Combining Adaptive MCMC and Nested Sampling for Robust Bayesian Model Selection with reduced prior sensitivity

Bayes Factors provide a rigorous methodology for the Bayesian assessment of competing models. However, this approach faces inherent challenges. The computation of Bayesian evidence often involves evaluating high-dimensional, analytically intractable integrals. Moreover, Bayesian evidence is particularly sensitive to prior assumptions, which can significantly bias model comparison. While extensive research has been conducted to address the former limitation, the latter remains a challenging open area of research. To address this issue, this work introduces DRAM-NS, a new methodology combining Nested Sampling (NS) with adaptive Markov Chain Monte Carlo (MCMC) techniques for Bayesian model selection. Specifically, the developed technique enhances the traditional NS algorithm by incorporating a preliminary MCMC step on a subset of the available data, allowing for natural integration of non-informative or improper priors. The effectiveness of the proposed approach is demonstrated through several case studies. Numerical results and discussion demonstrate that DRAM-NS provides a more reliable framework than standard NS alone for model selection in scenarios where prior knowledge is uncertain.