statisticalrethinkin..

4.4. ADDING A PREDICTOR 119stochastic definition in the first line. e Gaussian distribution on the first line tells us thatthe model expects observed heights to be distributed around µ, not right on top of it. Andthe spread around µ is governed by σ. All of this suggests we need to incorporate σ in thepredictions somehow.Here’s how you do it. Imagine simulating heights. For any unique weight value, yousample from a Gaussian distribution with the correct mean µ for that weight, using the correctvalue of σ sampled from the same posterior distributuon. If you do this for every samplefrom the posterior, for every weight value of interest, you end up with a collection of simulatedheights that embody the uncertainty in the posterior as well as the uncertainty in theGaussian likelihood.sim.height