The Bayesian Context Trees (BCT) framework is a recently introduced, general collection of statistical and algorithmic tools for modelling, analysis and inference with discrete-valued time series. The foundation of this development is built in part on some well-known information-theoretic ideas and techniques, including Rissanen's tree sources and Willems et al.'s context-tree weighting algorithm. This paper presents a collection of theoretical results that provide mathematical justifications and further insight into the BCT modelling framework and the associated practical tools. It is shown that the BCT prior predictive likelihood (the probability of a time series of observations averaged over all models and parameters) is both pointwise and minimax optimal, in agreement with the MDL principle and the BIC criterion. The posterior distribution is shown to be asymptotically consistent with probability one (over both models and parameters), and asymptotically Gaussian (over the parameters). And the posterior predictive distribution is also shown to be asymptotically consistent with probability one.

翻译：Bayesian 背景树(BCT)框架是最近推出的统计和算法工具总集,用于建模、分析和推断不同估值时间序列的统计和算法工具。这一发展的基础部分地建立在一些众所周知的信息理论想法和技术之上,包括Rissanen的树源和Willems等人的上下文树加权算法。本文介绍了一系列理论结果,这些理论结果为BCT建模框架和相关实用工具提供了数学理由和进一步的洞察力。它表明BCT先前的预测可能性(所有模型和参数平均观测时间序列的概率)符合MDL原则和BIC标准,是点度和微模量最佳的。后表分布显示与概率之一(相对于模型和参数)的概率之一(相对于参数)基本一致,并且不时态的标定值分布也显示与概率之一一致。