rank-based convergence metrics

[bob-carpenter]

Feature Request

Add rank-based version of R-hat for robust trunk and tail convergence diagnostics.

Motivation

Converting numerical values to ranks leads to a more robust R-hat, particularly for heavy-tailed distributions. Furthermore, Aki figured out how to evaluate convergence of tail quantiles, as well. We've converted to this analysis as default output for RStan 2.19, which was just released a few days ago. We haven't eliminated the ability to return the old mean-based metrics.

Reference

• Aki Vehtari, Andrew Gelman, Daniel Simpson, Bob Carpenter, Paul-Christian Bürkner. 2019. Rank-normalization, folding, and localization: An improved R-hat for assessing convergence of MCMC. arXiv preprint arXiv:1903.08008.

[joethorley]

@bob-carpenter Thanks for the interest - will do when I get a chance later in the summer