This question (Chapter 3 Problem 15) is from Bayesian Data Analysis, 3rd edition, by Gelman et al.It is a problem about a joint distribution from auto-regressive time-series model, y1,y2,….with mean level 0, auto-correlation 0.8, residual standard deviation 1. The normal errors can be written as (yt | yt-1, yt-2, …) ~ N(0.8*yt-1, 1) for all t.Q. what is the distribution of yt given yt-1 and yt+1? (i.e., given the observation ‘before’ and ;after’ yt) ?
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