Model . | Variant . | LF . | HF . | J21 . | F23 . | LF . | HF . | J21 . | F23 . |
---|---|---|---|---|---|---|---|---|---|
|$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | C/DOF . | C/DOF . | C/DOF . | C/DOF . | ||
(1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . |
A | 608.8 | 1309.6 | 160.4 | 268.4 | 5936/4674 | 8266/5764 | 3019/2593 | 3056/2671 | |
B | 158.8 | 75.2 | 62.7 | 89.6 | 5247/4672 | 6372/5762 | 2747/2591 | 2776/2669 | |
C | 12.8 | 3.3 | 14.5 | 13.6 | 4948/4671 | 6218/5761 | 2640/2590 | 2619/2668 | |
C2 | Cut-off PL | 1.9 | 0.6 | |$\bigstar$| | |$\bigstar$| | 4935/4670 | 6215/5760 | 2610/2589 | 2589/2667 |
C3 | nthcomp cont. | 9.8 | 10.8 | 4.1 | 7.9 | 4936/4670 | 6231/5760 | 2609/2589 | 2596/2667 |
C4 | Torus | 2.6 | 0.4 | 2.4 | 5.0 | 4942/4669 | 6197/5759 | 2622/2588 | 2600/2666 |
D|$_n$| | 13.9 | 18.0 | 12.9 | 10.8 | 4933/4670 | 6278/5760 | 2631/2589 | 2604/2667 | |
D|$_i$| | CF = 1 | 31.9 | 36.4 | 15.2 | 17.7 | 4985/4669 | 6245/5759 | 2693/2588 | 2641/2666 |
D|$_i$| | CF = 0.66 | 31.9 | 25.2 | 12.6 | 17.7 | 4985/4669 | 6444/5759 | 2751/2588 | 2634/2666 |
D|$_i$| | CF = 0.33 | 4.9 | 35.4 | 11.6 | 0.1 | 4998/4669 | 6438/5759 | 2656/2588 | 2637/2666 |
E | |$\log \xi =0$|, |$a_*=0$| | 100.4 | 208.5 | 46.1 | 58.6 | 5192/4672 | 6680/5761 | 2719/2590 | 2695/2668 |
E | |$\log \xi =1$|, |$a_*=0$| | 99.2 | 202.0 | 43.6 | 55.8 | 5129/4672 | 6656/5761 | 2702/2590 | 2691/2668 |
E | |$\log \xi =2$|, |$a_*=0$| | 89.0 | 188.0 | 41.6 | 52.6 | 5105/4672 | 7759/5671 | 2702/2590 | 2685/2668 |
E | |$\log \xi =3$|, |$a_*=0$| | 83.6 | 194.4 | 40.4 | 55.1 | 5094/4672 | 6618/5761 | 2690/2590 | 2680/2668 |
E | |$\log \xi =4$|, |$a_*=0$| | 116.8 | 200.2 | 51.4 | 75.3 | 5164/4672 | 6751/5761 | 2708/2590 | 2700/2668 |
E | |$\log \xi =0$|, |$a_*=0.98$| | 101.8 | 208.4 | 47.0 | 59.4 | 5154/4672 | 6850/5761 | 2741/2590 | 2710/2668 |
F | |$\log \xi =0$|, |$a_*=0$| | 52.8 | 52.8 | 39.6 | 40.1 | 5016/4670 | 6261/5760 | 2664/2589 | 2642/2667 |
F | |$\log \xi =1$|, |$a_*=0$| | 55.7 | 29.1 | 38.5 | 40.9 | 5022/4670 | 6266/5760 | 2664/2589 | 2643/2667 |
F | |$\log \xi =2$|, |$a_*=0$| | 59.2 | 39.7 | 38.8 | 43.6 | 5026/4670 | 6286/5760 | 2662/2589 | 2653/2667 |
F | |$\log \xi =3$|, |$a_*=0$| | 80.5 | 29.5 | 43.4 | 57.3 | 5055/4670 | 6266/5670 | 2674/2589 | 2672/2667 |
F | |$\log \xi =4$|, |$a_*=0$| | 114.1 | 33.2 | 37.8 | 56.7 | 5141/4670 | 6283/5760 | 2695/2589 | 2689/2667 |
F | |$\log \xi =0$|, |$a_*=0.98$| | 56.6 | 31.2 | 41.0 | 42.7 | 5023/4670 | 6269/5760 | 2666/2589 | 2645/2667 |
F | |$\log \xi =3$|, |$a_*=0.98$| | 81.8 | 33.0 | 43.9 | 57.8 | 5055/4570 | 6272/5760 | 2675/2589 | 2672/2667 |
