A Bayesian Analysis of Extrasolar Planet Data for HD 73526

A new Bayesian tool for nonlinear model fitting has been developed, that employs a parallel tempering Markov Chain Monte Carlo algorithm with a novel statistical control system. The algorithm has been used to re-analyze precision radial velocity data for HD 73526. For a single planet model, three possible orbits were found with periods of 127.88 +0.37 −0.09, 190.4 +1.8 −2.1 and 376.2 +1.4 −4.3 days. The 128 day orbit, with an eccentricity of 0.56 ± 0.03, has a maximum value of prior × likelihood which is 16 times larger than for the next highest solution at 376 days. However, the 376 day orbit, with an eccentricity of 0.10 +0.05 −0.10, is formally more probable because for this sparse data set there is a much larger volume of parameter space with a significant probability density in the vicinity of the 376 day peak. The previously reported orbit (Tinney et al. 2003) of 190.5 ± 3.0 days corresponds to our least probable orbit. The analysis highlights the need for measurements around phase 0.5 for the 376 day period. Subject headings: Bayesian methods, time series analysis, extrasolar planets: individual ( HD 73526) 1.