Bayesian Nonparametrics for Compliance to Exposure Standards

Abstract

A Bayesian nonparametric view of compliance to occupational standards is achieved through predictive distributions. The common assumption of lognormality of environmental exposures is relaxed while recognizing the practicality of a finite number of possible samples. These probability of compliance calculations are conditional on observing some of the samples. Familiar binomial and normal modes are identified with the classical perspective as limits of Bayesian nonparametric and parametric strategies, when the number of observed samples increases. In this situation, extensive previous sample data provide a correspondence between the classical and Bayesian approaches, rather than little or no previous information. Using an example, alternative procedures are illustrated and compared. Currently used methodology can be anti-conservative for protecting employees.

Key Words:

• Nuisance parameters
• Predictive distributions