Testing Order Constraints: Qualitative Differences Between Bayes Factors and Normalized Maximum Likelihood

TL;DR

This paper compares Bayes factors and normalized maximum likelihood in testing order constraints, highlighting key qualitative differences in data dependence and model preference.

Contribution

It provides a comparative analysis of two statistical methods for order-constrained model testing, revealing important qualitative distinctions.

Findings

Bayes factors and NML differ in data dependence.

They show different tendencies in model preference.

The comparison clarifies when each method is more suitable.

Abstract

We compared Bayes factors to normalized maximum likelihood for the simple case of selecting between an order-constrained versus a full binomial model. This comparison revealed two qualitative differences in testing order constraints regarding data dependence and model preference.