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tokens: to first order with b – which is degenerate with the function of σ n e – and the only way to break the degeneracy is to have enough variation in the secant of the zenith angle. In a sparse and noisy observation of ΔTEC, the secant variation is poor and it is expected that this degeneracy exists. Therefore we also show the product b σ n e , and we see that this compound value discrepancy is smaller by approximately 35%. Table 2. Average and standard deviation, over all experimental conditions, of the difference between the learned physical hyperparameters and the true hyperparameters. In Table 3 we summarise the performance of the physical kernel against each competitor kernel. We display the mean of ΔLPO C ( η ), and ΔLPH C ( η ) over all experimental conditions, as well as their values at the nominal experimental conditions of 30 directions per 12.6 deg 2 , and ΔTEC noise of 1 mTECU, which is indicated with η nom . We use bold font in Table 3 to indicate the best competitor model. Table 3. Probability ratio FOMs (see text) averaged over experimental conditions and at nominal conditions. Notes. Larger values indicate that the physical model is more probable. Bold face indicates the best performing competitor model (lower number). We first consider the ability of each model to represent the observed data. For the dawn ionosphere, the M52 competitor kernel has the best (lowest) ⟨ΔLPO C ⟩ η = 1.55 and , implying that the M52 kernel model is 55% and 46% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. We note that the M32 kernel produced similar results. For the dusk ionosphere, the EQ kernel model is likewise the best among all competitors, being only 73% and 54% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. In all experimental conditions, the physical model provides a significantly more probable explanation of the observed data. We now consider the ability of each model to infer the held-out data. For the dawn ionosphere, the M52 competitor kernel has the best (lowest) ⟨ΔLPH C ⟩ η = 1.49 and = 1.31, implying that the M52 kernel prediction is 49% and 31% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. We note that the M32 kernel produced similar results. For the dusk ionosphere, the EQ kernel model is likewise the best among all competitors, with predictions only 16% and 12% less probable than the physical kernel model on average over all experimental conditions, and at nominal conditions, respectively. In the case of the rougher dawn ionosphere, the physical model provides a significantly more probable prediction of the held-out data in all experimental conditions. However, for the smoother dusk ionosphere at nominal conditions, the physical model is only 12% more probable than the EQ kernel model,