Question: 3. (a) Write a program which carries out posterior simulation for the simple probit model of Section 9.3 (or take the program from the website

(a) Write a program which carries out posterior simulation for the simple probit model of Section 9.3 (or take the program from the website associated with this book and make sure you understand it) using an informative Normal prior for þ. Use artificial data to confirm your program is working.

(b) Extend your program of part

(a) to calculate Bayes factors for testing whether individual coefficients are equal to zero using both the Savage–

Dickey density ratio (see Chapter 4, Section 4.2.5) and the Chib method (see Chapter 7, Section 7.5). How many Gibbs sampler replications are necessary to ensure that these two methods give the same estimate of the Bayes factor (to two decimal places)?

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