242 research outputs found
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
Marked spatial point processes: current state and extensions to point processes on linear networks
Within the applications of spatial point processes, it is increasingly
becoming common that events are labeled by marks, prompting an exploration
beyond the spatial distribution of events by incorporating the marks in the
undertaken analysis. In this paper, we first consider marked spatial point
processes in , where marks are either integer-valued, real-valued, or
object-valued, and review the state-of-the-art to analyze the spatial structure
and type of interaction/correlation between marks. More specifically, we review
cross/dot-type summary characteristics, mark-weighted summary characteristics,
various mark correlation functions, and frequency domain approaches. Second, we
propose novel cross/dot-type higher-order summary characteristics,
mark-weighted summary characteristics, and mark correlation functions for
marked point processes on linear networks. Through a simulation study, we show
that ignoring the underlying network gives rise to erroneous conclusions about
the interaction/correlation between marks. Finally, we consider two
applications: the locations of two types of butterflies in Melbourne,
Australia, and the locations of public trees along the street network of
Vancouver, Canada, where trees are labeled by their diameters at breast height.Comment: submitted for publicatio
Summary characteristics for multivariate function-valued spatial point process attributes
Prompted by modern technologies in data acquisition, the statistical analysis
of spatially distributed function-valued quantities has attracted a lot of
attention in recent years. In particular, combinations of functional variables
and spatial point processes yield a highly challenging instance of such modern
spatial data applications. Indeed, the analysis of spatial random point
configurations, where the point attributes themselves are functions rather than
scalar-valued quantities, is just in its infancy, and extensions to
function-valued quantities still remain limited. In this view, we extend
current existing first- and second-order summary characteristics for
real-valued point attributes to the case where in addition to every spatial
point location a set of distinct function-valued quantities are available.
Providing a flexible treatment of more complex point process scenarios, we
build a framework to consider points with multivariate function-valued marks,
and develop sets of different cross-function (cross-type and also
multi-function cross-type) versions of summary characteristics that allow for
the analysis of highly demanding modern spatial point process scenarios. We
consider estimators of the theoretical tools and analyse their behaviour
through a simulation study and two real data applications.Comment: submitted for publicatio
intensitynet: Intensity-based Analysis of Spatial Point Patterns Occurring on Complex Networks Structures in R
The statistical analysis of structured spatial point process data where the
event locations are determined by an underlying spatially embedded relational
system has become a vivid field of research. Despite a growing literature on
different extensions of point process characteristics to linear network
domains, most software implementations remain restricted to either directed or
undirected network structures and are of limited use for the analysis of rather
complex real-world systems consisting of both undirected and directed parts.
Formalizing the network through a graph theoretic perspective, this paper
discusses a complementary approach for the analysis of network-based event data
through generic network intensity functions and gives a general introduction to
the intensitynet package implemented in R covering both computational details
and applications. By treating the edges as fundamental entities, the
implemented approach allows the computation of intensities and other related
values related to different graph structures containing undirected, directed,
or a combination of both edges as special cases. The package includes
characteristics for network modeling, data manipulation, intensity estimation,
computation of local and global autocorrelation statistics, visualization, and
extensions to marked point process scenarios. All functionalities are
accompanied by reproducible code examples using the chicago data as toy example
to illustrate the application of the package.Comment: submitted for publicatio
Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes
A method for dealing with multivariate analysis of marked spatio-temporal point processes is presented by introducing different partial point characteristics, and by extending the spatial dependence graph model formalism. The approach yields a unified framework for different types of spatio-temporal data, including both, purely qualitatively (multivariate) cases and multivariate cases with additional quantitative marks. The proposed graphical model is defined through partial spectral density characteristics; it is highly computationally efficient and reflects the conditional similarity amongst sets of spatio-temporal sub-processes of either points or marked points with identical discrete marks. Two applications, on crime and forestry data, are presented
Seasonality in extra-pulmonary tuberculosis notifications in Germany 2004-2014- a time series analysis
Background
Seasonality in tuberculosis (TB) has been found in different parts of the world, showing a peak in spring/summer and a trough in autumn/winter. The evidence is less clear which factors drive seasonality. It was our aim to identify and evaluate seasonality in the notifications of TB in Germany, additionally investigating the possible variance of seasonality by disease site, sex and age group.
Methods
We conducted an integer-valued time series analysis using national surveillance data. We analysed the reported monthly numbers of started treatments between 2004 and 2014 for all notified TB cases and stratified by disease site, sex and age group.
Results
We detected seasonality in the extra-pulmonary TB cases (N = 11,219), with peaks in late spring/summer and troughs in fall/winter. For all TB notifications together (N = 51,090) and for pulmonary TB only (N = 39,714) we did not find a distinct seasonality. Additional stratified analyses did not reveal any clear differences between age groups, the sexes, or between active and passive case finding.
Conclusion
We found seasonality in extra-pulmonary TB only, indicating that seasonality of disease onset might be specific to the disease site. This could point towards differences in disease progression between the different clinical disease manifestations. Sex appears not to be an important driver of seasonality, whereas the role of age remains unclear as this could not be sufficiently investigated.Peer Reviewe
- …