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2. [11 pts] Twelve separate case-control studies were run to investigate the potential link between presence ofa certain genetic trait [the
(a) Draw a directed acyclic graph (DAG) appropriate for this model. (Use the notationintroduced in lecture, including “plates”.)
(b) Using the template prob2template.txt provided on the Compass course web site, forman OpenBUGS model statement (corresponding to your graph). Also, set up statementsappropriate for loading the data into OpenBUGS.
[ Remember: OpenBUGS “dnorm”uses precisions, not variances! ]1From Burr, et al. (2003), Statistics in Medicine, 22: 1741–1760.
(c) Perform a preliminary run of your model using OpenBUGS, to check for convergence ofyour sampler. Use three chains, separately initialized. Include the lists of the initialvalues you used. Show the plots you used to monitor convergence. Determine how manyiterations to burn (i.e. exclude from inference).
(d) Perform at least 100000 iterations (after burn-in), and produce a summary of yourinference results, for both ψ0 and σ20. Be sure to include estimates of the posteriorexpected value and standard deviation, the Monte Carlo error, a 95% posterior credibleinterval, and graphical estimates of the densities.
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