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 11

Hybrid 3D Rosenbrock evidence estimation.

Method	$\overset{⌢}{Z}$ $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}$$	$ℒ_{\hat{Z}}$ $Mathematical equation: ${{\cal L}_{\hat {\cal Z}}}$$
SAR	1.562±0.062	0.021±0.001	4.233	0.771
SMD	1.516±0.065	0.023±0.002	8.519	–4.556
SGG	1.574±0.076	0.021±0.002	3.069	1.841
GAO	1.570±0.042	0.022±0.002	3.500	1.561
ETL	1.598±0.061	0.021±0.001	0.747	2.901

dyn-u	1.923±0.207	0.109±0.002	37.366	–2.944
dyn-s	1.625±0.883	0.111±0.004	1.967	1.264
dyn-rs	1.534±0.442	0.112±0.006	6.903	1.066

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=1.606 in percentage in percentage Δ_𝒵, and the log-likelihood of the estimator $ℒ (\overset{⌢}{Z})$ $Mathematical equation: ${\cal L}(\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over Z} )$$ .

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