Impact of the prior distribution: you will use Bugs to fit several versions of the varying-intercept model to the radon data using floor as a house-level predictor and uranium as a county-level predictor.

• How do the inferences change if you assign normal prior distributions with mean 5 and standard deviation 1000 to the coefficients for floor and uranium.
• How do the inferences change if you switch to normal prior distributions with mean 0 and standard deviation 0.1?
• Now try normal prior distributions with mean 5 and standard deviation 1.
• Now try t prior distributions with mean 5, standard deviation 1, and 4 degrees of freedom.
  

• Now try Uniform(−100,100) prior distributions, then Uniform(−1,1) prior distributions.
  

• Discuss the impact of the prior distributions on the inferences.