  We have developed a frequentist approach for model selection which determines
the consistency between any cosmological model and the data using the
distribution of likelihoods from the iterative smoothing method. Using this
approach, we have shown how confidently we can conclude whether the data
support any given model without comparison to a different one. In this current
work, we compare our approach with the conventional Bayesian approach based on
the estimation of the Bayesian evidence using nested sampling. We use simulated
future Roman (formerly WFIRST)-like type Ia supernovae data in our analysis. We
discuss the limits of the Bayesian approach for model selection and show how
our proposed frequentist approach can perform better in the falsification of
individual models. Namely, if the true model is among the candidates being
tested in the Bayesian approach, that approach can select the correct model. If
all of the options are false, then the Bayesian approach will select merely the
least incorrect one. Our approach is designed for such a case and we can
conclude that all of the models are false.
