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8.4. CARE AND FEEDING OF YOUR MARKOV CHAIN 261FIGURE 8.7. Diagnosing and healing a sick Markov chain. Le: Trace plotfrom two independent chains defined by model m8.2. ese chains are notstationary and should not be used for inference. Right: Adding weakly informativepriors (see m8.3) clears up the condition right away. ese chainsare fine to use for inference.chains=2 , iter=1e4 , warmup=1000 )precis(m8.3)Mean StdDev lower 0.95 upper 0.95a 0.02 1.78 -3.34 3.56sigma 2.03 2.19 0.42 5.28at’s much better. Take a look at the righthand panel in FIGURE 8.7. is trace plot lookshealthy. Both chains are stationary around the same values, and mixing is excellent. No morewild detours off to negative 30-million.To appreciate what has happened, take a look at the priors (dashed) and posteriors (blue)in FIGURE 8.8. Both the Gaussian prior for α and the Cauchy (KO-shee) prior for σ containvery gradual downhill slopes. ey are so gradual, that even with only two observations, asin this example, the likelihood almost completely overcomes them. e mean of the priorfor α is 1, but the mean of the posterior is zero, just as the likelihood says it should be. eprior for σ is maximized at zero. But the posterior has its median around 1.4. e standarddeviation of the data is 1.4.ese weakly informative priors have helped by providing a very gentle nudge towardsreasonable values of the parameters. Now values like 30-million are no longer equally plausibleas small values like 1 or 2. Lots of problematic chains want subtle priors like these,designed to tune estimation by assuming a little but of prior information about each parameter.And even though the priors end up getting washed out right away—two observationswere enough here—they still have a big effect on inference, by allowing us to get an answer.at answer is also a good answer.