G | |$\log \xi =0$|, |$a_*=0$| | 3.0 | |$\bigstar$| | 12.7 | 8.6 | 4918/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0$| | 22.9 | 39.9 | 7.1 | 9.2 | 4923/4668 | 6210/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =2$|, |$a_*=0$| | 14.2 | 38.4 | 4.7 | 6.3 | 4918/4668 | 6210/5759 | 2608/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0$| | 0.9 | 7.3 | 2.5 | 2.9 | 4913/4668 | 6206/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0$| | 16.8 | 39.9 | 23.2 | 6.9 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =0$|, |$a_*=0.98$| | 21.0 | 39.7 | 7.4 | 9.4 | 4921/4668 | 6210/5759 | 2611/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0.98$| | 23.3 | 40.8 | 7.4 | 9.7 | 4923/4668 | 6210/5759 | 2610/2588 | 2585/2666 |
G | |$\log \xi =2$|, |$a_*=0.98$| | 15.2 | 38.7 | 4.9 | 6.4 | 4919/4668 | 6211/5759 | 2609/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0.98$| | |$\bigstar$| | 9.2 | 2.2 | 2.6 | 4912/4668 | 6207/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0.98$| | 17.1 | 40.1 | 6.6 | 6.8 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
H | |$\log \xi =0$|, |$a_*=0$| | 79.8 | 182.4 | 27.4 | 38.3 | 5254/4670 | 7302/5760 | 2758/2589 | 2792/2667 |
H | |$\log \xi =1$|, |$a_*=0$| | 74.0 | 208.9 | 29.8 | 40.5 | 5037/4670 | 6666/5760 | 2670/2589 | 2637/2667 |
H | |$\log \xi =2$|, |$a_*=0$| | 57.9 | 208.1 | 24.3 | 36.2 | 5046/4670 | 6618/5760 | 2679/2589 | 2633/2667 |
H | |$\log \xi =3$|, |$a_*=0$| | 52.7 | 201.7 | 19.2 | 36.0 | 4994/4670 | 6603/5760 | 2659/2589 | 2633/2667 |
H | |$\log \xi =4$|, |$a_*=0$| | 75.6 | 307.9 | 29.0 | 48.0 | 5021/4670 | 6776/5760 | 2681/2589 | 2652/2667 |
Model . | Variant . | LF . | HF . | J21 . | F23 . | LF . | HF . | J21 . | F23 . |
---|---|---|---|---|---|---|---|---|---|
|$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | C/DOF . | C/DOF . | C/DOF . | C/DOF . | ||
(1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . |
A | 608.8 | 1309.6 | 160.4 | 268.4 | 5936/4674 | 8266/5764 | 3019/2593 | 3056/2671 | |
B | 158.8 | 75.2 | 62.7 | 89.6 | 5247/4672 | 6372/5762 | 2747/2591 | 2776/2669 | |
C | 12.8 | 3.3 | 14.5 | 13.6 | 4948/4671 | 6218/5761 | 2640/2590 | 2619/2668 | |
C2 | Cut-off PL | 1.9 | 0.6 | |$\bigstar$| | |$\bigstar$| | 4935/4670 | 6215/5760 | 2610/2589 | 2589/2667 |
C3 | nthcomp cont. | 9.8 | 10.8 | 4.1 | 7.9 | 4936/4670 | 6231/5760 | 2609/2589 | 2596/2667 |
C4 | Torus | 2.6 | 0.4 | 2.4 | 5.0 | 4942/4669 | 6197/5759 | 2622/2588 | 2600/2666 |
D|$_n$| | 13.9 | 18.0 | 12.9 | 10.8 | 4933/4670 | 6278/5760 | 2631/2589 | 2604/2667 | |
D|$_i$| | CF = 1 | 31.9 | 36.4 | 15.2 | 17.7 | 4985/4669 | 6245/5759 | 2693/2588 | 2641/2666 |
D|$_i$| | CF = 0.66 | 31.9 | 25.2 | 12.6 | 17.7 | 4985/4669 | 6444/5759 | 2751/2588 | 2634/2666 |
D|$_i$| | CF = 0.33 | 4.9 | 35.4 | 11.6 | 0.1 | 4998/4669 | 6438/5759 | 2656/2588 | 2637/2666 |
E | |$\log \xi =0$|, |$a_*=0$| | 100.4 | 208.5 | 46.1 | 58.6 | 5192/4672 | 6680/5761 | 2719/2590 | 2695/2668 |
E | |$\log \xi =1$|, |$a_*=0$| | 99.2 | 202.0 | 43.6 | 55.8 | 5129/4672 | 6656/5761 | 2702/2590 | 2691/2668 |
