Prior Distribution

There has been an emergence of researchers using Bayesian methods in studies and research on educational measurement, research, and evaluation. Bayesian methods differ from traditional methods in one key aspect—that of parameter uncertainty. All statistical probability models describe a mechanism, or relationship, between unobserved parameters that have given rise to observed data. In Bayesian methods, parameters are regarded as random variables to incorporate the uncertainty, and an entire distribution of possible parameter values is produced. In contrast, traditional methods consider parameters as fixed quantities, the result being a single-point estimate. Another distinction between Bayesian and traditional methods is found in the incorporation of information about the parameter before the data have been observed. This information is the prior information and is represented by an entire ...