CUED Publications database

Bayesian Context Trees: Modelling and exact inference for discrete time series

Kontoyiannis, I and Mertzanis, L and Panotopoulou, A and Papageorgiou, I and Skoularidou, M Bayesian Context Trees: Modelling and exact inference for discrete time series. (Unpublished)

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Abstract

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 algorithm can compute the prior predictive likelihood exactly (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.

Item Type: Article
Uncontrolled Keywords: stat.ME stat.ME cs.IT math.IT stat.AP stat.CO
Subjects: UNSPECIFIED
Divisions: Div F > Signal Processing and Communications
Depositing User: Cron Job
Date Deposited: 06 Aug 2020 03:10
Last Modified: 25 Aug 2020 01:30
DOI: