Bayesian Analysis of Order-Statistics Models for Ranking Data

Abstract

In modelling ranking data, order-statistics models are commonly used. The idea behind is that a judgement about the $i$th object (out of $k$ objects) can be represented by a random variable $U_i$ which follows a known distribution. Various distributions such as Normal, Exponential, have been suggested in the literature. One important problem in estimating the above models is the computational burden in evaluating the multidimensional numerical integration which could be highly inaccurate when $k$ is large. In order to overcome this problem, a Bayesian approach is proposed to fit the order-statistics models via the use of the Monte Carlo Markov Chain methods in this paper. The joint distribution of the utilities is assumed to be a multivariate $t$ distribution. The proposed techniques are demonstrated by simulation studies and an empirical investigation of motor vehicle preferences as illustrated in Dansie (1986) [{\it Applied Statistics}, 269-275].