EPA-Expo-Box (A Toolbox for Exposure Assessors)

# Deterministic and Probabilistic Assessments

#### Input Data

**Deterministic Assessments**

Descriptions of the data sources that can be used in deterministic assessments can be found in multiple tool sets on the EPA-Expo-Box website. The Indirect Estimation (Scenario Evaluation) module of the Approaches Tool Set of EPA-Expo-Box includes the following categories for input data:

Tools related to input data for fate and transport, concentrations, and exposure factors are also described in the Media and Routes Tool Sets of EPA-Expo-Box.

**Probabilistic Assessments **

Some of the input values for a probabilistic assessment will be data distributions instead of single values. However, selecting and fitting probability distributions for all of the input variables is often unnecessary since it can require considerable resources and might not increase the accuracy of the exposure assessment. Ideally, only those input variables found to contribute significantly to the overall variability and uncertainty as determined by the sensitivity analysis should be considered to include as probability distributions (U.S. EPA, 2001).

**Steps for Selecting and Fitting Probability Distributions:**

- Hypothesize a family of distributions
- Assess quality of fit of distribution
- Estimate distribution parameters
- Assess quality of fit of parameters

Appendix B of RAGS Volume 3, Part A (U.S. EPA, 2001)

When fitting the data to a distribution, exposure assessors might consider a variety of distributions or mathematical functions (e.g., normal, lognormal, uniform, Poisson, beta) and often more than one probability distribution may appear to be suitable. U.S. EPA (2001) recommends using a step-wise, tiered approach for incorporating probability distributions in a probabilistic assessment. Appendix B of RAGS Volume 3, Part A (U.S. EPA, 2001) reviews the methods available to select and fit distributions and includes guidance based on the questions the assessment is intended to answer and the data available to define the input variables. Similar to a point estimate approach, different sites may require different probability distributions for input variables, depending on the unique risk management issues and sources of uncertainty (U.S. EPA, 2001). U.S. EPA’s (1997b) *Guiding Principles for Monte Carlo Analysis* also includes guidance for assessors on selecting input data and distributions for probabilistic assessments. U.S. EPA (2000) Options for Development of Parametric Probability Distributions for Exposure Factors provides guidance for selecting probability distributions and fitting data from the 1997 edition of the *Exposure Factors Handbook* (U.S. EPA, 1997a) Three factors—tap water intake, population mobility, and inhalation rules—are used as test cases in the document and recommendations on the mathematical models that best fit the data are provided.