Bayesian linear regression with a categorical variable

When the predictor is categorical, such as a binary feature, we would set one parameter for each corresponding category. The following exercise demonstrates such an example.

Exercise 14.5 – Performing Bayesian inference with a categorical variable

In this exercise, we will examine the relationship between am (automatic or manual transmission, a categorical variable) and mpg (miles per gallon, a continuous variable). We will define the mean of the normal likelihood for mpg as a function of am, with a different mean mu[i] for each level of am. We’ll also give mu a normal prior and standard deviation s a uniform prior. Follow the next steps:

1. Specify the aforementioned model architecture, as follows:

   # define the model
   model = "model{
       # Define model for data Y[i]
       for(i in 1:length(Y)) {
         Y[i] ~ dnorm(mu[am[i]+1], s^(-2...