a mixture of prior and posterior densities, as discussed in @newton94 (see Eqs. 15 $\&$ 16). This is a version of importance sampling that uses a mixed distribution to obtain a sampling distribution that has “heavier” tails than the posterior (see [@nelson16] for further discussion of this method). We note that all of these signals are so strong that they would pass essentially any meaningful significance test, from likelihood-ratio tests to tests applying any other information criteria.

The log-Bayesian evidence ratio for the signal in the data of HD9174 was found to be 42.1 for the 1-planet model. The signal is also readily apparent in the MMSE periodogram. No secondary signal was detected. Considering we set the threshold boundary for a statistically significant signal to be at the level of $10^4$, or 9.21 in log-Bayesian units, it is clear that this signal is very significant. Our best fit to the data yields a non-circular eccentricity, only at the level of around 0.12, and with a stellar mass commensurate with that of the Sun, the orbiting planet has a minimum mass of 1.11 . The phase folded velocities and model fit are shown in Fig. \[phased1\]

HD48265
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HD48265 is classed 