  We present a Bayesian hierarchical framework for a principled data analysis
pipeline of peculiar velocity surveys, which makes explicit the inference
problem of constraining cosmological parameters from redshift-independent
distance indicators. We demonstrate our method for a Fundamental Plane-based
survey. The essence of our approach is to work closely with observables (e.g.
angular size, surface brightness, redshift, etc), through which we bypass the
use of summary statistics by working with the probability distributions. The
hierarchical approach improves upon the usual analysis in several ways. In
particular, it allows a consistent analysis without having to make prior
assumptions about cosmology during the calibration phase. Moreover, calibration
uncertainties are correctly accounted for in parameter estimation. Results are
presented for a new, fully analytic posterior marginalised over all latent
variables, which we expect to allow for more principled analyses in upcoming
surveys. A maximum a posteriori estimator is also given for peculiar velocities
derived from Fundamental Plane data.
