Closing the evidence gap: reddemcee, a fast adaptive parallel tempering sampler - Next-generation ladder adaptation and evidence estimators for parallel tempering

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Volume 706 (February 2026)

A&A, 706 (2026) A323

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Table 2

2D Gaussian shells SAR evidence estimation comparison.

Method	$\hat{z}$ $Mathematical equation: ${\hat z}$$	${\hat{σ}}_{\ln \hat{z}}$ $Mathematical equation: ${{\hat \sigma }_{\ln \hat z}}$$	$Δ_{Z} (%)$ $Mathematical equation: ${{\rm{\Delta }}_Z}({\rm{\% }})$$	$ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}(\hat {\cal Z})$$
TI	–1.833±0.008	0.066±0.005	8.394	0.917
SS	–1.744±0.008	0.005±0.001	0.117	4.326
H	–1.788±0.008	0.134±0.005	4.124	1.044

TI+	–1.749±0.008	0.024±0.005	0.324	2.801
SS+	–1.745±0.008	0.006±0.001	0.099	4.263
H+	–1.745±0.008	0.008±0.002	0.016	3.951

dyn-u	–1.763±0.054	0.040±0.001	1.751	2.206
dyn-s	–1.774±0.055	0.040±0.001	2.876	2.049
dyn-rs	–1.767±0.043	0.040±0.001	2.159	2.157

Notes. reddemcee’s adaptive algorithms compared to dynesty’s uniform (dyn-u), slice (dyn-s), and random-slice (dyn-rs) sampling methods. From left to right, the log-evidence estimator, the estimator uncertainty, the difference to the true value In $Z = - 1.746$ Mathematical equation: $Z = - 1.746$ in percentage $Δ_{Z}$ $Mathematical equation: ${{\rm{\Delta }}_Z}$$ , and the log-likelihood of the estimator $ℒ (\overset{⌢}{Ζ})$ $Mathematical equation: ${\cal L}\left( {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {\rm Z}} } \right)$$ .

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