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Posterior Representations for Bayesian Context Trees: Sampling, Estimation and Convergence
Methodology · Submitted 4 Feb 2022
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods.
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The abstract, sentence by sentence
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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | background 1.00 | 0.11 | 0.04 | asserted 0.99 |
| s1 | 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. | contribution 0.98 | 0.95 | 0.25 | asserted 1.00 |
| s2 | 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. | method 0.56 | 0.94 | 0.15 | asserted 1.00 |
| s3 | This sampler is found to be more efficient than earlier MCMC samplers for the same tasks. | result 1.00 | 0.94 | 0.14 | asserted 1.00 |
| s4 | 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. | result 0.80 | 0.95 | 0.19 | asserted 1.00 |
| s5 | Finally, an extensive study is carried out on the performance of the induced Bayesian entropy estimator. | contribution 0.96 | 0.95 | 0.09 | asserted 0.81 |
| s6 | Its utility is illustrated through both simulation experiments and real-world applications, where it is found to outperform several state-of-the-art methods. | result 1.00 | 0.94 | 0.25 | asserted 1.00 |
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Original abstract
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.
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References
How the literature uses it
2 arXiv papers cite this in 2 sentences
Papers citing it
Cites it as background 2 papers
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In this discrete setting, CTW has been used very widely for data compression [ref] , and BCTs have been used for a range of statistical tasks, including model selection, prediction, entropy estimation, and change-point detection [ref] .
Context-tree weighting for real-valued time series: Bayesian inference with hierarchical mixture models · Introduction · 0.93
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Recent work on Bayesian Context Trees (BCT) by [ref] and [ref] has provided posterior inference and predictive distributions for discrete-time sequence models.
Large Sample Properties of Higher Order Markov Models · Introduction · 0.97
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