The prior model

Modeling bayesiano con RJAGS

Alicia Johnson

Associate Professor, Macalester College

Course goals

  • Explore foundational, generalizable Bayesian models (eg: Beta-Binomial, Normal-Normal, and Bayesian regression)

  • Define, compile, and simulate Bayesian models using RJAGS

  • Conduct Bayesian posterior inference using RJAGS output

Modeling bayesiano con RJAGS

Bayesian elections: The prior

Modeling bayesiano con RJAGS

Bayesian elections: The prior

Modeling bayesiano con RJAGS

Bayesian elections: The prior

Modeling bayesiano con RJAGS

Bayesian elections: The data

Modeling bayesiano con RJAGS

Bayesian elections: The posterior

Modeling bayesiano con RJAGS

Bayesian elections: New data

Modeling bayesiano con RJAGS

Bayesian elections: New posterior

Modeling bayesiano con RJAGS

Bayesian elections: Newer data

Modeling bayesiano con RJAGS

Bayesian elections: Newer posterior

Modeling bayesiano con RJAGS

Bayesian thinking

A Bayesian posterior model:

  • Combines insights from the prior model & observed data
  • Evolves as new data come in

Modeling bayesiano con RJAGS

Building a prior model

  • $p$ = proportion that support you
  • $p$ is between 0 and 1
  • The prior model for $p$ is a Beta distribution with shape parameters 45 and 55

$$p \sim \text{Beta}(45, 55)$$

Modeling bayesiano con RJAGS

Tuning the prior

Modeling bayesiano con RJAGS

Let's practice!

Modeling bayesiano con RJAGS

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