Confidence Interval Estimation for Output of Discrete-Event Simulations Using the Kalman Filter
AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH SCHOOL OF ENGINEERING
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Discrete-event simulation is computer modeling of stochastic, dynamic systems. The Kalman filter is a Bayesian stochastic estimation algorithm. Because of the correlated nature of simulation output, it is difficult to apply the methods of classical statistics directly when constructing confidence intervals of discrete-event simulation parameters. Through the determination of a dynamics equation and application of the Kalman filter to simulation output data, three new confidence interval construction techniques have been developed. One technique obtains an estimate of the mean value and its associated variance from an estimated Kalman filter. The second technique utilizes Multiple Model Adaptive Estimation MMAE techniques to obtain an estimate of the simulation outputs mean value and its associated variance. The third technique also uses MMAE, but constructs a nonsymmetric confidence interval using the final MMAE filter probabilities. The purpose of this research was twofold. The first objective was to explore these new confidence interval construction techniques based on the information provided by Kalman filters. The second objective was to contrast these Kalman filter approaches to several accepted approaches. Both of these objectives were achieved and excellent results were obtained. In particular, a Monte Carlo analysis demonstrated that the third technique produced intervals that achieved nominal coverage rates with, when compared to currently accepted techniques, smaller average half widths and lower variability. Confidence-Intervals, Kalman Filters, Discrete-Event Simulation, Statistical Analysis, Computer Simulation.
- Statistics and Probability
- Operations Research
- Computer Programming and Software