Related papers: A J-function for inhomogeneous spatio-temporal poi…
We propose new summary statistics for intensity-reweighted moment stationary point processes that generalise the well known J-, empty space, and nearest-neighbour distance distribution functions, represent them in terms of generating…
We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the n-point correlation functions and reduce to cross J- and…
We introduce the notion of intensity reweighted moment pseudostationary point processes on linear networks. Based on arbitrary general regular linear network distances, we propose geometrically corrected versions of different higher-order…
We introduce new estimators of the inhomogeneous $K$-function and the pair correlation function of a spatial point process as well as the cross $K$-function and the cross pair correlation function of a bivariate spatial point process under…
Point processes are stochastic models generating interacting points or events in time, space, etc. Among characteristics of these models, first-order intensity and conditional intensity functions are often considered. We focus on…
We introduce a family of local inhomogeneous mark-weighted summary statistics, of order two and higher, for general marked point processes. Depending on how the involved weight function is specified, these summary statistics capture…
We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In…
The $K$-function is arguably the most important functional summary statistic for spatial point processes. It is used extensively for goodness-of-fit testing and in connection with minimum contrast estimation for parametric spatial point…
We propose new summary statistics to quantify the association between the components in coverage-reweighted moment stationary multivariate random sets and measures. They are defined in terms of the coverage-reweighted cumulant densities and…
We introduce a new variational estimator for the intensity function of an inhomogeneous spatial point process with points in the $d$-dimensional Euclidean space and observed within a bounded region. The variational estimator applies in a…
This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…
Point processes model the distribution of random point sets in mathematical spaces, such as spatial and temporal domains, with applications in fields like seismology, neuroscience, and economics. Existing statistical and machine learning…
A weighted U-statistic based on a random sample X_1,...,X_n has the form U_n=\sum_{1\le i,j\le n}w_{i-j}K(X_i,X_j), where K is a fixed symmetric measurable function and the w_i are symmetric weights. A large class of statistics can be…
This work proposes $\chi^2$-type test statistics to assess different hypotheses on the local structure of an observed marked point pattern. The test statistics is based on the local inhomogeneous extension of the mark-weighted $K$-function…
The K function and its related statistics have been an enduring tool in the analysis of spatial point processes, providing an easy to compute and interpret summary statistic for characterising the interactions between points of one type, or…
Modelling the first-order intensity function is one of the main aims in point process theory, and it has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate.…
U-statistics of spatial point processes given by a density with respect to a Poisson process are investigated. In the first half of the paper general relations are derived for the moments of the functionals using kernels from the Wiener-Ito…
This work proposes a new procedure for estimating the non-stationary spatial covariance function for Spatial-Temporal Deformation. The proposed procedure is based on a monotonic function approach. The deformation functions are expanded as a…
This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…