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In convergence diagnosis in WinBUGS/JAGS/Stan, there are different statistics reported for each variable. In WinBUGS/Stan, Rhat ($\hat{R}$) is reported. In JAGS with the runjags package, psrf (Potential Scale Reduction Factor) is reported (it is basically generated by coda::gelman.diag()). Values close to 1 (i.e. < 1.05) are considered to be "good" (i.e. the chains converged).

What is the difference between R hat and psrf?

Tomas
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1 Answers1

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$\hat{R}$ and "potential scale reduction factor" refer to the same thing. See Chapter 6 of the Handbook of Markov Chain Monte Carlo, "Inference from Simulations and Monitoring Convergence" by Andrew Gelman and Kenneth Shirley.

In Stan, the number reported is actually split $\hat{R}$; the calculation of $\hat{R}$ is computed with each of the chains split in half.

Areza
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syclik
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  • Thanks Daniel! What is the point of splitting the chain in half in Stan? Why is it done in Stan and not in WinBUGS/JAGS? – Tomas Nov 25 '14 at 06:33
  • I assume $\hat{R}$ is computed in half-chain, means excluding warm-up steps; that let you do, comparison not only within a Chain, but also across chains. – Areza Apr 26 '16 at 11:02
  • The point of splitting is to handle the cases where the individual chains cover the target distribution, but fail to converge to each other (simply: they wander independently on each othe over the parameter domain). See: A. Gelman, et. al., Bayesian Data Analysis, Third Edition. In the footnote 2, pg. 285, they explicitly address this issue. – Jaromír Adamec Apr 21 '17 at 16:05