# An Introduction to R

A good intro to R, especially on creating a new dataset.

# Example Bayesian Inference using R and OpenBUGS

1. Open the R console
Go to File/Change dir and set the working directory for R.
2. Use your favorite editor to save the following code as schools.bug in your R working directory.
model {
for (j in 1:J){
y[j] ~ dnorm (theta[j], tau.y[j])
theta[j] ~ dnorm (mu.theta, tau.theta)
tau.y[j] <- pow(sigma.y[j], -2)
}
mu.theta ~ dnorm (0.0, 1.0E-6)
tau.theta <- pow(sigma.theta, -2)
sigma.theta ~ dunif (0, 1000)
}
3. Save this data as schools.dat in your R working directory.
```school estimate sd
A  28  15
B   8  10
C  -3  16
D   7  11
E  -1   9
F   1  11
G  18  10
H  12  18```
4. Go back to the R console and type the following commands.
J <- nrow(schools)
y <- schools\$estimate
sigma.y <- schools\$sd
data <- list (“J”, “y”, “sigma.y”)
inits <- function(){list(theta=rnorm(J,0,100),mu.theta=rnorm(1,0,100),sigma.theta=runif(1,0,100))}
parameters <- c(“theta”, “mu.theta”, “sigma.theta”)
library (“BRugs”)

schools.sim <- bugs (data, inits, parameters, “schools.bug”, n.chains=3, n.iter=1000, program=”openbugs”)

From an example at columbia.edu.

# Bayesian Inference Using R

Here are the steps I took to create an environment for doing Bayesian Inference.