Filtered-Variate Prior Distributions for Histogram Smoothing

Abstract

We develop prior distributions for histogram inference favoring smooth population frequencies; that is, probability vectors with small differences for neighboring categories. We give a theory of prior-random probability vectors representable as a linear transform, or “filter,” of a standard random probability vector, or equivalently, a random weighted average of nonrandom smooth probability vectors. Promising methods of prior assessment are given based on elicitation of a list of typically smooth probability vectors, the empirical moments of which can then be matched by the mean vector and variance matrix of a constructed continuous-type filtered-variate prior distribution.

Key Words:

• Bayesian smoothing
• Carlson function
• Generalized Dirichlet distribution
• Generalized hypergeometric function
• Multinomial distribution
• Multinomial estimation.