Achieve full convergence of the PSR J1640+2224 Bayesian timing analyses

Achieve full MCMC convergence for the non-converged Bayesian timing analyses of PSR J1640+2224, particularly the model B analyses of the NANOGrav 5-year and 12.5-year datasets and the relevant analyses whose autocorrelation lengths remain excessive, so that the resulting timing-parameter distributions can be reliably characterized.

Background

The paper applies fully generalized Bayesian timing models to PSR J1640+2224 using the NANOGrav 5-year, 9-year, and 12.5-year datasets. The authors assess convergence using a Gelman–Rubin split R-hat statistic below 1.1 and autocorrelation lengths below 200. They report that the model C analyses for the 5-year and 12.5-year datasets meet these standards, whereas several model B analyses do not; the 9-year analyses have acceptable R-hat values but autocorrelation lengths above the stated threshold.

The lack of convergence is consequential because model B directly numerically marginalizes the full timing model, and the authors caution that its posterior distributions—especially for the 12.5-year dataset—may not represent the true parameter distributions. They attribute the unresolved convergence to computational constraints and indicate that sufficiently long chains are expected eventually to converge. Establishing convergence is therefore necessary before the model B posterior estimates for PSR J1640+2224 can be treated as definitive.