Robust Confidence Bands for Stochastic Processes Using Simulation

TL;DR

This paper introduces a robust optimization method for constructing confidence bands for stochastic processes using simulation, providing accurate coverage with fewer samples and applicability to continuous-time processes.

Contribution

The paper presents a novel, widely applicable optimization-based approach for confidence bands that effectively addresses bias and achieves accurate coverage with fewer simulations.

Findings

Achieves desired coverage with an order-of-magnitude fewer sample paths.

Applicable to continuous-time processes via discretization.

Effective for validating stochastic simulation models.

Abstract

We propose a robust optimization approach for constructing confidence bands for stochastic processes using a finite number of simulated sample paths. Our approach can be used to quantify uncertainty in realizations of stochastic processes or validate stochastic simulation models by checking whether historical paths from the actual system fall within the constructed confidence band. Unlike existing approaches in the literature, our methodology is widely applicable and directly addresses optimization bias within the constraints, producing tight confidence bands with accurate coverage probabilities. It is tractable, being only slightly more complex than the state-of-the-art baseline approach, and easy to use, as it employs standard techniques. Additionally, our approach is also applicable to continuous-time processes after appropriately discretizing time. In our first case study, we show that our approach achieves the desired coverage probabilities with an order-of-magnitude fewer sample paths than the state-of-the-art baseline approach. In our second case study, we illustrate how our approach can be used to validate stochastic simulation models.