# 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.

## Key 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.

---
Source: https://tomesphere.com/paper/1702.06221