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 A.1

15D Gaussian shells evidence-estimation comparison with the SAR method.

Method	$\ln \hat{Z}$ $Mathematical equation: $\ln \widehat Z$$	${\hat{σ}}_{\ln \hat{Z}}$ $Mathematical equation: ${\widehat \sigma _{\ln \widehat Z}}$$	Δ_𝒵	$ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}\left( {\widehat Z} \right)$$
TI	−26.1818±0.0417	1.1037±0.0526	71.9266	−1.6800
SS	−24.9374±0.0410	0.0205±0.0029	2.5617	2.1658
Hybrid	−24.9523±0.0423	2.9866±0.0661	4.0070	−2.0132

TI+	−25.0308±0.0375	0.5979±0.0266	11.2557	−0.4245
SS+	−24.9411±0.0369	0.0204±0.0021	2.9299	1.9090
Hybrid+	−24.9394±0.0373	0.0242±0.0027	2.7599	2.1337

dyn-u	−24.7176±0.3144	0.1246±0.0017	21.3853	−0.0460
dyn-s	−24.8765±0.3044	0.1243±0.0015	3.5620	1.1267
dyn-rs	−24.7292±0.2163	0.1242±0.0012	19.9854	0.0908

Notes. reddemcee’s adaptive algorithms compared to dynesty’s sampling methods. From left to right, the log-evidence estimate, the estimate uncertainty, the difference to the true value In 𝒵=−24.9114 in percentage Δ_𝒵, and the log-likelihood of the estimator $ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}\left( {\widehat Z} \right)$$ .

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