  We present a simple mathematical criterion for determining whether a given
statistical model does not describe several independent sets of measurements,
or data modes, adequately. We derive this criterion for two data sets and
generalise it to several sets by using the Bayesian updating of the posterior
probability density. To demonstrate the usage of the criterion, we apply it to
observations of exoplanet host stars by re-analysing the radial velocities of
HD 217107, Gliese 581, and \u{psion} Andromedae and show that the currently
used models are not necessarily adequate in describing the properties of these
measurements. We show that while the two data sets of Gliese 581 can be
modelled reasonably well, the noise model of HD 217107 needs to be revised. We
also reveal some biases in the radial velocities of \u{psion} Andromedae and
report updated orbital parameters for the recently proposed 4-planet model.
Because of the generality of our criterion, no assumptions are needed on the
nature of the measurements, models, or model parameters. The method we propose
can be applied to any astronomical problems, as well as outside the field of
astronomy, because it is a simple consequence of the Bayes' rule of conditional
probabilities.
