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()