3.1. Statistical Model

Learning Outcome

Students will be able to write and implement generative models for situations ranging from simple one-sample problems to more complex settings.

Sample Tasks

• Generate data from standard probability distributions such as the binomial distribution, the Poisson distribution, the normal distribution, and the gamma distribution.

• Draw a graphic (histogram / density estimate) to describe a sample of data.

• Write a statistical model that includes both structured components and stochastic components such as a simple linear regression model with normal errors, a multiple linear regression model, or a logistic regression model.

• Generate data from a complex statistical model.

• Write a statistical model that includes more than one stochastic component such as a mixed model for linear regression.

[OhioDoHEducation21]

Our first readings, from Computational and Inferential Thinking [ADW21], discuss ideas of randomness and generating data from a distribution using a simulation.

• 9. Randomness

  • 9.1. Conditional Statements

  • 9.2. Iteration

  • 9.3. Simulation

Reading Question

• One of the examples generates the number of Heads in 100 coin tosses. Which of the follow distributions does this number follow?

  • Binomial distribution

  • Poisson distribution

  • Normal distribution

  • Gamma distribution

Our second readings, also from Computational and Inferential Thinking [ADW21], discuss generating a distribution from data using sampling.

• 10. Sampling and Empirical Distributions

  • 10.1. Empirical Distributions

  • 10.2. Sampling from a Population

Reading Questions

• What does it mean for a distribution to be empirical?

• What is the Law of Averages?