Lecture L: Course Wrap Up (2019-11-26) – VRT Summary and Closing Course Comments

This lecture opens with a visual summary of four popular variance reduction techniques (VRTs), namely: common random numbers (CRN), antithetic variates (AV), importance sampling, and control variates. It then closes with a few concluding remarks about the IEE 475 course.

Lecture K2: Variance Reduction Techniques, Part 2 (2019-11-21) – Antithetic Variates and Importance Sampling

This lecture covers Variance Reduction Techniques (VRT) for stochastic simulation, covering: Common Random Numbers (CRNs), Control Variates (CVs), Antithetic Variates (AVs), and Importance Sampling. The lecture mainly focuses on AVs and Importance sampling with an overview of CRN and CV topics covered in Part 1 of this lecture.

Lecture K1: Variance Reduction Techniques, Part 1 (2019-11-19) – CRN and Control Variates

This lecture introduces the use of Variance Reduction Techniques (VRT), which combine tools from statistical experiment design with the idiosyncrasies of stochastic simulation studies to reduce the number of replications needed to make inferences by controlling sources of variance. This lecture primarily focuses on Common Random Numbers (CRN) and Control Variates.

Lecture J4: Estimation of Relative Performance (2019-11-14)

In this lecture, we solidify our geometric understanding of a confidence interval and further reinforce why interval estimation should always be preferred over point estimates. Some linear regression examples (with confidence intervals on regression coefficients) are demonstrated using data from the scientific literature. We then cover how to generate confidence intervals for 2-sample tests and use those pairwise confidence intervals with other techniques to do ranking and selection of more than 2 models within a simulation study. Thus, the main focus of this lecture is methods for comparing and contrasting among two-to-many simulation models.

Lecture J3: Estimation of Absolute Performance, Part 3 - Steady-State Simulations (2019-11-12)

This lecture stresses the importance of interval estimation over point estimation and demonstrates both how to interpret interval estimates as well as how the size of the intervals will change with sampling and variance parameters. It then concludes with discussion of how to avoid initialization bias in steady-state simulation models of non-terminating systems, making use of intelligent initialization, warm-up periods, and batch means.

Lecture J2: Estimation of Absolute Performance, Part 2 - Transient Simulations (2019-11-07)

This lecture reviews content from Lecture J1 on point estimators, estimator bias, interval estimation of means and quantiles, and the relationship between confidence intervals on means and t-tests. It also gives an introduction to data output facilities in Arena for stochastic simulation.

Lecture J1: Estimation of Absolute Performance, Part 1 (2019-11-05)

This lecture re-hashes the rationale behind the Student's t-test, the Chi-squared test, and methods in hypothesis testing in general (both parametric and non-parametric). It then discusses issues in taking data both across simulation replications and within simulation replications and introduces the concepts of non-terminating systems (and their steady-state simulation models) and terminating systems (and their transient simulation models). Finally, how these ideas are implemented in Arena is demonstrated. The rest of the Arena demonstration will be continued in the next lecture.