2 Full Days
This course introduces fundamental statistical concepts associated with probabilistic risk assessment and probability bounds analysis.

This course can be customized to support the specific needs of your organization. Please contact the course coordinator to inquire about the procedure for teaching the course at your facility.

Overview
Students will learn how variability and uncertainty can be incorporated into human health and ecological risk assessment, using Monte Carlo analysis and P-bounds analysis. Important modeling assumptions are presented in clear and understandable terms.

Introductory topics include selecting and fitting distributions, combining point estimates and distributions in simulations of variability, and using sensitivity analysis to identify key variables and parameter estimates. More advanced topics are also presented, including MicroExposure event analysis, combining variability and uncertainty in two-dimensional Monte Carlo analysis, and developing preliminary remediation goals based on post-remediation contaminant concentrations.

Students will receive hands-on training with commercial spreadsheet software, such as Crystal Ball^® and Riskcalc. Using practical examples, this course is designed to demonstrate both the utility and the limitations of Monte Carlo analysis as a tool for quantifying variability and uncertainty. The instructors will draw on their experience in supporting the U.S. EPA's Superfund Office.

Who Should Attend?
Human health and ecological risk assessors who are developing or reviewing Monte Carlo models; risk managers responsible for making site decisions and communicating risks to the public; toxicologists, scientists, and engineers interested in quantitative uncertainty analysis.

Course Outline
Day 1

• Introduction
• Basic Concepts of Probabilistic Modeling
  • Variability and Uncertainty
  • Point Estimates and Probability Distributions
  • Role of Uncertainty Analysis
• Selecting and Parameterizing Distributions
  • Tiered Approach
  • Maximum Entropy Methods
  • Families of PDFs
  • Goodness-of-Fit tests and Graphical Methods
• Hands-on Introduction to Software
  • Crystal Ball
    • Monte Carlo Analysis
    • Specifying Inputs and Evaluating Outputs
  • RiskCalc
    • Probability Bounds Analysis
    • Interval Analysis and Probability Theory
    • Generating and Interpreting P-boxes
• Closer Look at Monte Carlo Simulation
  • How many iterations?
  • Truncation of PDFs
  • Empirical Distribution Function
  • Sensitivity Analysis
• Case Study on Variability
  • Point Estimates and Probabilistic Estimates
  • Monte Carlo and P-bounds
  • Correlations and Dependencies
  • Microexposure Analysis

Day 2

• Tools for Characterizing Uncertainty – Monte Carlo
  • Distinction between Variability and Uncertainty
  • 2-D MCA
  • Parametric Uncertainty with Bootstrap Simulation, and Excel Toolkit
• Tools for Characterizing Uncertainty – P-bounds
  • Sources of Incertitude
  • Statistics for Interval Data
  • Censored Data
• Back-calculation

More Case Studies on Variability and Uncertainty

Instructors
Dr. Philip Goodrum, Syracuse Research Corporation
Dr. Scott Ferson, Applied Biomathematics