statisticalrethinkin..

262 8. MARKOV CHAIN MONTE CARLO ESTIMATIONDensity0.0 0.2 0.4Density0.0 0.2 0.4 0.6-10 0 10 20alpha0 5 10 15 20sigmaFIGURE 8.8. Prior (dashed) and posterior (blue) for the model with weaklyinformative priors, m8.3. Even with only two observations, the likelihoodeasily overcomes these priors. Yet the model cannot be successfully estimatedwithout them.Overthinking: Cauchy distribution. Need a box on Cauchy? Should explain here that Cauchy inmodel above is half-Cauchy.8.4.4. Non-identifiable parameters. Back in Chapter 5, you met the problem of highly correlatedpredictors and the non-identifiable parameters they can create. Here you’ll see whatsuch parameters look like inside of a Markov chain. You’ll also see how you can repair them,without re-estimating the posterior.To construct a non-identifiable model, we’ll first simulate 100 observations from a Gaussiandistribution with mean zero and standard deviation 1.R code8.13y