Bayesian Nonparametric Modeling of Higher Order Markov Chains

TL;DR

This paper introduces a Bayesian nonparametric approach using tensor factorizations to flexibly model higher order Markov chains, automatically selecting relevant lags and interactions while accounting for uncertainty.

Contribution

It presents a novel Bayesian nonparametric methodology for modeling higher order Markov chains with unknown order and dependence structure, including efficient MCMC algorithms.

Findings

Effective lag selection and interaction modeling demonstrated in simulations

Method successfully applied to real-world data

Bayes factors facilitate hypothesis testing on serial dependence

Abstract

We consider the problem of flexible modeling of higher order Markov chains when an upper bound on the order of the chain is known but the true order and nature of the serial dependence are unknown. We propose Bayesian nonparametric methodology based on conditional tensor factorizations, which can characterize any transition probability with a specified maximal order. The methodology selects the important lags and captures higher order interactions among the lags, while also facilitating calculation of Bayes factors for a variety of hypotheses of interest. We design efficient Markov chain Monte Carlo algorithms for posterior computation, allowing for uncertainty in the set of important lags to be included and in the nature and order of the serial dependence. The methods are illustrated using simulation experiments and real world applications.