We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a simple variable-dimensional Monte Carlo sampler for the joint posterior distribution on models and parameters, which can efficiently produce independent samples. This sampler is found to be more efficient than earlier MCMC samplers for the same tasks. Then, the branching process representation is used to establish the asymptotic consistency of the BCT posterior, including the derivation of an almost-sure convergence rate. Finally, an extensive study is carried out on the performance of the induced Bayesian entropy estimator. Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods.
翻译:我们重新审视了离散时间序列的Bayesian上下文树建模框架(BCT),最近发现这一建模框架在包括模型选择、估计和预测在内的许多任务中非常有效。从简单的分流过程得出了模型空间上诱导的后层分布的新颖的表述,并在理论和实践中探讨了其中的若干后果。首先,我们发现分支过程的表述导致一个简单的多维蒙特卡洛采集器,用于模型和参数上的联合后部分布,从而可以有效产生独立样本。这一取样器比早期的MCMC取样器在相同任务上的效率要高。然后,分流过程的表述被用来确立BCT后部外部分布的一致性,包括得出几乎可以保证的趋同率。最后,对导出的Bayesian entropy 估计仪的性能进行了广泛的研究,通过模拟实验和现实世界应用来说明其效用,在那里发现它优于几种最先进的方法。