Bayesian context trees: Modelling and exact inference for discrete time series

• 成果类型: Article
• 署名作者: Kontoyiannis, Ioannis; Mertzanis, Lambros; Panotopoulou, Athina; Papageorgiou, Ioannis; Skoularidou, Maria
• 署名单位: University of Cambridge; Dartmouth College; University of Cambridge; University of Cambridge; MRC Biostatistics Unit
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12511
• 发表日期: 2022
• 页码: 1287-1323
• 关键词: length markov-chains; ORDER; selection; prediction; methodology; complexity

摘要

We develop a new Bayesian modelling framework for the class of higher-order, variable-memory Markov chains, and introduce an associated collection of methodological tools for exact inference with discrete time series. We show that a version of the context tree weighting alg-orithm can compute the prior predictive likelihood exa-ctly (averaged over both models and parameters), and two related algorithms are introduced, which identify the a posteriori most likely models and compute their exact posterior probabilities. All three algorithms are deterministic and have linear-time complexity. A family of variable-dimension Markov chain Monte Carlo samplers is also provided, facilitating further exploration of the posterior. The performance of the proposed methods in model selection, Markov order estimation and prediction is illustrated through simulation experiments and real-world applications with data from finance, genetics, neuroscience and animal communication. The associated algorithms are implemented in the R package BCT.