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PEP 0006 Kernel Density Estimation
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========  ======================================
Author    Serge Rey <sjsrey@gmail.com>
          Charles Schmidt <schmidtc@gmail.com>
 
Status    Draft
Created   11-Oct-2010
Updated   11-Oct-2010
========  ======================================

Abstract
========

The kernel density estimation module will provide a uniform interface to a set
of kernel density estimation (KDE) methods. Currently KDE is used in various places
within PySAL
(e.g., :class:`~pysal.weights.Distance.Kernel`,
:class:`~pysal.esda.smoothing.Kernel_Smoother`) as well as in STARS and
various projects within the GeoDA Center, but these implementations were done
separately. This module would centralize KDE within PySAL as well as extend
the suite of KDE methods and related measures available in PySAL.

Motivation
==========

KDE is widely used throughout spatial analysis, from estimation of process
intensity in point pattern analysis, deriving spatial weights, geographically
weighted regression, rate smoothing, to hot spot detection, among others. 


Reference Implementation
========================


Since KDE would be used throughout existing (and likely future) modules in
PySAL, it makes sense to implement it as a top level module in PySAL.

Core KDE methods that would be implemented include:

   * triangular
   * uniform
   * quadratic
   * quartic
   * gaussian

Additional classes and methods to deal with KDE on restricted spaces would
also be implemented.

A unified KDE api would be developed for use of the module.

Computational optimization would form a significant component of the effort
for this PEP.

References
==========

in progress
