Bayesian periodic signal detection.: I.: Analysis of 20 years of radio flux measurements of the X-ray binary LS I+61°303

We extend the Bayesian method of Gregory and Loredo 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 nonuniformly 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 degrees 303, which exhibits periodic radio outbursts with a period of 26.5 days. Several authors have suggested that the peak flux density of the outbursts exhibit a periodic or quasi-periodic modulation of approximately 1600 days. Our Bayesian analysis of the outburst peak flux 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 flux density data. The probability density for the modulation period exhibits a broad peak in the range 1599-1660 days (68% credible region) with a mean value of 1632 days. The rms flux density deviation from the mean shape, amounting to 45 mJy, is much larger than the measurement errors of approximate to 10 mJy, which suggests additional complexity in the source that is yet to be understood. The next maximum in the long-term flux modulation is predicted to occur near 1999 July 22 (JD 2,451,382).