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W. H. Jefferys, T. G. Barnes (U. Texas)
The surface brightness (Baade-Wesselink) technique is one of the most important methods for establishing the Cepheid distance scale, but there is disagreement on how best to use it. The choice of color index for inferring the surface brightness and the mathematical process for combining the photometric and radial velocity information are both at issue. Here we examine the latter issue using Bayesian methods.
The Baade-Wesselink method infers the varying angular diameter of the pulsating star from the relation between the surface brightness and a color index, and the linear displacement of the stellar atmosphere by integrating the radial velocity curve. Fitting the angular diameters to the linear displacements yields the stellar radius and the distance. We must properly account for the errors in both photometry and velocities or risk biasing the results. On this basis Laney & Stobie (1995) have criticized the distances of Gieren et. al. (1993) for 100 Galactic Cepheids and have asserted that the results are biased. Moreover, we must convert radial velocities into linear displacements by integrating a model fitted to the observed radial velocity data. Neither Laney & Stobie nor Gieren et. al. address the issue of how to choose the appropriate number of Fourier terms for the fit.
We have applied an approximately Bayesian analysis to the complete problem and a fully Bayesian analysis to the errors-in-variables problem, and are developing a fully Bayesian analysis of the complete problem, including model selection/averaging. We describe these techniques and demonstrate their use on a subset of the Gieren et. al. data. Both methods are successful in accounting for errors in the data and in providing unbiased distance estimates. The approximately Bayesian analysis also provides effective model selection and model averaging. Our new analyses do not show bias in the distances and thus support that distance scale.