Please suggest the solutions a to e (attachments provided).

2. rI'welve separate case-control studies were run to investigate the potential link between presence of a certain genetic trait {the PlM polymorphism of the glycoprotein IlIa subunit of the brinogen receptor} and risk of heart attackEl For the jth study, an estimated logodds ratio, 19;, and its {estimated} standard error, 03-, 1were computed: vii-i Hi i i if}: 52' :i lbj 0:: 1 LESS [1.373 5 1.4368 [L471 9 [LEDT D. 186 2 one? one a once o.12o 1o anon 0.328 3 i 0.229 1" 4.1117 {1220' 11 H.385 GED-E 4 I].I]1'T I111? s o.331 ones 12 n.4o5 o.254 Consider this Bayesian hierarchical model: If): I a; N inden- Maa-,0?) j=1,...,12 a; I imcg ~ iid Mama) 3': 1,...,12 on m Monaco?) on N U{U,1D[II]) with an and on. independent, and the values erg, j = 1, . . . , 12, regarded as xed and known. {a} I2 ptsl Specify immper densities that the proper hyperpriors given above appear to be apprcodmating. {Which parameters are the hyperparameters'f] {b} [5 pts} Draw a directed acych graph [DAG]- appropriate for this model. [Use the notation introduced in lecture, including \"plates.\"} You may draw it neatly by hand or use software {c} [5 pts] Using the template aagntaanplano. bug pmided on the worse website, form a JAGS model statement [corresponding to your graph}. Mao, set up any R {rjags} statements appropriate for creating a JAGS model. [Rememberi JAGS \"Guam" uses precisions, not variances]: {d} [5 ptsI Run at least llltl iterations of burnin, then IEIJIII} iterations to use [or inference. For both 1,1111]. and 03 [not an}, produce a posterior numerical summary and also graphical estimates of the posterior densitiu. Emir'citiy give the approximations of the posterior expected values, posterior standard deviations, and IE?!) central posterior intervals. [Just showing 5'. output is not enough!) {e} Suppose a new casemntrol study is to be performedr and assume that its logodds standard error {new or] will be 11.2. {Assume the u': for the new study is exchangeable with those for the previous studies} {i} [2 pts] lie-draw your [32'thr adding new nodes to represent the new if? and iii. Conespondingly modify your JAGS model to answer the following parts. [Show the modied JAGS and R code and output that you used} |[iiJ'|I [3 pts] Estimate the posterior mean and pcsterinr standard deviation, and form a 95% central posterior predictive interval for the eatirnatei log-edit ratio that the new study will obtain. (Remember, this new estimated logodds ratio will he a new value of ll, out of u'rj l[iii]I [2 pts] Estimate the posterior predictive probability that the new estimatei log-odds ratio will be at least twice its standard error, i.e., at least two standard errors {Ear} greater than zero. {This is roughly the probability that the study will nd a statistically signicant result, and in the podtive direction] Suggestion: Add an indicator variable to your JAGS model one that equah 1 when the event occurs, and {l otherwise. {'What is its mean?)