# Marginal likelihood based model comparison in Fuzzy Bayesian Learning

## TL;DR

This paper extends Fuzzy Bayesian Learning by using marginal likelihood for model comparison, providing a Bayesian alternative to error minimization, validated through synthetic and real-world financial data.

## Contribution

It introduces a Bayesian model evidence approach for selecting the best fuzzy rule base within Fuzzy Bayesian Learning, enhancing model comparison capabilities.

## Key findings

- Marginal likelihood effectively distinguishes between competing fuzzy models.
- Bayesian model selection outperforms mean squared error minimization in case studies.
- Validated approach on synthetic and real financial data.

## Abstract

In a recent paper [1] we introduced the Fuzzy Bayesian Learning (FBL) 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.