Sensitivity analysis and estimation of extreme tail behavior in two-dimensional Monte Carlo simulation

Area of Science:

• Computational statistics
• Probabilistic risk assessment
• Extreme value theory

Background:

• Two-dimensional Monte Carlo simulation is standard for probabilistic risk models, quantifying uncertainty and variability.
• Estimating the proportion of a variable population exceeding a threshold, along with its uncertainty, is a common challenge.
• Conventional algorithms for these estimations can be computationally intensive.

Purpose of the Study:

• Introduce a novel, efficient method for estimating population risk proportions and associated uncertainties.
• Develop a technique to rapidly identify model parameters significantly impacting rare event probabilities.
• Demonstrate the practical application and efficiency gains of the new method.

Main Methods:

• Combines extreme value theory and Bayesian analysis of computer models.
• Applies a new algorithm for efficient estimation of risk proportions and parameter sensitivity.
• Utilizes sensitivity analysis (SA) to pinpoint influential model inputs.

Main Results:

• The new method accurately estimates risk proportions and identifies key parameters much more efficiently than conventional algorithms.
• Sensitivity analysis successfully identified the two most impactful parameters for rare event probabilities in a microbial contamination model.
• The new approach achieved results comparable to conventional simulation but in 43 seconds versus over 3 days.

Conclusions:

• The developed method offers a significant computational advantage for probabilistic risk modeling, particularly for rare events.
• This efficient approach facilitates rapid identification of critical model parameters, aiding in risk management and model refinement.
• The technique is validated through both exact and realistic microbial contamination models, demonstrating its practical utility.