Jump to main content or area navigation.

Contact Us

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

EPA-Expo-Box icon

Deterministic and Probabilistic Assessments


A deterministic assessment uses single values, or point estimates, as inputs to the exposure equation. As a result, the output of a deterministic assessment is a point value for exposure. Deterministic approaches can be used for both screening-level and higher-tier assessments and as components in the assessment of multiple stressors and multiple pathways. Deterministic assessments are relatively economical and straightforward, so they are used often by exposure assessors.

A probabilistic assessment uses distributions of data from which multiple points are selected as inputs to the exposure equation over the course of multiple simulations. As a result, the output of a probabilistic assessment is a distribution of potential exposure values. Probabilistic approaches are generally used only for higher-tier assessments, and they are applicable to assessments of multiple stressors and multiple pathways.

Below are characteristics typical of deterministic and probabilistic assessments. These are not necessarily components of all deterministic or probabilistic assessments.

  Deterministic Probabilistic
  • Point estimates
  • Probability or frequency distributions for media concentrations or exposure factors
Deterministic assessments use single values or point estimates as inputs to the exposure equation. Health-protective assessments typically use a deterministic approach with default high-end point estimates (e.g., reasonable maximum exposure, reasonable worst-case exposure, maximum exposure). Deterministic assessments might also use central tendency values to estimate “typical” exposure.

Assessments that use a probabilistic approach use distributions of data (i.e., probability or frequency) for some of the input variables. Probability distributions describe the range of values that certain variables (e.g., body weight, ingestion rate, concentration) might take and estimate the relative likelihood or probability that any of those values might occur in the given population (U.S. EPA, 2001).

Probabilistic approaches typically require more resources and expertise than using a deterministic approach given that the assessor must select and fit distributions for input parameters. Probability distributions need not be included for all input variables. Typically a sensitivity analysis is conducted to determine which exposure pathways and parameters contribute significantly to the overall variability and uncertainty in the exposure estimates. Probability distributions are used for sensitive variables to minimize the complexity of the assessment, and point estimates might be appropriate for other input variables.
  • Simple models and equations
  • Standardized methods
  • Sensitivity analysis based on point estimates
  • Complex models and equations
  • Sensitivity analysis based on probability distributions
  • Monte Carlo simulations
Tools available for deterministic assessments include default inputs and methods established by EPA to help standardize point estimate calculations among sites. These assessments often use simple models and equations. Because probabilistic assessments sample input variables from distributions, the mathematical equations and computer models used to implement them are more complex.

Monte Carlo simulations are the most common approach to estimate exposure with probability distributions. Using Monte Carlo, the probability distributions for one or more variables are sampled repeatedly and the exposure estimate is calculated each time to produce a distribution of possible values for exposure estimates. The distributions sampled in a Monte Carlo risk assessment can be either empirical data (i.e., actual ingestion rates recorded in scientific studies) or synthesized probability/statistical distributions such as ones estimated from mathematical equations that represent possible distributions of values.

Sensitivity analysis in a deterministic assessment allows the assessor to calculate the contribution of exposure pathways; in other words, each variable is independently changed by the same predetermined amount (e.g., +/- 5%) and the exposure estimate is calculated. Using the results of a sensitivity analysis, a risk assessor can determine which variables have the most influence on the exposure estimate and might choose to find distributions for those variables so that a probabilistic assessment can be conducted. In a probabilistic assessment the sensitivity analysis provides a quantitative ranking of the influence of the variables based on varying multiple variables with probability distributions.
  • Point estimate of exposure
  • Useful for prioritization, ruling out potential exposure pathways, and screening assessments
  • Results are easy to communicate
  • Limited ability to characterize uncertainty and variability
  • Uncertainty and variability characterized using multiple runs of the models
  • Distribution of possible exposure estimates
  • More robust estimate of the range of exposures
  • Used in refined assessments
  • Increased ability to characterize uncertainty and variability
  • Allows for identification of data gaps
Deterministic approaches produce a point estimate of exposure that falls somewhere within the full distribution of possible exposures. Carefully selected input values can provide assessors with meaningful estimates of central tendency or high-end exposures within a defined population. This approach is typically used in screening-level assessments in part due to the relatively economical and straightforward nature of the approach. Further, the results are simple to communicate.

Characterization of uncertainty and variability is limited when using deterministic approaches, but can be approximated by conducting multiple deterministic runs. This gives the assessor an idea of uncertainty and/or variability by evaluating potential exposure based on several point estimates, using inputs from various points on the frequency distribution.

Probabilistic assessments generate a distribution of possible exposure estimates that reflects the combined impact of variability of input parameters (U.S. EPA, 2001). This approach can provide a more comprehensive characterization of variability in exposure or risk estimates and uncertainty in input variables and identifies data gaps that can be evaluated further. Further, the exposure assessor has the ability to better characterize where (in the overall distribution of exposures) a high-end estimate falls (e.g., 90th, 99th, or further in the tail).

Monte Carlo simulations and other probabilistic approaches can provide estimates of exposure, but doing a probabilistic assessment using Monte Carlo techniques may not be necessary in situations where risk or costs of remediation are low. Typically, stressors, exposure pathways, and receptors of highest potential concern are selected for a probabilistic approach to conserve resources.

More effort is required by exposure assessors to communicate the methodology and results from a probabilistic assessment. Complexities of probabilistic approaches might obscure important assumptions or errors in basic exposure or risk models. Further, a probabilistic estimate is only as good as the underlying parameter distributions. If low quality data are used or important correlations are not accounted for, the results will be less informative.

Top of Page

Tools for Developing Probabilistic Assessments

The tools in this table are all informational resources for developing probabilistic assessments. Tools for deterministic approaches are included in other EPA-Expo-Box tool sets.

Top of Page

Jump to main content.