Department of Statistics, The Ohio State University
Statistics and Biostatistics Colloquium Series

During the past decade, a useful model for non-stationary random fields has been developed. This consists of reducing the random field of interest to isotropy via a bijective bi-continuous deformation of the index space. Then the problem consists of estimating this space deformation together with the isotropic correlation in the deformed index space. We propose to estimate both this space deformation and this isotropic correlation using a constrained continuous version of simulated annealing based on the Metropolis-Hastings algorithm. This method provides a non-parametric estimation of the deformation that has the required property to be bijective; previous non-parametric methods did not guarantee this property. We also give one idea of how spatial prediction should proceed in the new coordinate space. We illustrate our work with an example based on a precipitation dataset.