A theorem on a product of lognormal variables and hybrid models for children’s exposure to soil contaminants

Li, Zijian

A theorem on a product of lognormal variables and hybrid models for children’s exposure to soil contaminants

2020

Li, Zijian

This study developed hybrid Bayesian models to investigate the modeling process for children’s exposure to soil contaminants, which involves the intrinsic uncertainty of the exposure model, people’s judgments regarding random variables, and limited data resources. A hybrid Bayesian p-box was constructed, which was facilitated by a multiple integral dimensionality reduction (MIDR) theorem. The results indicated that exposure frequency (EF) dominated the exposure dose. The hybrid Bayesian p-box for the Frequentist-Bayesian (F–B) model at the 95th percentile of the simulated average daily dose (ADD) values corresponded to a 4.40 order-of-magnitude difference between the upper and lower bounds of the p-box. This considerable uncertainty was magnified by the combination of the highest posterior density (HPD) regions for three groups of the distribution parameters. For the Interior-Bayesian (I–B) hybrid model, the uncertainty of the outcomes, namely, [1.75 × 10⁻⁸, 2.18 × 10⁻⁸] mg kg⁻¹d⁻¹, was limited by the HPD regions for only one parameter unless the hyperparameters for the variables’ distributions were further evaluated. It was concluded that the hybrid models could provide a novel understanding of the complexity of the exposure modeling process compared to the traditional modeling method.

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