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 9

HD 20794 parameter estimation.

Parameter	Reference¹	dyn-rs	SAR
P₁ (days)	18.314±0.002	${18.314}_{- 0.004}^{+ 0.004}$ $Mathematical equation: $18.314_{ - 0.004}^{ + 0.004}$$	${18.313}_{- 0.001}^{+ 0.001}$ $Mathematical equation: $18.313_{ - 0.001}^{ + 0.001}$$
K₁ (m s⁻¹)	0.614±0.048	${0.632}_{- 0.066}^{+ 0.030}$ $Mathematical equation: $0.632_{ - 0.066}^{ + 0.030}$$	${0.608}_{- 0.009}^{+ 0.030}$ $Mathematical equation: $0.608_{ - 0.009}^{ + 0.030}$$
e₁	${0.064}_{- 0.046}^{+ 0.065}$ $Mathematical equation: $0.064_{ - 0.046}^{ + 0.065}$$	${0.109}_{- 0.068}^{+ 0.049}$ $Mathematical equation: $0.109_{ - 0.068}^{ + 0.049}$$	${0.057}_{- 0.057}^{+ 0.045}$ $Mathematical equation: $0.057_{ - 0.057}^{ + 0.045}$$

P₂ (days)	89.68±0.10	${89.67}_{- 0.16}^{+ 0.11}$ $Mathematical equation: $89.67_{ - 0.16}^{ + 0.11}$$	${89.73}_{- 0.03}^{+ 0.06}$ $Mathematical equation: $89.73_{ - 0.03}^{ + 0.06}$$
K₂ (m s⁻¹)	${0.502}_{- 0.049}^{+ 0.048}$ $Mathematical equation: $0.502_{ - 0.049}^{ + 0.048}$$	${0.510}_{- 0.054}^{+ 0.038}$ $Mathematical equation: $0.510_{ - 0.054}^{ + 0.038}$$	${0.474}_{- 0.001}^{+ 0.041}$ $Mathematical equation: $0.474_{ - 0.001}^{ + 0.041}$$
e₂	${0.077}_{- 0.055}^{+ 0.084}$ $Mathematical equation: $0.077_{ - 0.055}^{ + 0.084}$$	${0.055}_{- 0.054}^{+ 0.053}$ $Mathematical equation: $0.055_{ - 0.054}^{ + 0.053}$$	${0.026}_{- 0.026}^{+ 0.007}$ $Mathematical equation: $0.026_{ - 0.026}^{ + 0.007}$$

P₃ (days)	${647.6}_{- 2.7}^{+ 2.5}$ $Mathematical equation: $647.6_{ - 2.7}^{ + 2.5}$$	${652.1}_{- 5.5}^{+ 4.5}$ $Mathematical equation: $652.1_{ - 5.5}^{ + 4.5}$$	${648.2}_{- 2.4}^{+ 2.6}$ $Mathematical equation: $648.2_{ - 2.4}^{ + 2.6}$$
K₃ (m s⁻¹)	${0.567}_{- 0.064}^{+ 0.067}$ $Mathematical equation: $0.567_{ - 0.064}^{ + 0.067}$$	${0.521}_{- 0.091}^{+ 0.025}$ $Mathematical equation: $0.521_{ - 0.091}^{ + 0.025}$$	${0.589}_{- 0.055}^{+ 0.001}$ $Mathematical equation: $0.589_{ - 0.055}^{ + 0.001}$$
e₃	${0.45}_{- 0.10}^{+ 0.11}$ $Mathematical equation: $0.45_{ - 0.10}^{ + 0.11}$$	${0.428}_{- 0.412}^{+ 0.111}$ $Mathematical equation: $0.428_{ - 0.412}^{ + 0.111}$$	${0.467}_{- 0.024}^{+ 0.053}$ $Mathematical equation: $0.467_{ - 0.024}^{ + 0.053}$$

Notes. (1) Nari et al. (2025). Parameter estimation results for the different algorithms for the 3K model. In descending order, P corresponds to the period, K to the semi-amplitude, and e to the eccentricity, where the subscript denotes a particular planet.

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