Conclusion

Bayesian Modeling with RJAGS

Alicia Johnson

Associate Professor, Macalester College

Bayesian modeling with RJAGS

Define, compile, & simulate intractable Bayesian models.
Explore the Markov chain mechanics behind RJAGS simulation.

The power of Bayesian modeling

Combine insights from your data and priors to inform posterior insights.

The power of Bayesian modeling

Combine insights from your data and priors to inform posterior insights.
Conduct intuitive posterior inference: posterior credible intervals & probabilities.

Foundational, flexible, & generalizable Bayesian models

my_model <- "model{
  # Likelihood model
  for(i in 1:length(Y)) {
    Y[i] ~ dnorm(m, s^(-2))
  }

  # Prior models
  m ~ dnorm(...)
  s ~ dunif(...)
}"

Foundational, flexible, & generalizable Bayesian models

my_model <- "model{
  # Likelihood model
  for(i in 1:length(Y)) {
    Y[i] ~ dnorm(m[i], s^(-2))
    m[i] <- a + b * X[i]
  }

  # Prior models
  a ~ dnorm(...)
  b ~ dnorm(...)
  s ~ dunif(...)
}"

Foundational, flexible, & generalizable Bayesian models

my_model <- "model{
  # Likelihood model
  for(i in 1:length(Y)) {
    Y[i] ~ dnorm(m[i], s^(-2))
    m[i] <- a + b[X[i]]
  }

  # Prior models
  a ~ dnorm(...)
  b[1] <- 0
  b[2] ~ dnorm(...)
  s ~ dunif(...)
}"

Foundational, flexible, & generalizable Bayesian models

my_model <- "model{
  # Likelihood model
  for(i in 1:length(Y)) {
    Y[i] ~ dnorm(m[i], s^(-2))
    m[i] <- a + b[X[i]] + c * Z[i]
  }
  # Prior models
  a ~ dnorm(...)
  b[1] <- 0
  b[2] ~ dnorm(...)
  c ~ dnorm(...)
  s ~ dunif(...)
}"

Foundational, flexible, & generalizable Bayesian models

my_model <- "model{
 # Likelihood model
 for(i in 1:length(Y)) {
 Y[i] ~ dpois(l[i])
 log(l[i]) <- a + b[X[i]] + c*Z[i]
 }
 # Prior models
 a ~ dnorm(...)
 b[1] <- 0
 b[2] ~ dnorm(...)
 c ~ dnorm(...)
}"

Thank you!

Bayesian Modeling with RJAGS