A Bayesian Analysis of Extrasolar Planet Data for HD 73526

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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, 190.4, and 376.2 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, 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.

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