Bayesian Analysis for a Theory of Random Consumer Demand: The Case of Indivisible Goods

McCausland (2004a) describes a new theory of random consumer demand. Theoretically consistent random demand can be represented by a "regular" "L-utility" function on the consumption set X. The present paper is about Bayesian inference for regular L-utility functions. We express prior and posterior uncertainty in terms of distributions over the infinite-dimensional parameter set of a flexible functional form. We propose a class of proper priors on the parameter set. The priors are flexible, in the sense that they put positive probability in the neighborhood of any L-utility function that is regular on a large subset (line over X) of X; and regular, in the sense that they assign zero probability to the set of L-utility functions that are irregular on (line over X) X . We propose methods of Bayesian inference for an environment with indivisible goods, leaving the more difficult case of infinitely divisible goods for another paper. We analyse individual choice data from a consumer experiment described in Harbaugh et al. (2001).