Parmar, Drupad and Morgan, Lucy and Titman, Andrew and Williams, Richard (2024) Input Uncertainty and Data Collection Problems in Stochastic Simulation. PhD thesis, Lancaster University.
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Abstract
Stochastic simulation is an important tool within the field of operational research. It allows for the behaviour of random real-world systems to be analysed, evaluated, and optimised. It is critical to understand the uncertainty and error in outcomes from simulation experiments, to ensure that decisions are made with appropriate levels of confidence. Frequently, input models that actuate stochastic simulations are estimated using samples of real-world data. This introduces a source of uncertainty into the simulation model which propagates through to output measures, causing an error known as input uncertainty. Input uncertainty depends on the samples of data that are collected and used to estimate the input models for the simulation. In this thesis, we consider problems relating to input uncertainty and data collection in the field of stochastic simulation. Firstly, we propose an algorithm that guides the data collection procedure for a simulation experiment in a manner that minimises input uncertainty. Reducing the uncertainty around the simulation response allows for improved insights to be inferred from simulation results. Secondly, we outline an approach for comparing data collection strategies in terms of the input uncertainty passed to outputs in simulations of viral loads. This represents a different type of data collection problem to the ones usually studied in simulation experiments. Thirdly, we adapt two techniques for quantifying input uncertainty to consider a quantile of the simulation outputs, rather than the mean. Quantiles are regularly used to provide alternative information regarding the simulation outputs relative to the mean, therefore it is equally important to understand the uncertainty of such measures. Finally, we begin to investigate how input uncertainty impacts predictive models fit to simulation data. This relates to the field of simulation analytics, a novel and emergent area of research where the problem of input uncertainty has not previously been examined.