Bayesian Statistics and Decision Analysis

What this unit covers

The resources follow two threads. One is decision analysis: decision alternatives, states of nature, payoffs, payoff tables and expected monetary value. The other is Bayesian thinking: Bayes' theorem, likelihood, prior and posterior ideas, and how Bayesian and null hypothesis testing differ.

Where to start

Begin with the mind map Topic 2. Its objectives cover the rational approach to decision making, satisficing, alternatives to both, calculating and interpreting probabilities, and building and analysing decision trees. It gives you the frame before the detail.

1. Read the mind map Bayesian Theory of Decision for the vocabulary: event, experiment, consequence, a priori and a posteriori.
2. Go through the Decision Theory flashcards, which cover aleatoric and epistemic uncertainty, Type I and Type II errors and risk analysis.
3. Take the quiz Statistics Chapter 17, which tests the three components of a decision: event, act and outcome, along with EMV.
4. Try the quiz Design w TP, a worked problem about choosing between five space shuttle propulsion designs by cost and chance of failure.

Using quizzes and maps together

Use a map to see how ideas connect, then a quiz to check you can apply them. If a question on expected value goes wrong, open the map Expected Value =?? and follow its accept-or-decline offer and purchase cases. The Midterm Flashcards help you recall payoff table structure and which decision criteria are non-probabilistic.

Going further

The Markov Models map compares semi-Markov models with simpler ones, and the MCMC map and the Bayesian Data analysis flashcards take you towards computational Bayesian work. The Module 4 Review quiz looks at decision tree models.

Where it fits

This unit sits in the Statistical Inference strand of Statistics and probability. Pick one resource that matches where you are today and work outwards from there, adding your own notes as you go.