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In this article, using kernel convolution of order based dependent Dirichletprocess (Griffin and Steel (2006)) we construct a nonstationary, nonseparable,nonparametric space-time process, which, as we show, satisfies desirableproperties, and includes the stationary, separable, parametric processes asspecial cases. We also investigate the smoothness properties of our proposedmodel. Since our model entails an infinite random series, for Bayesian modelfitting purpose we must either truncate the series or more appropriatelyconsider a random number of summands, which renders the model dimension arandom variable. We attack the variable dimensionality problem usingTransdimensional Transformation based Markov Chain Monte Carlo introduced byDas and Bhattacharya (2019b), which can update all the variables and alsochange dimensions in a single block using essentially a single random variabledrawn from some arbitrary density defined on a relevant support. For the sakeof completeness we also address the problem of truncating the infinite seriesby providing a uniform bound on the error incurred by truncating the infiniteseries.  We illustrate the effectiveness of our model and methodologies on a simulateddata set and demonstrate that our approach significantly outperforms that ofFuentes and Reich (2013) which is based on principles somewhat similar to ours.We also fit two real, spatial and spatio-temporal datasets with our approachand obtain quite encouraging results in both the cases.

Nonstationary, Nonparametric, Nonseparable Bayesian Spatio-Temporal Modeling Using Kernel Convolution of Order Based Dependent Dirichlet Process