Frequentist or Bayesian? An exoplanet case study

The radial velocity method has for long been the by far most productive technique used to detect extrasolar planets orbiting around a star. We consider both, the frequentist (or neo-Fisherian) and the Bayesian frameworks, to estimate the orbital parameters of an extrasolar planet in a binary system. From the frequentist viewpoint, a likelihood-based fitting procedure is proposed. Bayesian computation uses adaptive Metropolis-Hastings sampling. Both approaches are compared. In particular we discuss how they address the number of methodological and computational issues inherent the radial velocity formula and, in particular, the strong correlation among some of the parameter estimates/posterior distributions. We focus also on the astronomical interpretation of the parameters and how the assumption of circularity of the orbit may be assessed.