Bayesian Context Trees: Modelling and Exact Inference for Discrete Time Series

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