Posterior distribution characterization for Binomial inference

Because the salary is a scale variable, the procedure first dichotomizes the variable (based on the condition whether Salary≥$50,000 as the cut point value specified in the syntax), and then conducts the Bayesian inference about the proportion of Salary≥$50,000. Under the uniform prior, the estimated posterior mode and mean are 0.152 and 0.153, respectively, both of which are very close to the observed proportion 72/474 = 0.152.

Given the observed data, the credible interval (0.122,0.187) gives the area that has a 95% Bayesian coverage for the proportion of Salary≥$50,000. The posterior distribution plot illustrates the entire information about the proportion given the observed data. A peak around 0.152 can be clearly observed.