3.10 Effects of New Data ?

summarize_beta_binomial(alpha = 45, beta = 55, y = 30, n = 50)

##       model alpha beta mean      mode         var         sd
## 1     prior    45   55 0.45 0.4489796 0.002450495 0.04950248
## 2 posterior    75   75 0.50 0.5000000 0.001655629 0.04068942

• A comparison illuminates the polling data’s influence on the posterior model. Mainly, after observing the poll in which 30 of 50 people supported Michelle, the expected value of her underlying support \(\pi\) nudged up from approximately 45% to 50%.