E | |$\log \xi =2$|, |$a_*=0$| | 89.0 | 188.0 | 41.6 | 52.6 | 5105/4672 | 7759/5671 | 2702/2590 | 2685/2668 |
E | |$\log \xi =3$|, |$a_*=0$| | 83.6 | 194.4 | 40.4 | 55.1 | 5094/4672 | 6618/5761 | 2690/2590 | 2680/2668 |
E | |$\log \xi =4$|, |$a_*=0$| | 116.8 | 200.2 | 51.4 | 75.3 | 5164/4672 | 6751/5761 | 2708/2590 | 2700/2668 |
E | |$\log \xi =0$|, |$a_*=0.98$| | 101.8 | 208.4 | 47.0 | 59.4 | 5154/4672 | 6850/5761 | 2741/2590 | 2710/2668 |
F | |$\log \xi =0$|, |$a_*=0$| | 52.8 | 52.8 | 39.6 | 40.1 | 5016/4670 | 6261/5760 | 2664/2589 | 2642/2667 |
F | |$\log \xi =1$|, |$a_*=0$| | 55.7 | 29.1 | 38.5 | 40.9 | 5022/4670 | 6266/5760 | 2664/2589 | 2643/2667 |
F | |$\log \xi =2$|, |$a_*=0$| | 59.2 | 39.7 | 38.8 | 43.6 | 5026/4670 | 6286/5760 | 2662/2589 | 2653/2667 |
F | |$\log \xi =3$|, |$a_*=0$| | 80.5 | 29.5 | 43.4 | 57.3 | 5055/4670 | 6266/5670 | 2674/2589 | 2672/2667 |
F | |$\log \xi =4$|, |$a_*=0$| | 114.1 | 33.2 | 37.8 | 56.7 | 5141/4670 | 6283/5760 | 2695/2589 | 2689/2667 |
F | |$\log \xi =0$|, |$a_*=0.98$| | 56.6 | 31.2 | 41.0 | 42.7 | 5023/4670 | 6269/5760 | 2666/2589 | 2645/2667 |
F | |$\log \xi =3$|, |$a_*=0.98$| | 81.8 | 33.0 | 43.9 | 57.8 | 5055/4570 | 6272/5760 | 2675/2589 | 2672/2667 |
G | |$\log \xi =0$|, |$a_*=0$| | 3.0 | |$\bigstar$| | 12.7 | 8.6 | 4918/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0$| | 22.9 | 39.9 | 7.1 | 9.2 | 4923/4668 | 6210/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =2$|, |$a_*=0$| | 14.2 | 38.4 | 4.7 | 6.3 | 4918/4668 | 6210/5759 | 2608/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0$| | 0.9 | 7.3 | 2.5 | 2.9 | 4913/4668 | 6206/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0$| | 16.8 | 39.9 | 23.2 | 6.9 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =0$|, |$a_*=0.98$| | 21.0 | 39.7 | 7.4 | 9.4 | 4921/4668 | 6210/5759 | 2611/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0.98$| | 23.3 | 40.8 | 7.4 | 9.7 | 4923/4668 | 6210/5759 | 2610/2588 | 2585/2666 |
G | |$\log \xi =2$|, |$a_*=0.98$| | 15.2 | 38.7 | 4.9 | 6.4 | 4919/4668 | 6211/5759 | 2609/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0.98$| | |$\bigstar$| | 9.2 | 2.2 | 2.6 | 4912/4668 | 6207/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0.98$| | 17.1 | 40.1 | 6.6 | 6.8 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
H | |$\log \xi =0$|, |$a_*=0$| | 79.8 | 182.4 | 27.4 | 38.3 | 5254/4670 | 7302/5760 | 2758/2589 | 2792/2667 |
H | |$\log \xi =1$|, |$a_*=0$| | 74.0 | 208.9 | 29.8 | 40.5 | 5037/4670 | 6666/5760 | 2670/2589 | 2637/2667 |
H | |$\log \xi =2$|, |$a_*=0$| | 57.9 | 208.1 | 24.3 | 36.2 | 5046/4670 | 6618/5760 | 2679/2589 | 2633/2667 |
H | |$\log \xi =3$|, |$a_*=0$| | 52.7 | 201.7 | 19.2 | 36.0 | 4994/4670 | 6603/5760 | 2659/2589 | 2633/2667 |
