statisticalrethinkin..

4.4. ADDING A PREDICTOR 113relative plausibility to each. is means that each combination of α and β has a posteriorprobability. It could be that there are many lines with nearly the same posterior probabilityas the MAP line. Or it could be instead that the posterior distribution is rather narrow nearthe MAP line.So how can we get that uncertainty onto the plot? Together, a combination of α andβ define a line. And so we could sample a bunch of lines from the posterior distribution.en we could display those lines on the plot, to visualize the uncertainty in the regressionrelationship.Let’s do that: sample from the posterior distribution and display a bunch of lines on theplot. What’s nice about working with samples here, as always, is that the samples will retainthe correlation structure of the posterior distribution. So the samples will be correlated inthe right way, and anything we compute from them will also be correlated in the right way.To extract some samples from the model:post