Kriging, cokriging, radial basis functions and the role of positive definiteness

AbstractThere are at least three developments for interpolators that lead to the same functional form for the interpolator; the thin plate spline, radial basis functions and the regression method known as kriging. The key to the interrelationship lies in the positive definiteness of the kernel function. Micchelli has known that a weak form of positive definiteness is sufficient to ensure a unique solution to the system of equations determining the coefficients in the interpolator. Both the positive definiteness and the interpolator can be extended to vector valued functions via the kriging approach which is also independent of the dimension of the underlying space. The kriging approach leads naturally to various methods for simulation as well