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

Joshua C. Chang

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arXiv · 1702.06221

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

Joshua C. Chang

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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.

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BibTeX RIS

Joshua C. Chang. 2017-02-21. Determination of hysteresis in finite-state random walks using Bayesian cross validation. https://arxiv.org/abs/1702.06221

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