A Bayesian latent Gaussian conditional autoregressive copula model for analyzing spatially-varying trends in rainfall

Assessing the availability of rainfall water plays a crucial role in rainfed agriculture. Given the substantial proportion of agricultural practices in India being rainfed and considering the potential trends in rainfall amounts across years due to climate change, we build a statistical model for analyzing monsoon total rainfall data for 34 meteorological subdivisions of mainland India available for 1951-2014. Here, we model the marginal distributions using a gamma regression model and the dependence through a Gaussian conditional autoregressive (CAR) copula model. Due to the natural variation in the monsoon total rainfall received across various dry through wet regions of the country, we allow the parameters of the marginal distributions to be spatially varying, under a latent Gaussian model framework. The neighborhood structure of the regions determines the dependence structure of both the likelihood and the prior layers, where we explore both CAR and intrinsic CAR structures for the priors. The proposed methodology also effectively imputes the missing data. We use the Markov chain Monte Carlo algorithms to draw Bayesian inferences. In simulation studies, the proposed model outperforms several competitors that do not allow a dependence structure at the data or prior layers. Implementing the proposed method for the Indian areal rainfall dataset, we draw inferences about the model parameters and discuss the potential effect of climate change on rainfall across India. While the assessment of the impact of climate change on rainfall motivates our study, the proposed methodology can be easily adapted to other contexts dealing with non-Gaussian non-stationary areal datasets where data from single or multiple temporal covariates are also available, and it is appropriate to assume their coefficients to be spatially varying.