The role of the Gregory-Loredo algorithm in astronomy:

a Bayesian search strategy for a periodic or nonperiodic signal of unknown shape

P.C. Gregory
Physics Department
University of British Columbia
2224 Agricultural Rd., Vancouver
British Columbia V6T 1Z1

T. J. Loredo
Department of Astronomy
Space Sciences Building
Cornell University
Ithaca, New York 14853

Abstract

In a series of papers Gregory and Loredo (Maximum Entropy and Bayesian Methods 1991, 1992 and Astrophysical Journal, 398, 1992) presented a new Bayesian approach to the detection of unknown periodic and nonperiodic signals. It is applicable to time series data consisting of discrete irregularly spaced events (binned or unbinned) in some coordinate. A key assumption in our analysis is that we have no prior knowledge of the signal (periodic or nonperiodic) or of its characteristics. The Bayesian analysis quantifies Ockham's razor, penalizing successively more complicated models for their greater complexity. The calculation thus balances model simplicity with goodness of fit, allowing us to determine both whether there is evidence for a signal, and the optimum number of model parameters for describing the structure in the data. The method is applicable to many fields and should be useful to anyone interested in the general problem of inferring the shape of an unknown function, periodic or nonperiodic, from discrete samples.

In this paper we will give a progress report on further developments to the method and illustrate applications in the field of X-ray astronomy.


MaxEnt 94 Abstracts / mas@mrao.cam.ac.uk