Bayesian context-tree methods for time series
Statistics Seminar
31st January 2025, 1:00 pm – 2:00 pm
Fry Building, 2.04
We introduce a collection of statistical ideas and algorithmic tools for modelling and performing exact inference with both discrete and real-valued time series. For discrete time series, we describe a novel Bayesian framework based on variable-memory Markov chains, called Bayesian Context Trees (BCT). A general prior structure is introduced, and a collection of methodological and algorithmic tools is developed, allowing for efficient, exact Bayesian inference. The proposed approach is then extended to real-valued time series, where it is employed to develop a general hierarchical Bayesian framework for building mixture models based on context trees. The proposed methods are found to outperform several state-of-the-art techniques on simulated and real-world data from a wide range of applications. This is joint work with Ioannis Kontoyiannis.
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