Inferring Markov chains: Bayesian estimation, model comparison, entropy rate, and out-of-class modeling

作     者：Christopher C. Strelioff James P. Crutchfield Alfred W. Hübler 

作者机构：Center for Computational Science & Engineering and Physics Department University of California at Davis One Shields Avenue Davis California 95616 USA Center for Complex Systems Research and Physics Department University of Illinois at Urbana-Champaign 1110 West Green Street Urbana Illinois 61801 USA 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2007年第76卷第1期

页      面：011106-011106页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

主　　题：STATISTICAL COMPLEXITY HOLLIDAY JUNCTIONS DYNAMICS INFORMATION INFERENCE INDUCTION ORDER 

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 kth 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 method that uses finite data-size scaling with model-order comparison to infer the structure of out-of-class processes.