Marginal Likelihood Based Model Comparison in Fuzzy Bayesian Learning

In a recent paper [1], we introduced the fuzzy Bayesian learning paradigm where expert opinions can be encoded in the form of fuzzy rule bases and the hyper-parameters of the fuzzy sets can be learned from data using a Bayesian approach. The present paper extends this work for selecting the most appropriate rule base among a set of competing alternatives, which best explains the data, by calculating the model evidence or marginal likelihood. We explain why this is an attractive alternative over simply minimizing a mean squared error metric of prediction and show the validity of the proposition using synthetic examples and a real world case study in the financial services sector.