Minimum Divergence Solutions for Incorporating Categorical Information in a Spatial Mapping Context

• Activity Number: 646
• Type: Topic Contributed
• Date/Time: Thursday, August 2, 2012 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Patrick Bogaert*+
• Companies: Universite Catholique de Louvain
• Keywords: maximum entropy ; minimum divergence ; probability tables ; spatial mapping

Abstract

In this presentation, we will show how the maximum entropy (MaxEnt) and minimum expected divergence (MinDiv) criteria can be used for including categorical information into a spatial mapping framework. The general case of the minimization of an expected divergence involving equality and inequality constraints is presented. It is shown how the MaxEnt problem can be approximated by a MinNorm problem, thus leading naturally to the idea of iterated MinNorm steps for finding the MaxEnt solution. It is then shown how the minimum divergence problem generalizes the idea and extends it to the case of inequalities as well. Finally, it is shown how topological properties are handy when it comes to account jointly for equalities and inequalities.

The potential benefits of the methodology are important for spatial applications in general, when mixing continuous and categorical variables is required. It also opens perspectives for integrating more diffuse information (expert opinions, prior beliefs, etc.) into the same framework, thanks to the possibility of accounting for inequality relationships. Accordingly, the whole methodology will be illustrated based on environmental real case studies.