TABLE OF CONTENTS Science is all about identifying and understanding organized structures or patterns in nature. In this regard, periodic patterns have proven especially important. Nowhere is this more evident than in the field of astronomy. Periodic phenomena allow us to determine fundamental properties like mass and distance, enable us to probe the interior of stars through the new techniques of stellar seismology, detect new planets, and discover exotic states of matter like neutron stars and black holes. Clearly, any fundamental advance in our ability to detect periodic phenomena will have profound consequences in our ability to unlock nature s secrets. The purpose of this chapter is to describe advances that have come about through the application of Bayesian probability theory, [2] and provide illustrations of its power through several examples in physics and astronomy. We also examine how non-uniform sampling can greatly reduce some signal aliasing problems.
[1]The term spectral analysis has been used in the past to denote a wider class of problems than will be considered in this chapter. For a brief introduction to stochastic spectrum estimation, see Appendix B.13.4.
[2]The first three sections of this chapter are a revised version of an earlier paper by the author (Gregory, 2001), which is reproduced here with the permission of the American Institute of Physics.
Arthur Schuster introduced the periodogram in 1905, as a means for detecting a periodicity and estimating its frequency. If the data are evenly spaced, the periodogram...
