Quantifying Uncertainty in Stochastic Models with Parametric Variability

TL;DR

This paper introduces a novel method combining Karhunen-Loeve decomposition, polynomial chaos, and Bayesian Gaussian processes to efficiently quantify uncertainty in stochastic models, distinguishing between parameter and stochastic sources.

Contribution

The paper presents a new statistical surrogate approach that separates different sources of uncertainty in stochastic models, reducing computational costs and improving interpretability.

Findings

Accurately quantifies uncertainty in a stochastic epidemic model

Surrogate method matches actual model results for key quantities

Separates uncertainty due to parameters and stochastic components

Abstract

We present a method to quantify uncertainty in the predictions made by simulations of mathematical models that can be applied to a broad class of stochastic, discrete, and differential equation models. Quantifying uncertainty is crucial for determining how accurate the model predictions are and identifying which input parameters affect the outputs of interest. Most of the existing methods for uncertainty quantification require many samples to generate accurate results, are unable to differentiate where the uncertainty is coming from (e.g., parameters or model assumptions), or require a lot of computational resources. Our approach addresses these challenges and opportunities by allowing different types of uncertainty, that is, uncertainty in input parameters as well as uncertainty created through stochastic model components. This is done by combining the Karhunen-Loeve decomposition, polynomial chaos expansion, and Bayesian Gaussian process regression to create a statistical surrogate for the stochastic model. The surrogate separates the analysis of variation arising through stochastic simulation and variation arising through uncertainty in the model parameterization. We illustrate our approach by quantifying the uncertainty in a stochastic ordinary differential equation epidemic model. Specifically, we estimate four quantities of interest for the epidemic model and show agreement between the surrogate and the actual model results.