  In astronomical and cosmological studies one often wishes to infer some
properties of an infinite-dimensional field indexed within a finite-dimensional
metric space given only a finite collection of noisy observational data.
Bayesian inference offers an increasingly-popular strategy to overcome the
inherent ill-posedness of this signal reconstruction challenge. However, there
remains a great deal of confusion within the astronomical community regarding
the appropriate mathematical devices for framing such analyses and the
diversity of available computational procedures for recovering posterior
functionals. In this brief research note I will attempt to clarify both these
issues from an "applied statistics" perpective, with insights garnered from my
post-astronomy experiences as a computational Bayesian / epidemiological
geostatistician.
