IEE 475: Simulating Stochastic Systems

Theodore P. Pavlic
  • 0,0 (0)
  • CORSI
  • BISETTIMANALE

Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic

  1. 02/12/2025

    Lecture M (2025-12-02): Final Exam Review

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

  2. 25/11/2025

    Lecture K2 (2025-11-25): Variance Reduction Techniques, Part 2 (Antithetic Variates and Importance Sampling)

    In this lecture, we review four different Variance Reduction Techniques (VRT's). Namely, we discuss common random numbers (CRNs), control variates, antithetic variates (AVs), and importance sampling. Each one of these is a different approach to reducing the variance in the estimation of relative or absolute performance of a simulation model. Variance reduction is an alternative way to increase the power of a simulation that is hopefully less costly than increasing the number of replications. We wrap up with a summary of the four VRT's that we have discussed in the class – Common Random Numbers (CRN's), Antithetic Variates (AV's), Importance Sampling, and Control Variates.

  3. 21/11/2025

    Lecture K1 (2025-11-20): Variance Reduction Techniques, Part 1 (CRNs and Control Variates)

    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, and then we introduce control variates (CVs), which allow for reducing the output variance of a measurement by leveraging information about other sources that may be corrupting the output.

  4. 19/11/2025

    Lecture J4 (2025-11-19): Estimation of Relative Performance

    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). Next time, we will generalize to the case of more than 2 systems, particularly for "ranking and selection (R&S)." That will let 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.

  5. 13/11/2025

    Lecture J3 (2025-11-13): Estimation of Absolute Performance, Part III (Non-Terminating Systems/Steady-State Simulations)

    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.

  6. 07/11/2025

    Lecture J2 (2025-11-06): Estimation of Absolute Performance, Part II (Terminating Systems/Transient 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.

  7. 04/11/2025

    Lecture J1 (2025-11-04): Estimation of Absolute Performance, Part I (Introduction to Point and Interval Estimation)

    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.

  8. 30/10/2025

    Lecture I (2025-10-30): Statistical Reflections

    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 Lecture H) 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. Peppered throughout the lecture are also comments about why normality is required for t-tests, why there is a minimum expected count for chi-squared tests, and how to avoid statistical inference issues when making multiple comparisons.

Elenco completo (25)

Descrizione

Archived lectures from undergraduate course on stochastic simulation given at Arizona State University by Ted Pavlic

Informazioni

  • Creatore
    Theodore P. Pavlic
  • Anni di attività
    2019 - 2025
  • Puntate
    25
  • Classificazione
    Contenuti adatti a tutti
  • Copyright
    © Copyright (c) 2019 by Theodore P. Pavlic
  • Sito web del podcast
    IEE 475: Simulating Stochastic Systems