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.2

15D Gaussian shells ln 𝒵 estimation with variable burn-in for the SAR method.

Method	N_adapt=50%		N_adapt=25%		N_adapt=10%		N_adapt=5%
	Δ_𝒵	$ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}\left( {\widehat Z} \right)$$	Δ_𝒵	$ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}\left( {\widehat Z} \right)$$	Δ_𝒵	$ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}\left( {\widehat Z} \right)$$	Δ_𝒵	$ℒ (\hat{Z})$ $Mathematical equation: ${\cal L}\left( {\widehat Z} \right)$$
TI	71.9266	−1.6800	72.9348	−1.6919	71.0282	−1.8322	70.176	−22.5295
SS	2.5617	2.1658	7.0111	−5.9413	6.7014	−4.9155	8.3851	−8.4817
Hybrid	4.0070	−2.0132	21.8509	−1.4656	27.8067	−1.0694	17.2876	−2.0419

TI+	11.2557	−0.4245	14.1321	−0.5039	12.6212	−0.3977	12.3431	−0.3729
SS+	2.9299	1.9090	6.3493	−4.2133	6.3843	−4.7487	8.1264	−8.5345
Hybrid+	2.7599	2.1337	6.6707	1.2514	6.9972	1.0890	8.1322	0.9562

Notes. reddemcee’s SAR method evidence estimation with different adaptation (and burn-in) times, starting at half of the chain N_adapt=50%, down to 25%, 10%, and 5% for 640 sweeps. Each sub-column shows the difference to the true value ln 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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