Answer part(b) or part(c), which does not require the data. Would be great if you can solve both!!!!!

The data set loan_data. cav contains data from the year 2018 on the loan status of 6536 personal loans issued in the US states of Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, Vermont. (Note: these 6 states comprise the 'New England' region of the northeastern part of the US). The variable loan status = 1 if the loan is in default, and = 0 otherwise. Treating each loan (as identified by a unique id ) as a 'trial' and 'defaults' as successes, the Binomial sampling model is a natural choice as the sampling distribution for this data. The objective is to learn about the probability of personal loan default , in each New England state, j = 1, ..., 6. (a) [3 marks] Consider a hierarchical Bayesian binomial model to estimate the 0j's. Discuss the advantages and disadvantages of the hierarchical modelling approach in contrast to the common probability model which assumes a common 0 applies to all states, and the separate-probability model which creates six separate Binomial sampling models, one for each state. (b) [1 mark] Let Yy denote the loan status for loan i in state j (i=1,..,n;, where n, is the sample size in state j). We have Y|0, " Binomial (0,). Write down your prior distribution assumption for e;. (c) [1 mark] As we are fitting a hierarchical model, we require a hyperprior distribution on the parameters of the prior distribution you wrote down in part (b). Write down your hyperprior distribution assumption(s). (d) [5 marks] To obtain posterior draws of the parameters in this model, we need to run a Markov Chain simulation. Write out the steps of a Metropolis-Hastings algorithm to be run at each iteration to obtain posterior draws of the parameters of your hierarchical model. (e) [4 marks] Run your Metropolis-Hastings algorithm. Insert your computer code here that you used to run your Metropolis-Hastings algorithm or upload it is a separate (clearly labelled) file. (f) [2 marks] Provide estimates for the loan default rate for each state and corresponding 95% posterior confidence intervals. (g) [1 mark] What was the acceptance rate of your Metropolis-Hastings algorithm? If the acceptance rate is too low or too high, briefly comment on how you could modify the sampling algorithm to improve the acceptance rate