Skip to main content

Come analyze HEASARC, IRSA, and MAST data in the cloud! The Fornax Initiative is now welcoming all interested beta users.

Xspec Home Page

next up previous contents
Next: Common pitfalls Up: Bayesian Methods Previous: Model comparison by evidence   Contents

Convergence diagnostics

No sampler is self-diagnosing; the user must check that the chains have converged before trusting credible intervals.

For the chain-based samplers (MH and GW), the standard chain stat output reports per-parameter mean, variance, Rubin–Gelman convergence statistic (across multiple chains, if present), Geweke convergence statistic (within a single chain), and the fraction of repeated steps. The classical Rubin–Gelman $\hat R$ should be below $1.1$ (a looser rule of thumb than the rank-normalized Rhat introduced below); the Geweke statistic should be within $\pm 2$. A fraction of repeats above about $0.8$ indicates the proposal scale is too large and the chain has effectively stalled.

For a fuller, rank-normalized assessment, chain diag prints the diagnostic suite of Vehtari et al. (2021): for every parameter it reports the classical and rank-normalized split Rhat, the bulk and tail effective sample sizes, the integrated autocorrelation time and the ratio $N/\tau$, and — for Goodman–Weare — a sticky-walker check, opening with a one-line [ OK ]/[WARN]/[SHORT] verdict. Its thresholds are tighter than the classical rule of thumb above: rank-normalized Rhat $<1.01$, bulk- and tail-ESS $\geq 400$, and at least $50$ samples per integrated autocorrelation time. The same report is printed automatically at the end of a chain run and its verdict is appended to chain info, so the convergence assessment is normally already in front of you when a run finishes; see the chain command entry for the full description.

For HMC, the implementation prints a final summary line per chain giving the number of divergences, the maximum tree depth reached, and the energy-conservation error. Divergences should be rare ( $\lesssim 1\%$); persistent divergences indicate the geometry of the posterior is incompatible with the diagonal-mass-matrix assumption, and a non-centered reparameterization may help.

For nested sampling, the algorithm terminates automatically when the remaining prior volume can contribute at most a user-controlled fraction of the evidence. The output reports the final $\log Z$ together with its estimated uncertainty, and the posterior sample is written along with importance weights so the user can verify that no single sample dominates the effective sample size.

In addition to the built-in diagnostics, the chain files produced by all four samplers are written in a FITS format compatible with external analysis tools (notably arviz and corner.py in Python). Loading the chain into one of those packages complements the built-in chain diag report and is especially useful for visualizing the joint posterior structure.

next up previous contents
Next: Common pitfalls Up: Bayesian Methods Previous: Model comparison by evidence   Contents