1. Reconduct the final normal distribution example again with an MH algorithm. Use good starting values this time, but run the algorithm at least seven times using different widths for the proposal distribution for the means. Can you develop a rule (for this model) for determining the appropriate proposal density width/variance given a desired acceptance rate?
1.Generate 100 observations from a normal distribution with a mean of 5 and variance of 4, as in the example. Now square these values, assume they come from a normal distribution, and estimate the parameters for this normal distribution using either a Gibbs sampler or an MH algorithm. Next, use posterior predictive simulation to determine whether the model fits the data. Does it?