H | |$\log \xi =4$|, |$a_*=0$| | 75.6 | 307.9 | 29.0 | 48.0 | 5021/4670 | 6776/5760 | 2681/2589 | 2652/2667 |
Note. Comparison of Bayesian evidence Z (columns 3–6) for different models (column 1) fitted to our joint data sets (3.3). Models A through H are described in Appendix B3. For models where we ‘step through’ discrete values of certain parameters, the relevant values are listed in column (2). The evidence (i.e. the marginal likelihood) is calculated using the BXA software (Buchner et al. 2014), over the parameter space defined by the bounds in Table B1. The model with the highest evidence, for a given data set, is indicated with a star symbol (|$\bigstar$|). For all other models, we tabulate the difference in log-evidence, |$\Delta \log (Z)=\log (Z_{\mathrm{best}})-\log (Z_{\mathrm{model}})$|, between that model and the best (|$\bigstar$|) model. Models with the difference in log-evidence listed in bold text have |$\Delta \log (Z)\lt 3$|; adopting a rather conservative threshold (Section 3.3.2), we do not consider such models to be decisively disfavoured compared to the best model. We also tabulate the Cash statistic and degrees of freedom (C/DOF, columns 7–10) for an x spec C-stat optimization, initiated at the posterior peak-likelihood parameter values obtained during the relevant BXA run, to provide an idea of the goodness of fit for that model.
Model . | Variant . | LF . | HF . | J21 . | F23 . | LF . | HF . | J21 . | F23 . |
---|---|---|---|---|---|---|---|---|---|
|$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | C/DOF . | C/DOF . | C/DOF . | C/DOF . | ||
(1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . |
A | 608.8 | 1309.6 | 160.4 | 268.4 | 5936/4674 | 8266/5764 | 3019/2593 | 3056/2671 | |
B | 158.8 | 75.2 | 62.7 | 89.6 | 5247/4672 | 6372/5762 | 2747/2591 | 2776/2669 | |
C | 12.8 | 3.3 | 14.5 | 13.6 | 4948/4671 | 6218/5761 | 2640/2590 | 2619/2668 | |
C2 | Cut-off PL | 1.9 | 0.6 | |$\bigstar$| | |$\bigstar$| | 4935/4670 | 6215/5760 | 2610/2589 | 2589/2667 |
C3 | nthcomp cont. | 9.8 | 10.8 | 4.1 | 7.9 | 4936/4670 | 6231/5760 | 2609/2589 | 2596/2667 |
C4 | Torus | 2.6 | 0.4 | 2.4 | 5.0 | 4942/4669 | 6197/5759 | 2622/2588 | 2600/2666 |
D|$_n$| | 13.9 | 18.0 | 12.9 | 10.8 | 4933/4670 | 6278/5760 | 2631/2589 | 2604/2667 | |
D|$_i$| | CF = 1 | 31.9 | 36.4 | 15.2 | 17.7 | 4985/4669 | 6245/5759 | 2693/2588 | 2641/2666 |
D|$_i$| | CF = 0.66 | 31.9 | 25.2 | 12.6 | 17.7 | 4985/4669 | 6444/5759 | 2751/2588 | 2634/2666 |
D|$_i$| | CF = 0.33 | 4.9 | 35.4 | 11.6 | 0.1 | 4998/4669 | 6438/5759 | 2656/2588 | 2637/2666 |
E | |$\log \xi =0$|, |$a_*=0$| | 100.4 | 208.5 | 46.1 | 58.6 | 5192/4672 | 6680/5761 | 2719/2590 | 2695/2668 |
E | |$\log \xi =1$|, |$a_*=0$| | 99.2 | 202.0 | 43.6 | 55.8 | 5129/4672 | 6656/5761 | 2702/2590 | 2691/2668 |
