Posterior comparisons: Reconsider the sample survey in Exercise 3.1. Suppose you are interested in comparing the rate of support in that county to the rate in another county. Suppose that a survey of sample size 50 was done in the second county, and the total number of people in the sample who supported the policy was 30. Identify the posterior distribution of θ2 assuming a uniform prior. Sample 5,000 values of each of θ1 and θ2 from their posterior distributions and estimate Pr (θ1 < θ2|the data and prior).
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