Table A1. Open in new tab Bayesian model...

Model	Evidence	Best-fit	Bayes	Significance
Full Chem	204.75	4.30	Ref.	Ref.
No H₂ + He	184.50	12.9	6.2 × 10⁸	6.7σ
No H₂O	164.66	9.21	2.6 × 10¹⁷	9.2σ
No Na	205.07	3.47	0.73	N/A
No K	205.37	3.51	0.54	N/A
No Li	204.76	3.60	0.99	N/A
No TiO	205.36	3.56	0.54	N/A
No VO	205.45	3.55	0.50	N/A
No AlO	204.98	3.45	0.79	N/A
No CaO	205.19	3.38	0.64	N/A
No TiH	205.02	3.70	0.76	N/A
No CrH	203.45	3.95	3.67	2.2σ
No FeH	205.02	3.56	0.76	N/A
No ScH	204.02	4.01	2.08	1.8σ
No M-Oxides	206.74	2.19	0.14	N/A
No M-Hydrides	203.03	3.12	5.58	2.4σ

Model	Evidence	Best-fit	Bayes	Significance
Full Chem	204.75	4.30	Ref.	Ref.
No H₂ + He	184.50	12.9	6.2 × 10⁸	6.7σ
No H₂O	164.66	9.21	2.6 × 10¹⁷	9.2σ
No Na	205.07	3.47	0.73	N/A
No K	205.37	3.51	0.54	N/A
No Li	204.76	3.60	0.99	N/A
No TiO	205.36	3.56	0.54	N/A
No VO	205.45	3.55	0.50	N/A
No AlO	204.98	3.45	0.79	N/A
No CaO	205.19	3.38	0.64	N/A
No TiH	205.02	3.70	0.76	N/A
No CrH	203.45	3.95	3.67	2.2σ
No FeH	205.02	3.56	0.76	N/A
No ScH	204.02	4.01	2.08	1.8σ
No M-Oxides	206.74	2.19	0.14	N/A
No M-Hydrides	203.03	3.12	5.58	2.4σ

Table A1.

Bayesian model comparison: composition of HAT-P-26b (Wakeford et al. 2017, data only).

Model	Evidence	Best-fit	Bayes	Significance
	\|$\mathrm{ln}\left(\mathcal {Z}_{i}\right)$\|	\|$\chi _{r, \mathrm{min}}^{2}$\|	Factor \|$\mathcal {B}_{0i}$\|	of Ref.
Full Chem	204.75	4.30	Ref.	Ref.
No H₂ + He	184.50	12.9	6.2 × 10⁸	6.7σ
No H₂O	164.66	9.21	2.6 × 10¹⁷	9.2σ
No Na	205.07	3.47	0.73	N/A
No K	205.37	3.51	0.54	N/A
No Li	204.76	3.60	0.99	N/A
No TiO	205.36	3.56	0.54	N/A
No VO	205.45	3.55	0.50	N/A
No AlO	204.98	3.45	0.79	N/A
No CaO	205.19	3.38	0.64	N/A
No TiH	205.02	3.70	0.76	N/A
No CrH	203.45	3.95	3.67	2.2σ
No FeH	205.02	3.56	0.76	N/A
No ScH	204.02	4.01	2.08	1.8σ
No M-Oxides	206.74	2.19	0.14	N/A
No M-Hydrides	203.03	3.12	5.58	2.4σ

Model	Evidence	Best-fit	Bayes	Significance
	\|$\mathrm{ln}\left(\mathcal {Z}_{i}\right)$\|	\|$\chi _{r, \mathrm{min}}^{2}$\|	Factor \|$\mathcal {B}_{0i}$\|	of Ref.
Full Chem	204.75	4.30	Ref.	Ref.
No H₂ + He	184.50	12.9	6.2 × 10⁸	6.7σ
No H₂O	164.66	9.21	2.6 × 10¹⁷	9.2σ
No Na	205.07	3.47	0.73	N/A
No K	205.37	3.51	0.54	N/A
No Li	204.76	3.60	0.99	N/A
No TiO	205.36	3.56	0.54	N/A
No VO	205.45	3.55	0.50	N/A
No AlO	204.98	3.45	0.79	N/A
No CaO	205.19	3.38	0.64	N/A
No TiH	205.02	3.70	0.76	N/A
No CrH	203.45	3.95	3.67	2.2σ
No FeH	205.02	3.56	0.76	N/A
No ScH	204.02	4.01	2.08	1.8σ
No M-Oxides	206.74	2.19	0.14	N/A
No M-Hydrides	203.03	3.12	5.58	2.4σ

Notes. The ‘Full Chem’ reference model includes chemical opacity due to H₂, He, H₂O, Na, K, Li, TiO, VO, AlO, CaO, TiH, CrH, FeH, and ScH. The ‘No M-Oxides’ model has TiO, VO, AlO, and CaO removed; the ‘No M-Hydrides’ model has TiH, CrH, FeH, and ScH removed. The number of degrees of freedom (d.o.f), given by N_data − N_params, is 4 for the reference model (N_data = 27). |$\chi _{r, \, \mathrm{min}}^{2}$| is the minimum reduced chi-square (χ²/d.o.f). The significance indicates the degree of preference for the reference model, highlighted in bold, over each alternative model. N/A indicates no (or negative) evidence (⁠|$\mathcal {B}_{\mathrm{ij}} \lesssim 1$|⁠) supporting a given chemical species.

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