A Wavelet - Based Procedure for Steady - State Simulation Output Analysis

LADA, EMILY KATE. A Wavelet-Based Procedure for Steady-State Simulation Output Analysis. (Under the direction of Dr. James R. Wilson.) The objective of this research is to develop an automated sequential procedure by which an asymptotically valid confidence interval is constructed for the steady-state mean of a simulation output process. This procedure, called WASSP, determines a batch size and a warm-up period beyond which the computed batch means constitute an approximately stationary Gaussian process. WASSP then uses wavelets to approximate the log of the smoothed periodogram of the batch means process, from which an estimate of the steady-state variance constant (SSVC) of the original (unbatched) process is obtained. Together with a sample mean that has been suitably truncated to eliminate initialization bias, the SSVC estimator is used to construct a reliable confidence-interval estimator of the steady-state mean that satisfies a user-specified absolute or relative precision requirement. An extensive performance evaluation includes testing WASSP on a suite of processes that include extreme examples of the warm-up and correlation problems. The results indicate that WASSP is successful in detecting and eliminating initialization bias as well as in constructing an approximately stationary process so that an asymptotically valid confidence interval for the steady-state mean can be generated even if the original process is highly correlated and has a pronounced initial transient period. Furthermore, the performance evaluation also includes a comparison of WASSP to other methods for steady-state output analysis. The results indicate that WASSP is in general a more robust procedure than the other methods, and we believe that WASSP represents an advance in spectral methods for steady-state output analysis. A WAVELET-BASED PROCEDURE FOR STEADY-STATE SIMULATION OUTPUT ANALYSIS