The prior represents beliefs about \theta before D is available, and it is often specified by choosing a particular distribution among a set of well-known and tractable families of distributions, such that both the evaluation of prior probabilities and random generation of values of \theta are relatively straightforward.
where the distance measure \rho(\hat{D},D) determines the level of discrepancy between \hat{D} and D based on a given metric (e.g., the Euclidean distance).