Functional inverted Wishart for Bayesian multivariate spatial modeling with application to regional climatology model data

Modern environmental and climatological studies produce multiple outcomes at high spatial resolutions. Multivariate spatial modeling is an established means to quantify cross‐correlation among outcomes. However, existing models typically suffer from poor computational efficiency and lack the flexibility to simultaneously estimate auto‐ and cross‐covariance structures. In this article, we undertake a novel construction of covariance by utilizing spectral convolution and by imposing an inverted Wishart prior on the cross‐correlation structure. The cross‐correlation structure with this functional inverted Wishart prior flexibly accommodates not only positive but also weak or negative associations among outcomes while preserving spatial resolution. Furthermore, the proposed model is computationally efficient and produces easily interpretable results, including the individual autocovariances and full cross‐correlation matrices, as well as a partial cross‐correlation matrix reflecting the outcome correlation after excluding the effects caused by spatial convolution. The model is examined using simulated data sets under different scenarios. It is also applied to the data from the North American Regional Climate Change Assessment Program, examining long‐term associations between surface outcomes for air temperature, pressure, humidity, and radiation, on the land area of the North American West Coast. Results and predictive performance are compared with findings from approaches using convolution only or coregionalization.