BROOKS_GELMAN_STAT

Name

BROOKS_GELMAN_STAT

Purpose

Computes the Brooks-Gelman statistic (i.e., the multivariate Gelman-Rubin statistic as given in Brooks & Gelman 1998) of multiple Markov chains. Uses the within-chain variance and between-chain variance for all parameters to compare convergence of the chains.

Calling Sequence

r_hat = brooks_gelman_stat(chain)

Input

chainint, float, or double array(Nparam, Ntrials, Nparallel)

An ensemble of Markov chains.

Output

r_hatdouble scalar

The Brooks-Gelman statistic of the chains. The \(\sqrt{\hat{R}}\) should be less than or equal to 1.2 if convergence of the chain was sufficiently reached.

References

• Gelman, A., & Rubin, D. B. 1992, StaSc, 7, 457

• Brooks, S. P., & Gelman, A. 1998, Journal of Computational and Graphical Statistics, 7, 434

Modification History

• 2020/06/10: Created (Keith Doore)

• 2022/07/14: Updated documentation and error handling (Keith Doore)