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.