A kernel-enriched order-dependent nonparametric spatio-temporal process

Spatio-temporal processes are necessary modeling tools for various environmental, biological, and geographical problems. The underlying model is commonly considered to be parametric and to be a Gaussian process. Additionally, the covariance function is expected to be stationary and separable. This structure need not always be realistic. Moreover, attempts have been made to construct nonparametric processes of neither stationary nor separable covariance functions. Nevertheless, as we elucidate, some desirable and necessary spatio-temporal properties are not guaranteed by the existing approaches, thus, calling for further innovative ideas. In this article, using kernel convolution of order-based dependent Dirichlet process, we construct a novel spatio-temporal model. We show that this satisfies desirable properties and includes the stationary, separable, parametric processes as special cases. Our resultant posterior distribution is variable dimensional, which we attack using Transdimensional Transformation based Markov Chain Monte Carlo, which can update all the variables and change dimensions using deterministic transformations of a random variable drawn from some arbitrary density defined on relevant support. We demonstrate our model’s performance on simulated and real data sets. In all situations, the findings are highly encouraging.