A simple application of FIC to model selection

TL;DR

This paper demonstrates how the Frequentist Information Criterion (FIC) can be applied to model selection, illustrating the emergence of model complexities with AIC-like and BIC-like scaling in a simplified, analytically tractable example.

Contribution

It provides a straightforward example of applying FIC, showing how model complexities naturally scale with data size in a clear, analytical manner.

Findings

Model complexities scale with data size similarly to AIC and BIC.

FIC can be applied in simple, analytically tractable scenarios.

The example illustrates the reconciliation of information-based and frequentist inference.

Abstract

We have recently proposed a new information-based approach to model selection, the Frequentist Information Criterion (FIC), that reconciles information-based and frequentist inference. The purpose of this current paper is to provide a simple example of the application of this criterion and a demonstration of the natural emergence of model complexities with both AIC-like ($N^0$) and BIC-like ($\log N$) scaling with observation number $N$. The application developed is deliberately simplified to make the analysis analytically tractable.