E | |$\log \xi =2$|, |$a_*=0$| | 89.0 | 188.0 | 41.6 | 52.6 | 5105/4672 | 7759/5671 | 2702/2590 | 2685/2668 |
E | |$\log \xi =3$|, |$a_*=0$| | 83.6 | 194.4 | 40.4 | 55.1 | 5094/4672 | 6618/5761 | 2690/2590 | 2680/2668 |
E | |$\log \xi =4$|, |$a_*=0$| | 116.8 | 200.2 | 51.4 | 75.3 | 5164/4672 | 6751/5761 | 2708/2590 | 2700/2668 |
E | |$\log \xi =0$|, |$a_*=0.98$| | 101.8 | 208.4 | 47.0 | 59.4 | 5154/4672 | 6850/5761 | 2741/2590 | 2710/2668 |
F | |$\log \xi =0$|, |$a_*=0$| | 52.8 | 52.8 | 39.6 | 40.1 | 5016/4670 | 6261/5760 | 2664/2589 | 2642/2667 |
F | |$\log \xi =1$|, |$a_*=0$| | 55.7 | 29.1 | 38.5 | 40.9 | 5022/4670 | 6266/5760 | 2664/2589 | 2643/2667 |
F | |$\log \xi =2$|, |$a_*=0$| | 59.2 | 39.7 | 38.8 | 43.6 | 5026/4670 | 6286/5760 | 2662/2589 | 2653/2667 |
F | |$\log \xi =3$|, |$a_*=0$| | 80.5 | 29.5 | 43.4 | 57.3 | 5055/4670 | 6266/5670 | 2674/2589 | 2672/2667 |
F | |$\log \xi =4$|, |$a_*=0$| | 114.1 | 33.2 | 37.8 | 56.7 | 5141/4670 | 6283/5760 | 2695/2589 | 2689/2667 |
F | |$\log \xi =0$|, |$a_*=0.98$| | 56.6 | 31.2 | 41.0 | 42.7 | 5023/4670 | 6269/5760 | 2666/2589 | 2645/2667 |
F | |$\log \xi =3$|, |$a_*=0.98$| | 81.8 | 33.0 | 43.9 | 57.8 | 5055/4570 | 6272/5760 | 2675/2589 | 2672/2667 |
G | |$\log \xi =0$|, |$a_*=0$| | 3.0 | |$\bigstar$| | 12.7 | 8.6 | 4918/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0$| | 22.9 | 39.9 | 7.1 | 9.2 | 4923/4668 | 6210/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =2$|, |$a_*=0$| | 14.2 | 38.4 | 4.7 | 6.3 | 4918/4668 | 6210/5759 | 2608/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0$| | 0.9 | 7.3 | 2.5 | 2.9 | 4913/4668 | 6206/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0$| | 16.8 | 39.9 | 23.2 | 6.9 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =0$|, |$a_*=0.98$| | 21.0 | 39.7 | 7.4 | 9.4 | 4921/4668 | 6210/5759 | 2611/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0.98$| | 23.3 | 40.8 | 7.4 | 9.7 | 4923/4668 | 6210/5759 | 2610/2588 | 2585/2666 |
G | |$\log \xi =2$|, |$a_*=0.98$| | 15.2 | 38.7 | 4.9 | 6.4 | 4919/4668 | 6211/5759 | 2609/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0.98$| | |$\bigstar$| | 9.2 | 2.2 | 2.6 | 4912/4668 | 6207/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0.98$| | 17.1 | 40.1 | 6.6 | 6.8 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
H | |$\log \xi =0$|, |$a_*=0$| | 79.8 | 182.4 | 27.4 | 38.3 | 5254/4670 | 7302/5760 | 2758/2589 | 2792/2667 |
H | |$\log \xi =1$|, |$a_*=0$| | 74.0 | 208.9 | 29.8 | 40.5 | 5037/4670 | 6666/5760 | 2670/2589 | 2637/2667 |
H | |$\log \xi =2$|, |$a_*=0$| | 57.9 | 208.1 | 24.3 | 36.2 | 5046/4670 | 6618/5760 | 2679/2589 | 2633/2667 |
H | |$\log \xi =3$|, |$a_*=0$| | 52.7 | 201.7 | 19.2 | 36.0 | 4994/4670 | 6603/5760 | 2659/2589 | 2633/2667 |
H | |$\log \xi =4$|, |$a_*=0$| | 75.6 | 307.9 | 29.0 | 48.0 | 5021/4670 | 6776/5760 | 2681/2589 | 2652/2667 |
