statisticalrethinkin..

66 3. SAMPLING THE IMAGINARYDensity0.000 0.001 0.002 0.003 0.00450% Percentile Interval0.00 0.25 0.50 0.75 1.00proportion water (p)Density0.000 0.001 0.002 0.003 0.00450% HPDI0.00 0.25 0.50 0.75 1.00proportion water (p)FIGURE 3.3. e difference between percentile and highest posterior densityconfidence intervals. e posterior density here corresponds to a flatprior and observing three water samples in three total tosses of the globe.Le: 50% percentile interval. is interval assigns equal mass (25%) to boththe le and right tail. As a result, it omits the most probable parameter value,p = 1. Right: 50% highest posterior density interval, HPDI. is intervalfinds the narrowest region with 50% of the posterior probability. Such aregion always includes the most probable parameter value.(flat) prior. It is highly skewed, having its maximum value at the boundary, p = 1. You cancompute it, via grid approximation, with:R code3.11p_grid