arXiv subjects

Matthias Eckardt

Publications and source records attributed to Matthias Eckardt.

23 records · Page 2Linked to original sources

arXiv2017

Second-order and local characteristics of network intensity functions

The last decade has witnessed an increase of interest in the spatial analysis of structured point patterns over networks whose analysis is challenging because of geometrical complexities and unique methodological problems. In this context, it is essential to incorporate the network specificity into the analysis as the locations of events are restricted to areas covered by line segments. Relying on concepts originating from graph theory, we extend the notions of first-order network intensity functions to second-order and local network intensity functions. We consider two types of local indicators of network association functions which can be understood as adaptations of the primary ideas of local analysis on the plane. We develop the node-wise and cross-hierarchical type of local functions. A real dataset on urban disturbances is also presented.

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arXiv2016

Graphical modelling of multivariate spatial point processes with continuous marks

This paper is the second in a series of papers which combine graphical modelling and marked spatial point patterns. Extending the previous results of \cite Eckardt (2016a), we introduce a marked spatial dependence graph model which depicts the global dependence structure of quantitatively marked multi-type points that occur in space based on the marked conditional partial spectral coherence. Most beneficial, no structural assumption with respect to the characteristics in the data are to be made prior to analysis. This approach presents a computationally efficient method of pattern recognition in highly structured and high dimensional multi-type spatial point processes where also quantitative marks are available. Unlike all previous methods, our new model permits the simultaneous analysis of all multivariate conditional interrelations. The new technique is illustrated analysing the diameter at breast hight of 37 different tree species recorded at 10053 locations in Duke Forest.

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arXiv2016

Graphical modelling of multivariate spatial point processes

This paper proposes a novel graphical model, termed the spatial dependence graph model, which captures the global dependence structure of different events that occur randomly in space. In the spatial dependence graph model, the edge set is identified by using the conditional partial spectral coherence. Thereby, nodes are related to the components of a multivariate spatial point process and edges express orthogonality relation between the single components. This paper introduces an efficient approach towards pattern analysis of highly structured and high dimensional spatial point processes. Unlike all previous methods, our new model permits the simultaneous analysis of all multivariate conditional interrelations. The potential of our new technique to investigate multivariate structural relations is illustrated using data on forest stands in Lansing Woods as well as monthly data on crimes committed in the City of London.

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arXiv2016

Structured network regression for spatial point patterns

The analysis of spatial point patterns that occur in the network domain have recently gained much attraction and various intensity functions and measures have been proposed. However, the linkage of spatial network statistics to regression models has not been approached so far. This paper presents a new regression approach which treats a generic intensity function of a planar point pattern that occurred on a network as the outcome of a set of different covariates and various graph statistics. Different to all alternative approaches, our model is the first which permits the statistical analysis of complex regression data in the context of network intensity functions for spatial point patterns. The potential of our new technique to model the structural dependencies of network intensity functions on various covariates and graph statistics is illustrated using call-in data on neighbour and community disturbances in an urban context.

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arXiv2016

Point patterns occurring on complex structures in space and space-time: An alternative network approach

This paper presents an alternative approach of analyzing possibly multitype point patterns in space and space-time that occur on network structures, and introduces several different graph-related intensity measures. The proposed formalism allows to control for processes on undirected, directional as well as partially directed network structures and is not restricted to linearity or circularity.

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