1 Introduction to modeling and simulation
In this unit, you will explore ideas of randomness. Randomness permeates, and is, in fact, fundamental to statistics. You will learn how to use TinkerPlots™ to model several random processes and generate outcomes from those models. By generating data from different models, you will gain experience in considering the variation in outcomes that is produced by these random processes. This consideration will help you understand and overcome many misleading human intuitions about randomness.
You will also be introduced to the Monte Carlo simulation process and learn how to carry out a Monte Carlo simulation using TinkerPlots™. This process allows you to quickly generate multiple data sets from a model in order to carry out hypothetical experiments. For example, we could ask the question: How likely is it to rain three out of the five days on my vacation given a particular forecast? By modeling the forecast and repeatedly generating data for the five days of vacation, we can then answer this question.
Lastly, you will learn how to describe and summarize distributions of data, including summarizing the “typical” value of a distribution and quantifying the variation in a distribution. Together, these help us determine the likely results of a Monte Carlo model.
Outline and goals of Unit 1
The following schematic outlines the course readings and in-class activities for Unit 1.
|1.1 📖 Modeling and simulation|
|1.2 📖 Generating data from models|
|1.3 🔨 Pet factories|
|1.4 📖 Monte Carlo simulation|
|1.5 🔨 Building Monte Carlo simulations|
|1.6 📖 Regularity in randomness|
|1.7 📖 Describing distributions|
|1.8 🔨 Football kicking contest|
|1.9 📖 The mean and standard deviation|
|1.10 🔨 Review activity: Montana political parties|
|1.11 📖 Unit 1 summary|
As you progress through the unit, remember that the modeling process is a creative process that can often be very challenging. At times, this might lead to frustration as you are learning and practicing some of the material. But, as Mosteller et al. (1973) remind us, it is also a profitable experience since, “modeling is not only a technique of statistics…it is a method of study which can be applied in many other fields as well” (p. xii).2
Mosteller, F., Kruskal, W. H., Link, R. F., Pieters, R. S., & Rising, G. R. (1973). Statistics by example: Finding models. Reading, MA: Addison–Wesley.↩︎