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 reanalyze precision radial velocity data for HD 73526. For a single-planet model, three possible orbits were found with periods of 127.88(-0.09)(+0.37), 190.4(-2.1)(+1.8), and 376.2(-4.3)(+1.4) days. The 128 day orbit, with an eccentricity of 0.56 +/- 0.03, has a maximum value of prior; likelihood that is 16 times larger than for the next highest solution at 376 days. However, the 376 day orbit, with an eccentricity of 0.10(-0.10)(+0.05), 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.