other ways, perhaps aiding in the exploration of modern astronomy's data cornucopia. The goal is to describe principled approaches to some ubiquitous problems, such as detection and characterization of periodic and aperiodic signals, estimation of time delays between multiple time series, and source detection in noisy images with noisy backgrounds. The latter problem is related to detection of clusters in data spaces of various dimensions. A goal of this work is to achieve a unifying view of several related topics: signal detection and characterization, cluster identification, classification, density estimation, and multivariate regression. In addition to being useful for analysis of data from space-based and ground-based missions, these algorithms may be a basis for a future automatic science discovery facility, and in turn provide analysis tools for the Virtual Observatory. This chapter has ties to those by Larry Bretthorst, Tom Loredo, Alanna Connors, Fionn Murtagh, Jim Berger, David van Dyk, Vicent Martinez & Enn Saar. The paper is followed by commentaries by Thomas J. Loredo and Peter E. Freeman. "The unconscious goal of the scientific philosopher is the automation of science." Irving John Good, The Estimation of Probabilities, 1965 "Automate or die." Silicon Valley Billboard, June, 2001.