Comparing Bayesian model selection with a frequentist approach using iterative method of smoothing residuals

We have developed a frequentist approach for model selection which determines consistency of a 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 distinguish different models without comparison with one another. In this current work, we compare our approach with conventional Bayesian approach based on estimation of Bayesian evidence using nested sampling for the purpose of model selection. We use simulated future Roman (formerly WFIRST)-like type Ia supernovae data in our analysis. We discuss limits of the Bayesian approach for model selection and display how our proposed frequentist approach, if implemented appropriately, can perform better in falsification of individual models.