Summary of the GP model, the priors on its hyperparameters, and the estimated median and 68 per cent confidence intervals obtained using an MCMC procedure for the 10 nights data set (see Appendix B. All covariance functions are Matern functions.
| Hyperparameter . | Prior . | MCMC estimate (10 nights) . |
|---|---|---|
| ηsky | +∞ | − |
| |$\sigma ^2_{\mathrm{sky}} / \sigma ^2_{\mathrm{n}}$| | − | |$611\substack{+22\\-19}$| |
| lsky | |$\mathcal {U}(10, 100)$| | |$47.5\substack{+3.1\\-2.8}$| |
| ηmix | 3/2 | − |
| |$\sigma ^2_{\mathrm{mix}} / \sigma ^2_{\mathrm{n}}$| | − | |$50.4\substack{+2.1\\-1.9}$| |
| lmix | |$\mathcal {U}(1, 10)$| | |$2.97\substack{+0.09\\-0.08}$| |
| ηex | 5/2 | − |
| |$\sigma ^2_{\mathrm{ex}} / \sigma ^2_{\mathrm{n}}$| | − | |$2.18\substack{+0.09\\-0.14}$| |
| lex | |$\mathcal {U}(0.2, 0.8)$| | |$0.26\substack{+0.01\\-0.01}$| |
| η21 | 1/2 | − |
| |$\sigma ^2_{\mathrm{21}} / \sigma ^2_{\mathrm{n}}$| | − | <0.77 |
| l21 | |$\mathcal {U}(0.1, 1.2)$| | >0.73a |
| αn | − | |$1.17\substack{+0.06\\-0.06}$| |
| Hyperparameter . | Prior . | MCMC estimate (10 nights) . |
|---|---|---|
| ηsky | +∞ | − |
| |$\sigma ^2_{\mathrm{sky}} / \sigma ^2_{\mathrm{n}}$| | − | |$611\substack{+22\\-19}$| |
| lsky | |$\mathcal {U}(10, 100)$| | |$47.5\substack{+3.1\\-2.8}$| |
| ηmix | 3/2 | − |
| |$\sigma ^2_{\mathrm{mix}} / \sigma ^2_{\mathrm{n}}$| | − | |$50.4\substack{+2.1\\-1.9}$| |
| lmix | |$\mathcal {U}(1, 10)$| | |$2.97\substack{+0.09\\-0.08}$| |
| ηex | 5/2 | − |
| |$\sigma ^2_{\mathrm{ex}} / \sigma ^2_{\mathrm{n}}$| | − | |$2.18\substack{+0.09\\-0.14}$| |
| lex | |$\mathcal {U}(0.2, 0.8)$| | |$0.26\substack{+0.01\\-0.01}$| |
| η21 | 1/2 | − |
| |$\sigma ^2_{\mathrm{21}} / \sigma ^2_{\mathrm{n}}$| | − | <0.77 |
| l21 | |$\mathcal {U}(0.1, 1.2)$| | >0.73a |
| αn | − | |$1.17\substack{+0.06\\-0.06}$| |
Note. aThe upper confidence interval hits the prior boundaries, hence we report here only the lower limit.
Summary of the GP model, the priors on its hyperparameters, and the estimated median and 68 per cent confidence intervals obtained using an MCMC procedure for the 10 nights data set (see Appendix B. All covariance functions are Matern functions.
| Hyperparameter . | Prior . | MCMC estimate (10 nights) . |
|---|---|---|
| ηsky | +∞ | − |
| |$\sigma ^2_{\mathrm{sky}} / \sigma ^2_{\mathrm{n}}$| | − | |$611\substack{+22\\-19}$| |
| lsky | |$\mathcal {U}(10, 100)$| | |$47.5\substack{+3.1\\-2.8}$| |
| ηmix | 3/2 | − |
| |$\sigma ^2_{\mathrm{mix}} / \sigma ^2_{\mathrm{n}}$| | − | |$50.4\substack{+2.1\\-1.9}$| |
| lmix | |$\mathcal {U}(1, 10)$| | |$2.97\substack{+0.09\\-0.08}$| |
| ηex | 5/2 | − |
| |$\sigma ^2_{\mathrm{ex}} / \sigma ^2_{\mathrm{n}}$| | − | |$2.18\substack{+0.09\\-0.14}$| |
| lex | |$\mathcal {U}(0.2, 0.8)$| | |$0.26\substack{+0.01\\-0.01}$| |
| η21 | 1/2 | − |
| |$\sigma ^2_{\mathrm{21}} / \sigma ^2_{\mathrm{n}}$| | − | <0.77 |
| l21 | |$\mathcal {U}(0.1, 1.2)$| | >0.73a |
| αn | − | |$1.17\substack{+0.06\\-0.06}$| |
| Hyperparameter . | Prior . | MCMC estimate (10 nights) . |
|---|---|---|
| ηsky | +∞ | − |
| |$\sigma ^2_{\mathrm{sky}} / \sigma ^2_{\mathrm{n}}$| | − | |$611\substack{+22\\-19}$| |
| lsky | |$\mathcal {U}(10, 100)$| | |$47.5\substack{+3.1\\-2.8}$| |
| ηmix | 3/2 | − |
| |$\sigma ^2_{\mathrm{mix}} / \sigma ^2_{\mathrm{n}}$| | − | |$50.4\substack{+2.1\\-1.9}$| |
| lmix | |$\mathcal {U}(1, 10)$| | |$2.97\substack{+0.09\\-0.08}$| |
| ηex | 5/2 | − |
| |$\sigma ^2_{\mathrm{ex}} / \sigma ^2_{\mathrm{n}}$| | − | |$2.18\substack{+0.09\\-0.14}$| |
| lex | |$\mathcal {U}(0.2, 0.8)$| | |$0.26\substack{+0.01\\-0.01}$| |
| η21 | 1/2 | − |
| |$\sigma ^2_{\mathrm{21}} / \sigma ^2_{\mathrm{n}}$| | − | <0.77 |
| l21 | |$\mathcal {U}(0.1, 1.2)$| | >0.73a |
| αn | − | |$1.17\substack{+0.06\\-0.06}$| |
Note. aThe upper confidence interval hits the prior boundaries, hence we report here only the lower limit.
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