Model . | Variant . | LF . | HF . | J21 . | F23 . | LF . | HF . | J21 . | F23 . |
---|---|---|---|---|---|---|---|---|---|
|$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | |$\Delta \log (Z)$| . | C/DOF . | C/DOF . | C/DOF . | C/DOF . | ||
(1) . | (2) . | (3) . | (4) . | (5) . | (6) . | (7) . | (8) . | (9) . | (10) . |
A | 608.8 | 1309.6 | 160.4 | 268.4 | 5936/4674 | 8266/5764 | 3019/2593 | 3056/2671 | |
B | 158.8 | 75.2 | 62.7 | 89.6 | 5247/4672 | 6372/5762 | 2747/2591 | 2776/2669 | |
C | 12.8 | 3.3 | 14.5 | 13.6 | 4948/4671 | 6218/5761 | 2640/2590 | 2619/2668 | |
C2 | Cut-off PL | 1.9 | 0.6 | |$\bigstar$| | |$\bigstar$| | 4935/4670 | 6215/5760 | 2610/2589 | 2589/2667 |
C3 | nthcomp cont. | 9.8 | 10.8 | 4.1 | 7.9 | 4936/4670 | 6231/5760 | 2609/2589 | 2596/2667 |
C4 | Torus | 2.6 | 0.4 | 2.4 | 5.0 | 4942/4669 | 6197/5759 | 2622/2588 | 2600/2666 |
D|$_n$| | 13.9 | 18.0 | 12.9 | 10.8 | 4933/4670 | 6278/5760 | 2631/2589 | 2604/2667 | |
D|$_i$| | CF = 1 | 31.9 | 36.4 | 15.2 | 17.7 | 4985/4669 | 6245/5759 | 2693/2588 | 2641/2666 |
D|$_i$| | CF = 0.66 | 31.9 | 25.2 | 12.6 | 17.7 | 4985/4669 | 6444/5759 | 2751/2588 | 2634/2666 |
D|$_i$| | CF = 0.33 | 4.9 | 35.4 | 11.6 | 0.1 | 4998/4669 | 6438/5759 | 2656/2588 | 2637/2666 |
E | |$\log \xi =0$|, |$a_*=0$| | 100.4 | 208.5 | 46.1 | 58.6 | 5192/4672 | 6680/5761 | 2719/2590 | 2695/2668 |
E | |$\log \xi =1$|, |$a_*=0$| | 99.2 | 202.0 | 43.6 | 55.8 | 5129/4672 | 6656/5761 | 2702/2590 | 2691/2668 |
E | |$\log \xi =2$|, |$a_*=0$| | 89.0 | 188.0 | 41.6 | 52.6 | 5105/4672 | 7759/5671 | 2702/2590 | 2685/2668 |
E | |$\log \xi =3$|, |$a_*=0$| | 83.6 | 194.4 | 40.4 | 55.1 | 5094/4672 | 6618/5761 | 2690/2590 | 2680/2668 |
E | |$\log \xi =4$|, |$a_*=0$| | 116.8 | 200.2 | 51.4 | 75.3 | 5164/4672 | 6751/5761 | 2708/2590 | 2700/2668 |
E | |$\log \xi =0$|, |$a_*=0.98$| | 101.8 | 208.4 | 47.0 | 59.4 | 5154/4672 | 6850/5761 | 2741/2590 | 2710/2668 |
F | |$\log \xi =0$|, |$a_*=0$| | 52.8 | 52.8 | 39.6 | 40.1 | 5016/4670 | 6261/5760 | 2664/2589 | 2642/2667 |
F | |$\log \xi =1$|, |$a_*=0$| | 55.7 | 29.1 | 38.5 | 40.9 | 5022/4670 | 6266/5760 | 2664/2589 | 2643/2667 |
F | |$\log \xi =2$|, |$a_*=0$| | 59.2 | 39.7 | 38.8 | 43.6 | 5026/4670 | 6286/5760 | 2662/2589 | 2653/2667 |
F | |$\log \xi =3$|, |$a_*=0$| | 80.5 | 29.5 | 43.4 | 57.3 | 5055/4670 | 6266/5670 | 2674/2589 | 2672/2667 |
F | |$\log \xi =4$|, |$a_*=0$| | 114.1 | 33.2 | 37.8 | 56.7 | 5141/4670 | 6283/5760 | 2695/2589 | 2689/2667 |
F | |$\log \xi =0$|, |$a_*=0.98$| | 56.6 | 31.2 | 41.0 | 42.7 | 5023/4670 | 6269/5760 | 2666/2589 | 2645/2667 |
F | |$\log \xi =3$|, |$a_*=0.98$| | 81.8 | 33.0 | 43.9 | 57.8 | 5055/4570 | 6272/5760 | 2675/2589 | 2672/2667 |
