A Bayesian Analysis of Extrasolar Planet Data for HD 73526

Abstract

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+0.37-0.09, 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 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+0.05-0.10, 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.