Determination of hysteresis in finite-state random walks using Bayesian cross validation

TL;DR

This paper presents a Bayesian method with leave-one-out cross validation to determine the hysteresis in finite-state random walks modeled by higher-order Markov chains, addressing biases of traditional criteria.

Contribution

It introduces a Bayesian framework and a closed-form formula for model selection, improving the detection of hysteresis in finite-state processes.

Findings

LOO cross validation effectively determines hysteresis.

Bayes factors are biased with large data, favoring complex models.

AIC favors simpler models with limited data.

Abstract

Consider the problem of modeling hysteresis for finite-state random walks using higher-order Markov chains. This Letter introduces a Bayesian framework to determine, from data, the number of prior states of recent history upon which a trajectory is statistically dependent. The general recommendation is to use leave-one-out cross validation, using an easily-computable formula that is provided in closed form. Importantly, Bayes factors using flat model priors are biased in favor of too-complex a model (more hysteresis) when a large amount of data is present and the Akaike information criterion (AIC) is biased in favor of too-sparse a model (less hysteresis) when few data are present.