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tokens: parameters as reported in Table C1 . The N comp = 2 results are fully consistent with those reported by Patruno et al. ( 2017 ) within their confidence intervals. Table C1. GMM results for the f spin data set for NSs in LMXBs from Patruno et al. ( 2017 ), assuming negligible measurement errors. Looking at the various statistical criteria as a function of number of components N comp = 1, 2, 3 (also illustrated in Fig. C1 ), these are also fully consistent with the findings of Patruno et al. ( 2017 ): again the likelihood ratio alone is already in favour of two components (), but only additional criteria can yield a robust decision, and on its own, the additional gain of could tempt us to use an even more complex model. Fortunately, in this case AICc and BIC agree in clearly preferring 2 components over 1 (with Δ of 7–11), and also prefer 2 over 3 by Δ of almost 5. A leave-one-out CV test (see Fig. C2 ) also shows the two-component fit to be almost as stable as a single component in this case. A MixtureInf EM-test reports a nominal p -value of 0.008 which also seems to reject a single-component hypothesis much more clearly than in the DNS case. As in Section 2.6 the exact value needs to be interpreted with caution due to the low N data , but this being only a comparison example, no further simulation tests have been conducted in this case. Figure C1. Model selection criteria for GMMs with N comp = 1, 2, 3 applied to the Patruno + data set of f spin for NSs in LMXBs. The first three panels are for sklearnGMM fits. The last panel gives the average Bayesian evidence from 10 cpnest runs at each N comp . AICc, BIC, and are plotted as differences to the N comp = 1 value. Figure C2. Illustration of leave-one-out CV on the Patruno + f spin data set. Each dotted line corresponds to a fit after leaving out one data point. In this case, the fitted distributions are relatively stable not just for N comp = 1, but also for the preferred fit with N comp = 2, and only for even more components they start becoming unstable. Figure C3. Posteriors from cpnest runs on the LMXB data set for a single Gaussian (left-hand panel) and for a two-component GMM (remaining panels). Note that σ 1 appears twice on the x -axis of the last two panels. Figure C4. Median GMM distribution functions p ( f spin ) inferred with cpnest for one (blue solid line) or two components (orange dashed line), superimposed on a data histogram, and with 90 per cent quantiles background ‘haze’. cpnest results for this data set (with uniform priors in C k , log-uniform in σ k within Hz and Gaussian μ k priors of width 70 Hz) are very consistent with the other GMM fits, except for some differences in the more degenerate N comp = 3 case. The evidence ratio is in favour by ≥16 of 2 components over 1, with 3 components preferred by a marginal factor of only 3 and much less robust results. Overall, the LMXB data set seems to be a good example for information criteria, EM-test and Bayesian evidence