Lecture G3 (2025-10-23) Input Modeling, Part 3 (Parameter Estimation and Goodness of Fit)

In this lecture, we (nearly) finish our coverage of Input Modeling, where the focus of this lecture is on parameter estimation and assessing goodness of fit. We review input modeling in general and then briefly review fundamentals of hypothesis testing. We discuss type-I error, p-values, type-II error, effect sizes, and statistical power. We discuss the dangers of using p-values at very large sample sizes (where small p-values are not meaningful) and at very small sample sizes (where large p-values are not meaningful). We give some examples of this applied to best-of-7 sports tournaments and voting. We then discuss different shape parameters (including location, scale, and rate), and then introduce summary statistics (sample mean and sample variance) and maximum likelihood estimation (MLE), with an example for a point estimate of the rate of an exponential. We introduce the chi-squared (lower power) and Kolmogorov–Smirnov (KS, high power) tests for goodness of fit, but we will go into them in more detail at the start of the next lecture.