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Table 4

Model probabilities for HD 1461.

log p(D | Mn,I)−1100 p(Mn | D,I) /p(M3 | D,I) σO−C
n Periods [d] CJ01 P14 TPM BIC CJ01 P14 [m s-1] [m s-1]

3 {5.77, 13.5, 3500} 80.44 ± 0.06 81.15 ± 0.05 132.51 93.76 1.0 1.0 2.20 ± 0.19 2.257 ± 0.071

4 {5.77, 13.5, 22.9, 3500} 76.31 ± 0.11 79.84 ± 0.05 143.52 93.18 0.016 ± 0.002 0.274 ± 0.016 2.15 ± 0.18 2.242 ± 0.075

4 {5.77, 13.5, 620, 3500} 84.57 ± 0.04 84.16 ± 0.11 145.74 97.07 60.8 ± 4.0 19.6 ± 2.4 1.87 ± 0.19 1.965 ± 0.092

5 {5.77, 13.5, 22.9, 620, 3500} 77.24 ± 0.17 76.92 ± 0.14 153.97 93.94 (2.25 ± 0.30) × 10-4 0.015 ± 0.003 1.81 ± 0.19 1.946 ± 0.098

Notes. Estimate of the evidence (marginal likelihood) for models with n = 3,...,5 Keplerians. The periods of the included signals are listed in the second column. The estimates based on the method of Chib & Jeliazkov (2001, CJ01) and Perrakis et al. (2014, P14) are given in Cols. 3 and 4. For comparison, we also report the estimate obtained based on the Tuomi & Jones (2012) TPM estimator and on the Bayesian information criterion (BIC) in Cols. 5 and 6. For clarity, we have subtracted 1100 from each estimation, which corresponds to a change of units in the observed radial velocities. Columns 7 and 8 list the odds ratio between model i with respect to the three-Keplerian model. Additionally, the posterior estimates of the amplitude of the additional base-level noise and the dispersion of the residuals are given in Cols. 9 and 10.

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