Detecting Renewal States in Chains of Variable Length via Intrinsic Bayes Factors

TL;DR

This paper introduces a Bayesian method using Intrinsic Bayes Factors to detect renewal states in variable-length Markov chains, enabling the segmentation of sequences into independent blocks.

Contribution

It proposes a novel Bayesian approach with Monte Carlo methods for identifying renewal states in variable-length Markov chains, improving sequence segmentation accuracy.

Findings

Effective detection of renewal states demonstrated on artificial datasets.

Method successfully applied to linguistic data.

Bayesian approach outperforms traditional methods.

Abstract

Markov chains with variable length are useful parsimonious stochastic models able to generate most stationary sequence of discrete symbols. The idea is to identify the suffixes of the past, called contexts, that are relevant to predict the future symbol. Sometimes a single state is a context, and looking at the past and finding this specific state makes the further past irrelevant. States with such property are called renewal states and they can be used to split the chain into independent and identically distributed blocks. In order to identify renewal states for chains with variable length, we propose the use of Intrinsic Bayes Factor to evaluate the hypothesis that some particular state is a renewal state. In this case, the difficulty lies in integrating the marginal posterior distribution for the random context trees for general prior distribution on the space of context trees, with Dirichlet prior for the transition probabilities, and Monte Carlo methods are applied. To show the strength of our method, we analyzed artificial datasets generated from different binary models models and one example coming from the field of Linguistics.