Upper and Lower Probability Inferences from Ordered Multinomial Data
Herbert I. Weisberg · Journal of the American Statistical Association · 1972
Dempster's method of upper and lower probabilities represents an attempt to obtain posterior probability statements about parameters without the necessity to incorporate prior information. We apply Dempster's method to the case of multinomial data for which there is some natural ordering of the categories. Inferences are derived for the sum of an arbitrary set of categories, the ratio of two such sums, and linear combinations of the category probabilities. Numerical examples are given, and some effort is made to interprete Dempster's approach and relate it to the standard approaches to statistical inference.