2. Small Worlds and Large Worlds

Overview

Fast and frugal in the large world

• 2.1 The garden of forking data

  • 2.1.1 Counting possibilities

    • Justification

  • 2.1.2 Using prior information

    • Original ignorance

  • 2.1.3 From counts to probability

    • Randomization

• 2.2 Building a model

  • 2.2.1 A data story

    • The value of storytelling

  • 2.2.2 Bayesian updating

    • Sample size and reliable inference

  • 2.2.3 Evaluate

    • Deflationary statistics

• 2.3 Components of the model

  • 2.3.1 Likelihood

    • Names and probability distributions

    • A central role for likelihood

  • 2.3.2 Parameters

    • Datum or parameter?

  • 2.3.3 Prior

    • Prior as probability distribution

    • Prior, prior pants on fire

  • 2.3.4 Posterior

    • Bayesian data analysis isn’t about Bayes’ theorem

• 2.4 Making the model go

  • How you fit the model is part of the model

  • 2.4.1 Grid approximation

    • Vectorization

  • 2.4.2 Quadratic approximation

    • Maximum likelihood estimation

    • The Hessians are coming

  • 2.4.3 Markov chain Monte Carlo

• 2.5 Summary