(e) Suppose a new case-control study is to be performed, and assume that its log-odds standard error (new 0') will be 0.25. Assume the b for the new study is exchangeable with those for the previous studies. (i) [2 pts] Re-draw your DAG, adding new nodes to represent the new 1,; and new a. (ii) [2 pts] Correspondingly modify your JAGS model to answer the following parts. Show the modied JAGS and R code and output that you used. (iii) [3 pts] Estimate the posterior mean and posterior standard deviation, and form a 95% central posterior predictive interval for the estimated log-odds ratio that the new study will obtain. (Remember, this new estimated log-odds ratio will be the new 1/3, not the new 1/1.) (iv) [1 pt] Estimate the posterior predictive probability that the new estimated log-odds ratio will be at least twice its standard error, i.e., at least two standard errors (20') greater than zero. (This is roughly the posterior probability that the new study will nd a statistically signicant result, and in the positive direction.) Suggestion: Add an indicator variable to your J AGS model one that equals 1 when the event occurs, and 0 otherwise. (What is its mean?) Use at least 10,000 iterations of burn-in, and 100,000 for inference as before