Quantifying Uncertainty in Stochastic Models with Parametric Variability
This work addresses the need for efficient uncertainty quantification in simulations for researchers and practitioners, though it appears incremental as it builds on existing techniques like Karhunen-Loeve decomposition and polynomial chaos expansion.
The authors tackled the problem of quantifying uncertainty in stochastic model predictions by developing a method that separates uncertainty from input parameters and stochastic components, and they demonstrated its effectiveness on an epidemic model with agreement between surrogate and actual results.
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.