Bayesian Periodic Signal Detection

We extend the Bayesian method of Gregory and Loredo (1992) for the detection of a periodic signal of unknown shape and period, to the case where the noise sampling distribution is independent Gaussian. The analysis readily handles nonuniformily sampled data and allows for an unknown noise variance. The method is applied to the radio astronomy data for the interesting X-ray binary system LS I +61 303, which exhibits periodic radio outbursts with a period of 26.5 days. Several authors have suggested that the peak ux density of the outbursts exhibit a periodic or quasi-periodic modulation of approximately 1600 days. Our Bayesian analysis of the outburst peak ux densities provides strong support for such a modulation. We derive the posterior probability density function of the modulation period and the estimated mean shape of the modulation based on the available ux density data. The probability density for the modulation period exhibits a broad peak in the range 1599 to 1660 days (68 % credible region) with a mean value of 1632 days. The RMS ux density deviation from the mean shape, amounting to 45 mJy, is much larger than the measurement errors of 10 mJy which suggest additional complexity in the source which is yet to be understood. The next maximum in the long term ux modulation is predicted to occur near July 22, 1999 (Julian day 2,451,382). Subject headings: Bayesian methods, period detection, Gregory-Loredo method, LS I +61 303, X-ray binaries, pulsars, time series analysis