Interpolation with Positive Definite Functions

I t i s well-known t h a t k r i g i n g and i n t e r p o l a t i o n by s p l i n e s a r e e q u i v a l e n t . Kr ig ing i s based on a s t o c h a s t i c f o r m u l a t i o n whereas s p l i n e s a r e f o r m u l a t e d I n a d e t e r m i n i s t i c way. A t h i r d p r e s e n t a t i o n i s g i v e n i n terms of Rad ia l P a s i s F u n c t i o n s . The c n n n e c t l o n s between t h e s e t h r e e a r e d e s c r i b e d i n e l emen ta ry terms and implications f o r t h e properties of t h e k r i g i n g e s t i m a t c r a r e r e v i c w ~ d a s t h e y r e l a t e t o i n t e r p o l d t i o n by R a d i a l B d ~ 1 5 function^. R e s u l t s g i v e n by M i c c h e l l i d r e used t c o b t a i n new models f o r g e n e r a l i z e d c o v a r i a n c e s .