  In this paper we outline the framework of mathematical statistics with which
one may study the properties of galaxy distance estimators. We describe, within
this framework, how one may formulate the problem of distance estimation as a
Bayesian inference problem, and highlight the crucial question of how one
incorporates prior information in this approach. We contrast the Bayesian
approach with the classical `frequentist' treatment of parameter estimation,
and illustrate -- with the simple example of estimating the distance to a
single galaxy in a redshift survey -- how one can obtain a significantly
different result in the two cases. We also examine some examples of a Bayesian
treatment of distance estimation -- involving the definition of Malmquist
corrections -- which have been applied in recent literature, and discuss the
validity of the assumptions on which such treatments have been based.
