Detecting Renewal States in Chains of Variable Length via Intrinsic Bayes Factors
This work addresses a specific statistical modeling problem for researchers in stochastic processes and linguistics, but it appears incremental as it applies an existing Bayesian method to a known bottleneck in context tree models.
The authors tackled the problem of identifying renewal states in variable-length Markov chains, which can split the chain into independent blocks, by proposing the use of Intrinsic Bayes Factors to evaluate hypotheses about renewal states, with results demonstrated on artificial binary datasets and a linguistic example.
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.