This article presents a Bayesian sparse modeling method to analyze extended x-ray absorption fine structure (EXAFS) data with basis functions built on two-body signals. This method does not require any structural model and allows us to evaluate regression coefficients proportional to the radial distribution functions of the respective elements and their errors and is very effective for analysis of EXAFS with weak absorption intensity and severe signal-to-noise ratios. As an application example, we used it to analyze the EXAFS of an yttrium oxyhydride (YO_xH_y) epitaxial thin film. These EXAFS data show weak absorption intensity and a severe signal-to-noise ratio due to the small amount of x-ray absorption in the thin film sample. However, this approach revealed that the radial distance ratio of the second neighbor yttrium to the first neighbor oxygen coincides with that of a tetrahedral configuration. This result demonstrates that the interstitial oxygen position is tetrahedral in the YO_xH_y thin film.