A Locally Correlated Process and Its Applications in Bayesian Estimation

A class of local correlation functions is obtained from B-spline bases and the corresponding stationary processes are constructed through local integration. Then a local Bayes estimate (LBE) is proposed using this process as a prior in a signal estimation problem. Mean square convergence of this LBE is given as for the case of kriging when the correlation is correctly specified. Moreover, a local convergence is obtained regardless of correct specification of the correlation functions. Finally, some comparisons are conducted to show the outperformance of the LBE to the other methods.