Bayesian Modeling for Nonlinear Time Series of Counts

• Main Authors: Khamthong, Khemmanant, 康凱蘭
• Other Authors: Chen, Cathy W.S.
• Format: Others
• Language: en_US
• Published: 2019
• Online Access: http://ndltd.ncl.edu.tw/handle/7s68v4

博士 === 逢甲大學 === 統計學系應用統計博士班 === 107 === Dengue, a mosquito-borne viral disease, is a main endemic health problem found in many tropical countries. Climatic conditions are significant factors that directly influence the degree of dengue outbreak. In practice, current dengue outbreak forecasting is based on the meteorological reports. In this thesis we propose three types of Bayesian modeling for nonlinear time series of counts with Poisson and negative binomial distributions: Markov switching integer-valued GARCHX (INGARCHX), threshold INGARCHX, and hysteretic INGARCHX models. We design these proposed models through three meteorological variables: rainfall, temperature, and relative humidity. We use one-week-ahead forecasting based on the best-fitted models to monitor and provide an early warning alarm signal of outbreak detection. To demonstrate the pertinence of the approach presented herein, we estimate the nonlinear Poisson (and negative binomial) INGARCHX proposed models using twelve-year weekly dengue cases of four and/or five provinces in northeastern Thailand. This study adopts Bayesian methods, including parameter estimation, forecasting, diagnosis,andmodelselection,whichareflexiblyabletoaccommodatenon-standarddistributional shapesaswellasnonlinearrelationshipsbetweenvariablesfortimeseriesofcountsmodels that are described in the following three parts. In the first part we focus on modeling weekly dengue hemorrhagic fever cases through weekly cumulative precipitation, weekly mean temperature, and weekly relative humidity. Weproposethreenonlinearinteger-valuedGARCHXmodels(Markovswitching,threshold, andlog-linkedMarkovswitchingspecification)withaPoissondistribution. Weperformparameter estimation and model comparison based on Bayesian Markov chain Monte Carlo (MCMC)schemes. Asademonstration,wecarrysimulationstudiestoinvestigatetheeffectiveness of the Bayesian method and also conduct an empirical analysis for weekly dengue cases from five provinces in northeastern Thailand. The evidence strongly confirms that the log-linked Markov switching Poisson INGARCHX model is able to describe consecutive zeros, nonlinear dynamics, and asymmetric effects for the meteorological variables. The posterior probabilities present clear insight into the state change that the model captures in the dataset. Finally, we utilize one-week-ahead forecasting based on prediction intervals to monitor and provide early warning signals for detecting outbreaks. In the second part, we provide two nonlinear negative binomial integer-valued GARCHX models (Markov switching and threshold specification) by incorporating weekly cumulative precipitation, weekly mean maximum temperature, and weekly relative humidity for the weekly dengue cases. These models take account for consecutive zeros, overdispersion, laggeddependence,nonlineardynamics,andasymmetriceffectsfortheclimatologicalvariables. We employ Bayesian MCMC approaches for making inferences and predictions and utilizebothaBayesfactoranddevianceinformationcriterion(DIC)formodelcomparisons. Simulation studies and analytic results emphasize that the Markov switching negative binomial INGARCHX model goes well beyond its potential in describing weekly dengue cases. Finally, we provide one-week-ahead predictions that leads to a useful early warning signal for outbreak detection. The third part introduces modeling weekly dengue hemorrhagic fever cases related to weekly cumulative precipitation, weekly mean temperature, and weekly relative humidity. We propose three types of nonlinear hysteretic integer-valued GARCHX models using Poisson and negative binomial distributions: hysteretic Poisson integer-valued GARCHX model, log-linked hysteretic Poisson integer-valued GARCHX model, and hysteretic negative binomial integer-valued GARCHX models. The three proposed models take into account the statistical features of dengue cases consisting of consecutive zeros, nonlinear dynamics, overdispersion, lagged dependence, and asymmetric effects for the meteorological variables. We apply Bayesian MCMC methods for parameter estimation and model selection based on DIC and IC. The presented results proffer distinct support for the hysteretic negative binomial integer-valued GARCHX model over other competitors. Finally, we offer one-week-ahead predictions to monitor and provide an early warning signal of outbreak detection.