有限状态随机游动滞后的贝叶斯交叉验证
Determination of hysteresis in finite-state random walks using Bayesian cross validation
摘要：
考虑使用高阶马尔可夫链对有限状态随机游动的滞后建模问题。这封信介绍了一个贝叶斯框架，以确定，从数据中，在最近的历史上，一个轨迹是统计依赖的先前状态的数量。一般的建议是使用留一交叉验证，使用以封闭形式提供的易于计算的公式。重要的是，当存在大量数据时，使用平面模型先验的贝叶斯因子偏向于过于复杂的模型（更多滞后），而赤池信息准则（AIC）偏向于过于稀疏的模型（较少滞后）。
英文摘要：
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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