statisticalrethinkin..

12.3. VARIABLE PROBABILITIES: BETA-BINOMIAL 323Density0 2 4 6FIGURE 12.3. Estimated distributionof survival probabilities (blacklines) over the empirical distributionof survival proportions (blue),for the tadpole data. Dashed curvesshow 95% percentile confidence intervalof the Beta density estimates,sampled from the posterior.0.2 0.4 0.6 0.8 1.0proportion survivingθ (α + β). So when we characterize the posterior distribution of the beta distribution, wehave to account for the covariance between these two parameters. at is, we aren’t going tocompute a confidence interval for each or either parameter, but rather for the distributionimplied by correlated samples of both parameters. Weird to say, but the code will make iteasier to understand. Here’s how we do it:p.seq