I am searching for spatial statistics software which has many powerful features and supports a GIS interface.
Can anyone give me some advice?
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In a nutshell: Start with QGIS.
There are several Free and Open Source tools for geospatial statistics.
There are several spatial statistics plugins in Quantum GIS, such as
QGIS 2.0 Processing is a graphical modelling environment that integrates with several prominent projects, including SAGA and GRASS, some of which contain various statistical algorithms.
SAGA has over 400 modules for geoprocessing and statistical analysis.
GRASS contains several zonal statistics functions.
The R Language has several spatial extensions.
The Spatstat module for R provides a host of spatial statistics functions.
R Studio is a very nice IDE for the R Language, and will help you to easily locate and install the R spatial libraries.
GeoDa is free, cross-platform software designed for dynamic visualization, exploratory spatial data analysis, and spatial statistics. It has been around for almost 15 years (starting as an ArcView 3.x extension, it was recoded to be independent of ArcView after ESRI abandoned the old AV architecture). It is associated with an illustrious group of GIS educators and researchers.
See also GRASS and R integration:
For example boxplots:
... or decision trees (rpart example):
ArcGIS has Spatial Statistics Toolbox for statistical information. it analyze spatial distributions, patterns, processes, and relationships.
Spatial statistics allow you to:
Summarize the key characteristics of a distribution. Identify statistically significant spatial clusters (hot spots/cold spots) and spatial outliers. Assess overall patterns of clustering or dispersion. Model spatial relationships.
you can get information here.
A new software that is now also available is insensa GIS at www.insensa.org, "free and open source software for statistical computing and display of GIS data." You can also e.g. calculate correlations, view scatterplots ... In case the function you want to use is not available, you may also write your own plugin.
There are few interesting packages from the Spatial Data Mining and Visual Analytics Lab, especially:
CrimeStat is also worth having a look. Although focused on crime analysis, the functionality can be adapted to other purposes.
SANET is an ArcGIS toolset for analysis based on networks.
GeoSOM is a package for creating spatial Self-Organizing Maps.