Bayesian Analysis of Occupational Exposure Data with Conjugate Priors

Abstract

Bayesian analysis is a flexible method that can yield insight into occupational exposures as the methods quantify plausible values for exposure parameters of interest, such as the mean, variance, and specific percentiles of the exposure distribution. We describe three Bayesian analysis methods for the analysis of normally distributed data (e.g. the logarithm of measurements of chemical hazards) that use conjugate prior distributions (normal for the mean, and inverse-χ2, inverse-Γ, or vague for the variance) to provide analytical expressions for the posterior distributions of the sufficient statistics of the normal distribution (e.g. the mean and variance). From these posterior distributions, the posterior distribution of any parameter of interest about the exposure distribution can be tabulated.The methods are illustrated using lead exposure data collected by the Occupational Safety and Health Administration at a copper foundry on multiple occasions. A unique feature of the normal-inverse-Γ method is that dependence of the mean and variance prior distributions is integrated out of the posterior distributions expressions, suggesting that a ‘default’ prior distribution on variance may be used: candidate default distributions are proposed based on the literature. Relative to other Bayesian analysis methods used in industrial hygiene, the methods described are flexible, and can be implemented without specialized software.