  Deriving the total masses of galaxy clusters from observations of the
intracluster medium (ICM) generally requires some prior information, in
addition to the assumptions of hydrostatic equilibrium and spherical symmetry.
Often, this information takes the form of particular parametrized functions
used to describe the cluster gas density and temperature profiles. In this
paper, we investigate the implicit priors on hydrostatic masses that result
from this fully parametric approach, and the implications of such priors for
scaling relations formed from those masses. We show that the application of
such fully parametric models of the ICM naturally imposes a prior on the slopes
of the derived scaling relations, favoring the self-similar model, and argue
that this prior may be influential in practice. In contrast, this bias does not
exist for techniques which adopt an explicit prior on the form of the mass
profile but describe the ICM non-parametrically. Constraints on the slope of
the cluster mass--temperature relation in the literature show a separation
based the approach employed, with the results from fully parametric ICM
modeling clustering nearer the self-similar value. Given that a primary goal of
scaling relation analyses is to test the self-similar model, the application of
methods subject to strong, implicit priors should be avoided. Alternative
methods and best practices are discussed.
