Estimating the Probability that a Simulated

Consider a stochastic simulation experiment that generates v independent vector replications consisting of an observation from each of k systems. Typical system comparisons are based on mean (long-run) performance. However, the probability that a system will actually be the best is sometimes more relevant , and can provide a very diierent perspective than the systems' means. Empirically, we select one system as the best performer (i.e., it wins) on each replication. Each system has an unknown constant probability of winning on any replication and the numbers of wins for the individual systems follow a multinomial distribution. Procedures exist for nding the system with the largest probability of being the best. This paper addresses the companion problem of estimating the probability that each system will be the best. The maximum likelihood estimators (MLEs) of the multinomial cell probabilities for a set of v vector replications across k systems are well known. We use these same v vector replications to form v k unique vectors (termed pseudo-replications) that contain one observation from each system and develop estimators based on All Vector Comparisons (AVC). In other words, we compare every observation from each system with every combination of observations from the remaining systems and select the best performer in each pseudo-replication. AVC provides lower variance estimators of the probability that each system will be the best than the MLEs. We also derive conndence intervals for the AVC point estimators, present a portion of an extensive empirical evaluation and provide a realistic example.