3.3. Simulation-Based Estimation and Prediction

Learning Outcome

Students will be able to use simulation methods to understand the implications of statistical models.

Sample Tasks

• Estimate the probability of an event for a simple probability model from a simulation.

• Assess the accuracy of an estimated probability.

• Estimate the probability of an event in a complex statistical model from a simulation.

• Estimate the conditional probability of one event given another event for models with a single component of variation and for models with more than one component of variation.

• Estimate implications (features) of a statistical model. These features might be a percentile of a distribution for a specified value of the predictor, the regression coefficient itself, or the odds for logistic regression.

• Make a prediction for new data from the model.

[OhioDoHEducation21]

Our first readings, from Computational and Inferential Thinking [ADW21], continue from the readings in Section 3.1. They discuss the simulation of probabilities and conditional probabilities in a fun, real-world problem and then discuss computing and simulating probabilities more generally.

• 9.4. The Monty Hall Problem

• 9.5. Finding Probabilities

Reading Questions

• Should you switch doors?

• If you roll two 6-sided dice, what is the probability that their sum is even?

Our second reading, also from Computational and Inferential Thinking [ADW21], discusses how to use simulations to estimate percentiles.

• 13. Estimation

  • 13.1. Percentiles

Reading Questions

• If 37 people take a test:

  • How many will score less than the median?

  • How many will score less than or equal to the median?

Our third reading, from Learning Data Science [LGN23], discusses simulating the probabilities in a classic model of drawing balls from an urn.

• 3.1. The Urn Model

Reading Question

• What is an urn?