Determination of hysteresis in finite-state random walks using Bayesian cross validation
This work addresses model selection bias in hysteresis modeling for random walks, which is incremental as it refines existing methods for a specific statistical problem.
The authors tackled the problem of determining hysteresis in finite-state random walks by introducing a Bayesian cross-validation framework to identify the number of prior states influencing trajectories, finding that Bayes factors favor overly complex models with large datasets while AIC favors overly sparse models with small datasets.
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.