A comparison of Bayesian models for daily ozone concentration levels

Abstract

Recently, there has been a surge of interest in Bayesian space-time modeling of daily maximum eight-hour average ozone concentration levels. Hierarchical models based on well known time series modeling methods such as the dynamic linear models (DLM) and the auto-regressive (AR) models are often used in the literature. The DLM, developed as a result of the popularity of Kalman filtering methods, provide a dynamical state-space system that is thought to evolve from a pair of state and observation equations. The AR models, on the other hand, cast in a Bayesian hierarchical setting, have recently been developed through a pair of models where a measurement error model is formulated at the top level and an AR model for the true ozone concentration levels is postulated at the next level. Each of the modeling scenarios is set in an appropriate multivariate setting to model the spatial dependence. This paper compares these two methods in hierarchical Bayesian settings. A simplified skeletal version of the DLM taken from Dou et al. (2009) is compared theoretically with a matching hierarchical AR model. The comparisons reveal many important differences in the induced space-time correlation structures. Further comparisons of the variances of the predictive distributions by conditioning on different sets of data for each model show superior performances of the AR models under certain conditions. These theoretical investigations are followed-up by a simulation study and a real data example implemented using Markov chain Monte Carlo (MCMC) methods for modeling daily maximum eighthour average ozone concentration levels observed in the state of New York in the months of July and August, 2006. The hierarchical AR model is chosen by all the model choice criteria considered in this example.

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Identifiers

ORCID for Sujit K. Sahu: orcid.org/0000-0003-2315-3598

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