In this lecture, we outline the structure and purpose of IEE 475 (Simulating Stochastic Systems) for the Fall 2024 semester at Arizona State University. We go over topics covered in the syllabus and on the course learning management system website.

In this lecture, we prepare for the final exam and give a brief review of all topics from the course.

In this lecture, we wrap up the course content in IEE 475. We first do a quick overview of the four variance reduction techniques (VRT's) covered in the previous unit. That is, we cover: common random numbers (CRN's), antithetic variates (AV's), importance sampling, and control variates. We then  remember some general comments about the goal of modeling and commonalities seen across simulation platforms (as well as the different types of simulation platforms in general).

In this lecture, we start by reviewing approaches for absolute and relative performance estimation in stochastic simulation. This begins with a reminder of the use of confidence intervals for estimation of performance for a single simulation model. We then move to different ways to use confidence intervals on mean DIFFERENCES to compare two different simulation models. We then move to the ranking and selection problem for three or more different simulation models, which allows us to talk about analysis of variance (ANOVA) and post hoc tests (like the Tukey HSD or Fisher's LSD). After that review, we move on to introducing variance reduction techniques (VRTs) which reduce the size of confidence intervals by experimentally controlling/accounting for alternative sources of variance (and thus reducing the observed variance in response variables). We discuss Common Random Numbers (CRNs), which use a paired/blocked design to reduce the variance caused by different random-number streams. We start to discuss control variates (CVs), but that discussion will be picked up at the start of the next lecture.

In this lecture, we review what we have learned about one-sample confidence intervals (i.e., how to use them as graphical versions of one-sample t-tests) for absolute performance estimation in order to motivate the problem of relative performance estimation. We introduce two-sample confidence intervals (i.e., confidence intervals on DIFFERENCES based on different two-sample t-tests) that are tested against a null hypothesis of 0. This means covering confidence interval half widths for the paired-difference t-test, the equal-variance (pooled) t-test, and Welch's unequal variance t-test. Each of these different experimental conditions sets up a different standard error of the mean formula and formula for degrees of freedom that are used to define the actual confidence interval half widths (centered on the difference in sample means in the pairwise comparison of systems). We then generalize to the case of more than 2 systems, particularly for "ranking and selection (R&S)." This lets us review the multiple-comparisons problem (and Bonferroni correction) and how post hoc tests (after an ANOVA) are more statistically powerful ways to do comparisons.

In this lecture, we start by further reviewing confidence intervals (where they come from and what they mean) and prediction intervals and then use them to motivate a simpler way to determine how many replications are needed in a simulation study (focusing first on transient simulations of terminating systems). We then shift our attention to steady-state simulations of non-terminating systems and the issue of initialization bias. We discuss different methods of "warming up" a steady-state simulation to reduce initialization bias and then merge that discussion with the prior discussion on how to choose the number of replications. In the next lecture, we'll finish up with a discussion of the method of "batch means" in steady-state simulations.

In this lecture, we review estimating absolute performance from simulation, with focus on choosing the number of necessary replications of transient simulations of terminating systems. The lecture starts by overviewing point estimation, bias, and different types of point estimators. This includes an overview of quantile estimation and how to use quantile estimation to use simulations as null-hypothesis-prediction generators. We the introduce interval estimation with confidence intervals and prediction intervals. Confidence intervals, which are visualizations of t-tests, provide an alternative way to choose the number of required replications without doing a formal power analysis.

In this lecture, we introduce the estimation of absolute performance measures in simulation – effectively shifting our focus from validating input models to validating and making inferences about simulation outputs. Most of this lecture is a review of statistics and reasons for the assumptions for various parametric and non-exact non-parametric methods. We also introduce a few more advanced statistical topics, such as non-parametric methods and special high-power tests for normality. We then switch to focusing on simulations and their outputs, starting with the definition of terminating and non-terminating systems as well as the related transient and steady-state simulations. We will pick up next time with discussing details related to performance measures (and methods) for transient simulations next time and steady-state simulations after that. Our goal was to discuss the difference between point estimation and interval estimation for simulation, but we will hold off to discuss that topic in the next lecture.

In this lecture, we review statistical fundamentals – such as the origins of the t-test, the meaning of type-I and type-II error (and alternative terminology for both, such as false positive rate and false negative rate) and the connection to statistical power (sensitivity). We review the Receiver Operating Characteristic (ROC) curve and give a qualitative description of where it gets its shape in a hypothesis test. We close with a validation example (from the previous lecture) where we use a power analysis on a one-sample t-test to help justify whether we have gathered enough data to trust that a simulation model is a good match for reality when it has a similar mean output performance to the real system.

In this lecture, we mostly cover slides from Lecture G3 (on goodness of fit) that were missed during the previous lecture. In particular, we review hypothesis testing fundamentals (type-I error, type-II error, statistical power, sensitivity, false positive rate, true negative rate, receiver operating characteristic, ROC, alpha, beta) and then go into examples of using Chi-squared and Kolmogorov–Smirnov tests for goodness of fit for arbitrary distributions. We also introduce Anderson–Darling (for flexibility and higher power) and Shapiro–Wilk (for high-powered normality testing). We close with where we originally intended to start – with definitions of testing, verification, validation, and calibration. We will pick up from here next time.