Chapter 2 Bayes’ Rule

Learning objectives:

• Explore foundational probability tools

  • conditional probability: probability of \(A\) given \(B\), \(P(A|B)\)

  • joint probability: probability of \(A\) and \(B\) occurring together, \(P(A \cap B)\)

  • marginal probability: probability of an event \(A\), \(P(A)\)

  • law of total probability: if a probability of an event \(A\) is unknown it can be calculated using the known probability of other related events such as \(A \cap B\) and \(A|B\)

• Conduct first formal Bayesian analysis

• Practice your Bayesian grammar

  • Prior

  • Likelihood

  • Normalizing constant

• Simulate Bayesian models

  • sample()

  • sample_n()

  • rbinon()