This paper details a Bayesian alternative to the use of least squares and equal weighting coefficients in regression. An equal weight prior distribution for the linear regression parameters is described with regard to the conditional normal regression model, and resulting posterior distributions for these parameters are detailed. (Author/CTM)

The utility of least squares multiple regression in predicting new scores from previously established equations is considered. It is shown that in the absence of useful prior information, and when normality assumptions are not violated, least squares multiple regression weights are superior to alternatives recently presented in the literature.…

Bayesian techniques are adapted to the estimation of stimulus-response curves. Illustrative examples deal with estimation of person characteristic curves and item characteristic curves in the context of mental testing, and with estimation of a stimulus-response curve using data from a psychophysical experiment. (Author/JKS)

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)

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)