A statistical technique for modelling non-stationary spatial processes

A deficiency of kriging is the implicit assumption of second-order stationarity. We present a generalisation to kriging by spatially evolving the spectral density function of a stationary kriging model in the frequency domain. The resulting non-stationary covariance functions are of the same form as the evoloved stationary model, and provide an interpretable view of the local effects underlying the process. The method employs a Bayesian formulation with Markov Chain Monte Carlo(MCMC) sampling, and is demonstrated using a 1D Doppler function, and 2D precipitation data from Scotland.