G | |$\log \xi =0$|, |$a_*=0$| | 3.0 | |$\bigstar$| | 12.7 | 8.6 | 4918/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0$| | 22.9 | 39.9 | 7.1 | 9.2 | 4923/4668 | 6210/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =2$|, |$a_*=0$| | 14.2 | 38.4 | 4.7 | 6.3 | 4918/4668 | 6210/5759 | 2608/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0$| | 0.9 | 7.3 | 2.5 | 2.9 | 4913/4668 | 6206/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0$| | 16.8 | 39.9 | 23.2 | 6.9 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
G | |$\log \xi =0$|, |$a_*=0.98$| | 21.0 | 39.7 | 7.4 | 9.4 | 4921/4668 | 6210/5759 | 2611/2588 | 2586/2666 |
G | |$\log \xi =1$|, |$a_*=0.98$| | 23.3 | 40.8 | 7.4 | 9.7 | 4923/4668 | 6210/5759 | 2610/2588 | 2585/2666 |
G | |$\log \xi =2$|, |$a_*=0.98$| | 15.2 | 38.7 | 4.9 | 6.4 | 4919/4668 | 6211/5759 | 2609/2588 | 2584/2666 |
G | |$\log \xi =3$|, |$a_*=0.98$| | |$\bigstar$| | 9.2 | 2.2 | 2.6 | 4912/4668 | 6207/5759 | 2608/2588 | 2585/2666 |
G | |$\log \xi =4$|, |$a_*=0.98$| | 17.1 | 40.1 | 6.6 | 6.8 | 4921/4668 | 6209/5759 | 2610/2588 | 2586/2666 |
H | |$\log \xi =0$|, |$a_*=0$| | 79.8 | 182.4 | 27.4 | 38.3 | 5254/4670 | 7302/5760 | 2758/2589 | 2792/2667 |
H | |$\log \xi =1$|, |$a_*=0$| | 74.0 | 208.9 | 29.8 | 40.5 | 5037/4670 | 6666/5760 | 2670/2589 | 2637/2667 |
H | |$\log \xi =2$|, |$a_*=0$| | 57.9 | 208.1 | 24.3 | 36.2 | 5046/4670 | 6618/5760 | 2679/2589 | 2633/2667 |
H | |$\log \xi =3$|, |$a_*=0$| | 52.7 | 201.7 | 19.2 | 36.0 | 4994/4670 | 6603/5760 | 2659/2589 | 2633/2667 |
H | |$\log \xi =4$|, |$a_*=0$| | 75.6 | 307.9 | 29.0 | 48.0 | 5021/4670 | 6776/5760 | 2681/2589 | 2652/2667 |
Note. Comparison of Bayesian evidence Z (columns 3–6) for different models (column 1) fitted to our joint data sets (3.3). Models A through H are described in Appendix B3. For models where we ‘step through’ discrete values of certain parameters, the relevant values are listed in column (2). The evidence (i.e. the marginal likelihood) is calculated using the BXA software (Buchner et al. 2014), over the parameter space defined by the bounds in Table B1. The model with the highest evidence, for a given data set, is indicated with a star symbol (|$\bigstar$|). For all other models, we tabulate the difference in log-evidence, |$\Delta \log (Z)=\log (Z_{\mathrm{best}})-\log (Z_{\mathrm{model}})$|, between that model and the best (|$\bigstar$|) model. Models with the difference in log-evidence listed in bold text have |$\Delta \log (Z)\lt 3$|; adopting a rather conservative threshold (Section 3.3.2), we do not consider such models to be decisively disfavoured compared to the best model. We also tabulate the Cash statistic and degrees of freedom (C/DOF, columns 7–10) for an x spec C-stat optimization, initiated at the posterior peak-likelihood parameter values obtained during the relevant BXA run, to provide an idea of the goodness of fit for that model.
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