BAYESIAN NONHOMOGENEOUS MARKOV MODELS VIA POLYA-GAMMA DATA AUGMENTATION WITH APPLICATIONS TO RAINFALL MODELING

• 成果类型: Article
• 署名作者: Holsclaw, Tracy; Greene, Arthur M.; Robertson, Andrew W.; Smyth, Padhraic
• 署名单位: University of California System; University of California Irvine; Columbia University
• 刊物名称: ANNALS OF APPLIED STATISTICS
• ISSN/ISSBN: 1932-6157
• DOI: 10.1214/16-AOAS1009
• 发表日期: 2017
• 页码: 393-426
• 关键词: synoptic atmospheric patterns; Multinomial probit model; summer monsoon rainfall; chain monte-carlo; daily precipitation; indian monsoon; interannual variability; inference; oscillation; SPACE

摘要

Discrete-time hiddenMarkov models are a broadly useful class of latentvariable models with applications in areas such as speech recognition, bioinformatics, and climate data analysis. It is common in practice to introduce temporal nonhomogeneity into such models by making the transition probabilities dependent on time-varying exogenous input variables via a multinomial logistic parametrization. We extend such models to introduce additional nonhomogeneity into the emission distribution using a generalized linear model (GLM), with data augmentation for sampling-based inference. However, the presence of the logistic function in the state transition model significantly complicates parameter inference for the overall model, particularly in a Bayesian context. To address this, we extend the recently-proposed Plya-Gamma data augmentation approach to handle nonhomogeneous hidden Markov models (NHMMs), allowing the development of an efficient Markov chain Monte Carlo (MCMC) sampling scheme. We apply our model and inference scheme to 30 years of daily rainfall in India, leading to a number of insights into rainfall-related phenomena in the region. Our proposed approach allows for fully Bayesian analysis of relatively complex NHMMs on a scale that was not possible with previous methods. Software implementing the methods described in the paper is available via the R package NHMM.