3,698 research outputs found
A Statistical Toolbox For Mining And Modeling Spatial Data
Most data mining projects in spatial economics start with an evaluation of a set of attribute variables on a sample of spatial entities, looking for the existence and strength of spatial autocorrelation, based on the Moran’s and the Geary’s coefficients, the adequacy of which is rarely challenged, despite the fact that when reporting on their properties, many users seem likely to make mistakes and to foster confusion. My paper begins by a critical appraisal of the classical definition and rational of these indices. I argue that while intuitively founded, they are plagued by an inconsistency in their conception. Then, I propose a principled small change leading to corrected spatial autocorrelation coefficients, which strongly simplifies their relationship, and opens the way to an augmented toolbox of statistical methods of dimension reduction and data visualization, also useful for modeling purposes. A second section presents a formal framework, adapted from recent work in statistical learning, which gives theoretical support to our definition of corrected spatial autocorrelation coefficients. More specifically, the multivariate data mining methods presented here, are easily implementable on the existing (free) software, yield methods useful to exploit the proposed corrections in spatial data analysis practice, and, from a mathematical point of view, whose asymptotic behavior, already studied in a series of papers by Belkin & Niyogi, suggests that they own qualities of robustness and a limited sensitivity to the Modifiable Areal Unit Problem (MAUP), valuable in exploratory spatial data analysis
Isotropic Multiple Scattering Processes on Hyperspheres
This paper presents several results about isotropic random walks and multiple
scattering processes on hyperspheres . It allows one to
derive the Fourier expansions on of these processes. A
result of unimodality for the multiconvolution of symmetrical probability
density functions (pdf) on is also introduced. Such
processes are then studied in the case where the scattering distribution is von
Mises Fisher (vMF). Asymptotic distributions for the multiconvolution of vMFs
on are obtained. Both Fourier expansion and asymptotic
approximation allows us to compute estimation bounds for the parameters of
Compound Cox Processes (CCP) on .Comment: 16 pages, 4 figure
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