标题： 推断马尔可夫链：贝叶斯估计、模型比较、熵率及类外建模 显示英文标题

标题： Inferring Markov Chains: Bayesian Estimation, Model Comparison, Entropy Rate, and Out-of-class Modeling

摘要： 马尔可夫链是一种自然且易于理解的工具，用于描述时间或空间中的单维模式。 我们展示了如何通过应用贝叶斯方法来进行参数估计和模型阶数选择，从而从有限数据推断出任意阶次 $k$ 的马尔可夫链 $k$。 通过扩展离散数据多项式模型的现有结果，我们利用信息论（类型理论）技术将推理与统计力学联系起来。 我们建立了贝叶斯证据与配分函数之间的直接关系，这使得相对熵条件期望和源熵率的方差计算变得简单明了。 最后，我们介绍了一种新颖的方法，该方法利用模型阶数比较与有限数据规模缩放来推断非类内过程的结构。 显示英文摘要

摘要： Markov chains are a natural and well understood tool for describing one-dimensional patterns in time or space. We show how to infer $k$-th order Markov chains, for arbitrary $k$, from finite data by applying Bayesian methods to both parameter estimation and model-order selection. Extending existing results for multinomial models of discrete data, we connect inference to statistical mechanics through information-theoretic (type theory) techniques. We establish a direct relationship between Bayesian evidence and the partition function which allows for straightforward calculation of the expectation and variance of the conditional relative entropy and the source entropy rate. Finally, we introduce a novel method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.