EPAExpoBox (A Toolbox for Exposure Assessors)
Deterministic and Probabilistic Assessments
Methods
Deterministic exposure assessments use a combination of point values selected to be either healthprotective (i.e., highend values) or to represent a “typical” exposure (i.e., central tendency values). They produce an exposure estimate that is also a point estimate that falls somewhere within the full distribution of possible exposures (U.S. EPA, 2004).
Multiple iterations of an assessment can be conducted using the deterministic approach. For example, default point estimates can be used for a screeninglevel assessment to create a basic picture of highend or typical exposures. If the results of the initial assessment are not sufficient for use in decisionmaking, a refined deterministic assessment can be completed using more sitespecific data, if available, to create a more precise picture of expected exposures.
Central Tendency Estimates 


Bounding Estimates 


HighEnd Estimates 










Probabilistic exposure assessments give the assessor flexibility in generating exposure estimates for the spectrum of highend percentiles (e.g., from the 90^{th} to 99.9^{th} percentiles) from which the assessor can select the most appropriate upperbound level (U.S. EPA, 2004). Many of the same algorithms and data distributions used to derive point estimates in deterministic assessments can also be used in probabilistic assessments.
To be healthprotective, risk management decisions are often based on estimates of the highend exposure to an individual. As the exposure estimate moves higher within the percentile range, the level of uncertainty increases. Using a probabilistic approach allows for better characterization of variability and/or uncertainty in exposure estimates (U.S. EPA, 2004). This is accomplished by using a set of “random variables” in the exposure equation. Random variables are those variables like body weight, exposure frequency, and ingestion rate that are assumed to be independent and not correlated with one another (e.g., body weight is not correlated with exposure frequency) and are expressed as probability distributions, which account for variability within the population. Any known correlations between variables are taken into account (e.g., food intake may be correlated with body weight).
Random variables allow for a unique estimate of exposure to be calculated by sampling each set of probability distributions and calculating a result. Each iteration of the calculation represents a plausible combination of input values and therefore a plausible estimate of exposure. However, the "individuals" represented in each iteration are not meant to represent a single person; rather, the total distribution of exposure values is meant to demonstrate the likelihood or probability of different exposure levels within a population with characteristics and behaviors that vary.
Below are the steps an assessor might take to conduct a probabilistic approach.
Identify Variables to Evaluate Probabilistically
 Prior to carrying out a probabilistic assessment, the assessor decides which of the input variables are going to be evaluated probabilistically. Ideally, the model will use probability distributions for input variables that are uncertain or variable as identified by the sensitivity analyses. More often, the choices are limited by available data (U.S. EPA, 2004)
Select and Fit Distributions
 The assessor selects and fits the best distributions for the variables that will be input as probability distributions (see Input Data for more information and resources on selecting and fitting distributions).
Sample the Probability Distributions
 The most popular (but not the only) approach to estimating exposure with probability distributions is the Monte Carlo simulation. A Monte Carlo simulation is "a technique for characterizing the uncertainty and variability in exposure estimates by repeatedly sampling the probability distributions of the exposure equation inputs and using these inputs to calculate a range of exposure values" (U.S. EPA, 2001).
Monte Carlo simulations can vary in complexity: Onedimensional Monte Carlo Analysis (1D MCA) "combine[s] point estimates and probability distributions to yield a probability distribution that characterizes variability or uncertainty in risks within a population" (U.S. EPA, 2001).
 Twodimensional Monte Carlo Analysis (2D MCA) “simultaneously characterize[s] variability and uncertainty in multiple variables and parameter estimates” and is typically employed in more refined assessments (U.S. EPA, 2001).
Many userfriendly programs are available for conducting Monte Carlo simulations, but if the model is not appropriately parameterized or the input distributions are not appropriately defined, the results of a Monte Carlo simulation will not be useful. Some knowledge of probabilistic analysis and critical evaluation of the input distributions is therefore required to generate highquality results using a Monte Carlo simulation tool.
Presenting the Results of Probabilistic Assessments
 Presenting the results of a probabilistic assessment can be challenging due to the complexity of the approach while the results of a deterministic assessment are often simple to understand and a decision point for taking action is often clear. For example, if the point estimate of risk is above a certain level, take action. If not, another action or no action might be advised (U.S. EPA, 2004).
The results of a probabilistic assessment are not as intuitive to interpret and the distribution of exposures or risks should be characterized as representing variability among the population based on differences in exposure (U.S. EPA, 2004).
U.S. EPA recommends early and continuous involvement with stakeholders, including a communication plan, and developing effective graphics to ensure the results are understood by affected parties (U.S. EPA, 2004). Further, information might be presented in multiple ways (e.g., using probability density functions and cumulative density functions) to communicate the results effectively. Chapter 31 – Probabilistic Risk Assessment (12 pp, 345KB, About PDF) in ATRA Volume I (U.S. EPA, 2004) and Chapter 6 – Exposure Assessment (20 pp, 1.92MB, About PDF) in RAGS Volume 1 (U.S. EPA, 1989) include discussions of factors to consider when presenting the results of a probabilistic assessment. Hypothetical results showing probability density and cumulative density functions are also included in this chapter.
Tools for Conducting Probabilistic Assessments
The tools in this table are all models that can be used to conduct probabilistic assessments. Tools for deterministic approaches are included in other EPAExpoBox tool sets.