A BAYESIAN-APPROACH TO ESTIMATION OF GPAS OF UNIVERSITY-OF-IOWA FRESHMEN UNDER ORDER RESTRICTIONS

The problem of interest is to estimate a two-way table of means of gra de point averages (GPAs) of University of Iowa freshmen grouped by lev els of ACT scores and high school percentiles. Suppose one believes a priori that the table means satisfy a specific partial order. The use of two different classes of prior distributions is considered in model ing this prior information. The use of simulation and, in particular, the Gibbs sampler are outlined to summarize various posterior distribu tions of interest. The posterior distribution is used to predict the g rade point averages of future Iowa freshmen.