This is page 1 Printer Opaque this Empirical Bayesian Spatial Prediction Using Wavelets(4)

Thus, it is a simple matter to predict optimally the signal S once E ( j w) has been found. The Gaussian assumptions (1) and (2) make the calculation of^ (; 2; ) E ( j w) a very simple exercise (Section 3). Most of this chapter is concerned with speci cation of the hyperparameters; 2, and . Our approach is empirical, but we show that it o ers improvements over the a priori speci cation of ( 0J0;:::; 0J?1 )0=

0 and previous methods of estimating 2 . In Section 3, we outline our methodology for estimating based on Q-Q plots and for estimating 2 based on the variogram. Section 4 contains a brief

0 0 E (S j Y )= E (Wn j w)= Wn E ( j w):

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