Hydrologists are often faced with selecting amongst a set of competing models with different numbers of parameters and ability to fit available data. Bayes’ factor is a tool that can be used to compare models; however, it is very difficult to compute Bayes' factor numerically. In our paper, we explore and develop highly efficient algorithms for computing Bayes’ factor of hydrological systems, which will introduce this useful tool for selecting models into everyday hydrological practice.