FILTERED-VARIATE PRIOR DISTRIBUTIONS FOR HISTOGRAM SMOOTHING

We develop prior distributions for histogram inference favoring smooth population frequencies; that is, probability vectors with small diffe rences for neighboring categories. We give a theory of prior-random pr obability vectors representable as a linear transform, or ''filter,'' of a standard random probability vector, or equivalently, a random wei ghted average of nonrandom smooth probability vectors. Promising metho ds of prior assessment are given based on elicitation of a list of typ ically smooth probability vectors, the empirical moments of which can then be matched by the mean vector and variance matrix of a constructe d continuous-type filtered-variate prior distribution.