A Bayesian model for inference on population proportions

Abstract In recent times and even up to now, traffic congestion and parking difficulties, especially during morning and evening rush hours, have become a major concern to members of the University of Lagos (UNILAG) community and visitors alike. UNILAG has witnessed unprecedented growth in student enrollment during the past 10 years or so culminating in the current total enrollment of more than 35,000 students, of which about 25,000 are undergraduates. In order to study the worrisome traffic situation at UNILAG in the wake of these large numbers, independent, although similar, sample surveys of undergraduate students of the eight faculties on the main campus of UNILAG were conducted in 2007. The purpose of the surveys was to collect data on undergraduate students who owned or used motor vehicles on campus. Furthermore, to investigate possible temporal trends, the surveys were repeated in 2009. The types of data obtained from the surveys provided veritable impetus for the application of empirical Bayes (EB) analysis to estimate the proportions of students of individual faculties who used motor vehicles on campus roads during the periods under reference. The EB technique, being a Bayesian method, combines prior information and sample information in a manner that ‘shrinks’ an EB estimator toward the sample estimator if a vague prior (proper prior with a large variance) is used. The main result is that in 2007 about one in four students used motor vehicles, and this result held almost across the eight faculties. Although results of the 2009 surveys were generally similar there were faculties that recorded some reduction in the estimated proportions of students who used motor vehicles. WIREs Comput Stat 2012 doi: 10.1002/wics.1218 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory