Lecture I (2020-10-29): Statistical Reflections

 In this lecture, we review the basics of hypothesis testing (type-I error, type-II error, statistical power) and the fundamental processes underlying hypothesis testing that create relationships among these things. We then dig deeper into the assumptions necessary for using parametric tests, like the Student's t-test, and non-exact parametric tests, like the Chi-square test (e.g., what the "continuity assumption" is with regard to the Chi-square test and the related inference).

Lecture H (2020-10-27): Verification, Validation, and Calibration of Simulation Models

In this lecture, we revisit some basics of hypothesis testing and then go on to introduce verification, validation, and calibration in the context of simulation models. This will ultimately move us away from goodness-of-fit tests of input models toward hypothesis tests of output performance (e.g., to detect differences from different simulations scenarios and confirm that simulations of real-world scenarios match our expectations from real-world data).

Lecture G3 (2020-10-22): Input Modeling, Part 3

In this lecture, we continue our discussion of statistically rigorous methods for input modeling in simulation of stochastic systems. We first cover the basics of hypothesis testing, including a review of type-I error (alpha), p-values, and how they relate to critical values for goodness-of-fit tests (like Chi-squared and KS). We then review Q-Q and P-P probability plots to identify candidate families for input models from collected data. Then we discuss how maximum likelihood estimation (MLE) provides a bridge from summary statistics to mathematically justifiable choices for parameter values of the distributions we have chosen. Next time, we will discuss Chi-square testing and KS testing as applied to general probability distributions (i.e., not just as tests for uniformity).

Lecture G2 (2020-10-20): Input Modeling, Part 2

This is the second part in a unit on input modeling for simulating stochastic systems (stochastic simulation). In the this part, we describe how to start making sense of data collected from real-world systems. We start with an example that builds a model of a single-server, single-channel queue based on summary statistics alone and demonstrate that the resulting model is a poor fit for a realistic system. We then use a histogram to reveal insights into how the system can be re-structured to be more realistic while also requiring simpler input models. This leads into a discussion on building histograms to be maximally insightful.

Lecture F2 (2020-10-13): Review Before Midterm Retake

In this lecture period, we discuss student-generated questions as a means of reviewing for the upcoming midterm retake. Most of the discussion centers around the solution set from the first midterm.

Lecture G1 (2020-10-08): Input Modeling, Part 1

In this lecture, we re-motivate the topic of Input Modeling in stochastic simulation. Input modeling is the process of choosing probabilistic models to represent realistic variation that is statistically similar to measured data even though the probabilistic models leave out the real-world details underlying that variation. This lecture focus primarily on issues relating to collecting data (when to use old data, issues related to data censoring, issues related to correlated variables, issues related to multi-modal distributions, etc.).

Lecture F (2020-10-01): Midterm Review

Midterm review lecture for Fall 2020. Starts with an introduction to inverse-transform sampling for discrete random variables (including sampling from empirical CDF's).