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 4

Egg-box evidence SAR estimation comparison.

$\overset{⌢}{Z}$ $Mathematical equation: ${\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over Z} }$$	${\hat{σ}}_{\ln \hat{z}}$ $Mathematical equation: ${{\hat \sigma }_{\ln \hat z}}$$	$Δ_{Z} (%)$ $Mathematical equation: ${{\rm{\Delta }}_Z}({\rm{\% }})$$	$ℒ (\overset{⌢}{Ζ})$ $Mathematical equation: ${\cal L}(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {\rm Z}} )$$
TI	235.733±0.013	0.748±0.008	11.532	–0.643
SS	235.843±0.012	0.008±0.001	1.252	2.618
H	235.802±0.013	0.130±0.006	5.283	1.036

TI+	235.842±0.013	0.023±0.008	1.425	2.648
SS+	235.844±0.013	0.008±0.001	1.211	2.771
H+	235.845±0.013	0.010±0.003	1.099	3.082

dyn-u	235.858±0.104	0.064±0.001	0.201	1.828
dyn-s	235.903±0.104	0.064±0.001	4.812	1.560
dyn-rs	235.953±0.118	0.064±0.001	10.186	0.679

Notes. reddemcee’s adaptive algorithms compared to dynesty’s sampling methods. From left to right, we show the log-evidence estimate, the estimate error, the difference to the true value ln 𝒵 = 235.856 in percentage Δ_𝒵, and the log-likelihood of the estimator $ℒ (\overset{⌢}{Ζ})$ $Mathematical equation: ${\cal L}(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {\rm Z}} )$$ .

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