Aproximation-Prediction Theory based on Partitions of the
Unity (PU)
This Aproximation-Prediction Theory based on Partitions of the unity
has been designed for isotropic phenomena on metric spaces; however,
this method can be easy modified for versions of prediction theory for anisotropic properties.
The mathematical model analyses many different aspects such as
the study of associated simplicial sets,
the analysis of the precision and
the construction of error estimators,
the choice of the value of parameters to obtain
the `best' approximation-prediction function,
et cetera.
This theorical model has been complemented with some programs which
are able to compute the necessary functions, plots, approximations, predictions,
critical points, etc. This family of miniprograms are contained in
several packages (
download PUP2006) which have been developed
using Mathematica 5.1.
We include, as an example, a preprint entittled
"Spatial prediction by the partition of the unity procedure and its
applications to the calculus of the annual density of the grape moth
Lobesia botrana Den & Schiff (Lepidoptera:Tortricidae) in La Rioja"
(
download pdf)