Application of a Gibbs Sampler to estimating parameters of a hierarchical normal model with a time trend and testing for existence of the global warming

Abstract

This research is devoted to studying statistical inference implemented using the Gibbs Sampler for a hierarchical Bayesian linear model with first order autoregressive structure. This model was applied to global-mean monthly temperatures from January 1880 to April 2008 and used to estimate a time trend coefficient and to test for the existence of global warming. The global temperature increase estimated by Gibbs Sampler was found to be between 0.0203℃ and 0.0284℃ per decade with 95% credibility. The difference between Gibbs Sampler estimate and ordinary least squares estimate for the time trend was insignificant. Further, a simulation study with data generated from this model was carried out. This study showed that the Gibbs Sampler estimators for the intercept and for the time trend were less biased than corresponding ordinary least squares estimators, while the reverse was true for the autoregressive parameter and error standard deviation. The difference in precision of the estimators found by the two approaches was insignificant except for the samples of small sizes. The Gibbs Sampler estimator of the time trend has significantly smaller mean square error than ordinary least squares estimator for the smaller sample sizes studied. This report also describes how the software package WinBUGS can be used to carry out the simulations required to implement a Gibbs Sampler.