ABSTRACT
Specifying Bayesian models necessarily means providing prior distributions for unknown
parameters. The prior plays a critical role in Bayesian inference through the updating
statement: π(θ) ∝ p(θ)L(θ|X). Central to the Bayesian philosophy is that all unknown quantities are described probabilistically, even before the data has been observed. Generally
these unknown quantities are the model parameters, θ in the general notational sense, but
missing data are handled in the same fashion. This is very much at odds with the frequentist
notion that unknown parameters are fixed, unyielding quantities that can be estimated with
procedures that are either repeated many times or imagined to be repeated many times.
The immobile parameter perspective, although widespread, is contradictory to the way
that most social and behavioral scientists conduct research. It simply is not possible to
rerun elections, repeat surveys under exactly the same conditions, replay the stock market
with exactly matching economic forces, fight the same war, or re-expose clinical subjects to
identical stimuli.
