This paper develops theory and methods for the application of the Bayesian Model II method to the estimation of binomial proportions and demonstrates its application to educational data. (Author/RK)

A computer simulation of Bayes' Theorem was conducted in order to determine the probability that an examinee was a master conditional upon his test score. The inputs were: number of mastery states assumed, test length, prior expectation of masters in the examinee population, and conditional probability of a master getting a randomly selected test…

Empirical Bayes methods are shown to provide a practical alternative to standard least squares methods in fitting high dimensional models to sparse data. An example concerning prediction bias in educational testing is presented as an illustration. (Author)

Bayesian estimation procedures are summarized and numerically illustrated by means of simulation methods. Procedures of data generation for simulation purposes are also delineated and computationally demonstrated. The logistic model basic to the Bayesian estimation procedures is shown to be explicit with respect to the probability distribution…