Bayesian Nonparametric Modeling of Higher Order Markov Chains. Issue 516 (1st October 2016)

• Record Type: Journal Article
• Authors: Sarkar, Abhra; Dunson, David B.
• Is Part Of: Journal of the American Statistical Association. Volume 111:Issue 516(2016)
• Page Start: 1791
• Page End: 1803
• Publication Date: 2016-10-01
• Subjects: Bayesian nonparametrics -- Categorical time series -- Conditional tensor factorization -- Higher order Markov chains -- Sequential categorical data; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2015.1115763
• Languages: English
• ISSNs: 0162-1459

Abstract

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. Supplementary materials for this article are available online.