Thus far in your statistical career at Knox College, you have been taught “frequentist statistics.” This is very typical of such undergraduate programs. These methods are called “frequentist” because they are not statements of probability. They are statements of relative frequency. That is, they are only truly valid if the experiment is repeated many times.

In this learning module, you will learn about Bayesian methods. They methods arise from Bayes’ Law, which you experienced (in great detail) in the middle of MATH 321. These methods require the researcher to quantify prior information about the parameter of interest. Then, using Bayes’ Law and our knowledge of distributions, we can update that prior information with observed data to create the new assumed distribution of the parameter. With this distribution, we can actually make statements about probabilities, rather than statements about “confidence” — whatever that means.

Objectives

By the end of this module, the student will

• formulate a prior distribution
• understand the importance of the prior distribution to an Bayesian
• use the structure of the data-generating process to determine the likelihood
• know the importance of the kernel in Bayesian analysis
• determine the posterior distribution of the parameter
• calculate credible intervals and use the odds ratio appropriately
• properly use Bayesian decision theory

Readings

All readings are from our official textbook.

• Sections 11.1 to 11.5
• Guided Thought Questions

Example Scripts

The following R script provide some additional practice in statistical computing. Consider these to be required activities.

• Introduction to Bayes, II

Statistical Computing Activity

• SCA 8: Bayesian Analysis
• This is not submitted. It is only done in class

Assignment

• No assignment for this learning module