论文标题
贝叶斯语境树的后验表示：采样，估计和收敛
Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence
论文作者
论文摘要
我们重新审视离散时间序列的贝叶斯上下文树（BCT）建模框架，最近发现在包括模型选择，估计和预测在内的许多任务中非常有效。模型空间上诱导的后验分布的新颖表示是根据简单的分支过程得出的，从理论和实践中探讨了这一点的几种后果。首先，表明分支过程表示会导致模型和参数上的联合后验分布，从而导致一个简单的变量蒙特卡洛采样器，该分布可以有效地产生独立的样品。对于相同任务，发现该采样器比早期的MCMC采样器更有效。然后，使用分支过程表示来建立BCT后部的渐近一致性，包括几乎纯净的收敛速率的推导。最后，对诱导的贝叶斯熵估计器的性能进行了广泛的研究。通过仿真实验和现实世界应用程序来说明其实用性，在该应用程序中，发现它的表现优于几种最新方法。
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.
