Galvao Scheidegger, Anna Paula (2021-07). The Implications of Uncertainty in the Results of Simulation Models and Applications of Entropy Measures as a Method for Uncertainty Quantification in Simulation Models. Doctoral Dissertation.
Thesis
This dissertation explores the use of Shannon's entropy and mutual information to quantify uncertainty and to support experimental planning and parameter selection in simulation models. The implications of uncertainty in the results of simulation models are highlighted through an illustrative example where a queue system is modeled using stationary univariate distributions. In section 2, entropy measures are estimated using histogram-based method with probability density function and discrete empirical distribution. Different number of bins and different normalization methods are investigated. Challenges of working with entropy measures for continuous variables are identified and solutions to these challenges are developed. In section 3, entropy measures are estimated using kernel-based method, k-nearest neighbors, and fuzzy-histogram-based methods. Different parameters of each method, such as bandwidth, number of k-nearest neighbors, and number of bins, are investigated. This section is an extension of section 2. A different solution to handle the challenges of calculating entropy measures for continuous variables is proposed, which has the advantage of being independent of the choice of the number of bins. In section 4, entropy measures are applied to investigate the measures' ability to support input parameter selection and experiment planning in simulation models. By using statistical methods, such as regression analysis and contingency analysis, and by comparing the results of the entropy measures with the results from the standard error of the mean and ANOVA, there is empirical evidence that entropy measures can support the identification of the number of replications that leads to the largest uncertainty and the selection of the most important parameters. With respect to the group of seeds, entropy measures can identify differences among the groups consistently with the standard error of the mean, but not the group of seed that leads to the largest uncertainty. Overall, the experimental results indicate that entropy measures when estimated using the histogram-based method with discrete empirical distribution appear to be capable to support uncertainty quantification, experimental planning, and parameter selection in simulation models. However, there are still open questions about this topic and directions for further research on this area are articulated at the end of this dissertation.
