PRIORS - An Interactive Computer Program for Formulating and Updating Prior Distributions

• NCJ Number: 91864
• Author(s): J Vandevate
• Date Published: 1982
• Length: 35 pages
• Grant Number(s): 80-IJ-CX-0048
• Agencies: NIJ-Sponsored
• Publication Type: Research (Applied/Empirical)

Annotation

This report applies PRIORS, an interactive PL/I program, to hypothesis testing, parameter estimation, posterior distributions and updating, plots of cumulative distributions, and modifying distributions.

Abstract

After defining the why and the what of prior distribution, hypothesis testing is portrayed in the formulation of requirements for admission to a public assistance program based on applicants' assets. The problem resolved is the determination of a decision threshold that will eliminate applicants whose assets exceed the threshold value. It is shown how the interactive program OPT2 assists evaluators in formulating decision rules for hypothesis tests involving Gaussian (normal) distributions. Since many of the processes studied by evaluators can be accurately represented by underlying probability distributions and described by the parameters characterizing these distributions, the report discusses the common distributions addressed by PRIORS, their conjugate prior distributions, and how to use PRIORS to assess them. Consideration is given to the Bernoulli process, the Poisson process, the Uniform process, the normal process with independent samples, and normal regression. It is advised that the prior distributions formulated with PRIORS readily allow the addition of improved information. This process of adding information to a prior distribution is called 'updating,' and the resulting updated distribution is a 'posterior distribution.' This process is described. Additional features of PRIORS analyzed are plots of cumulative distributions and modifying distributions. The appendix describes the mathematical equations for the various distributions discussed.