Which statement distinguishes prior distribution from prior probability?

• A. Prior distribution is a distribution over parameter values; prior probability is the belief in a specific model before data.
• B. Prior distribution is the belief in a specific model before data; prior probability is a distribution over parameter values.
• C. Prior distribution is always non-informative; prior probability is always informative.
• D. Prior distribution equals posterior after data.

Answer: (A)

In Bayesian statistics, priors express beliefs before seeing data. The prior distribution is a distribution over parameter values; it assigns probabilities to different possible values of the parameter, reflecting what we think could be true before observing data. The prior probability, on the other hand, is often the probability assigned to a specific model or hypothesis before seeing data. It concerns choosing among competing models rather than describing uncertainty about parameter values within a given model.

So, the statement that a prior distribution is a distribution over parameter values and a prior probability is the belief in a specific model before data captures the essential distinction. Priors can be informative or non-informative, and the posterior is not equal to the prior—it’s the result of updating the prior with the data through the likelihood.