Ege Holger Rubak

Aalborg University

19Publications

7H-index

501Citations

Publications 19

Newest

#1M. Mehdi MoradiH-Index: 2

#2Ottmar Cronie (Umeå University)H-Index: 6

Last.Adrian Baddeley (Curtin University)H-Index: 35

view all 6 authors...

Voronoi estimators are non-parametric and adaptive estimators of the intensity of a point process. The intensity estimate at a given location is equal to the reciprocal of the size of the Voronoi/Dirichlet cell containing that location. Their major drawback is that they tend to paradoxically under-smooth the data in regions where the point density of the observed point pattern is high, and over-smooth where the point density is low. To remedy this behaviour, we propose to apply an additional smo...

#1Adrian Baddeley (Curtin University)H-Index: 35

#2Ege Holger Rubak (AAU: Aalborg University)H-Index: 7

Last.Rolf Turner (University of Auckland)H-Index: 13

view all 3 authors...

Abstract For point process models fitted to spatial point pattern data, we describe diagnostic quantities analogous to the classical regression diagnostics of leverage and influence. We develop a simple and accessible approach to these diagnostics, and use it to extend previous results for Poisson point process models to the vastly larger class of Gibbs point processes. Explicit expressions, and efficient calculation formulae, are obtained for models fitted by maximum pseudolikelihood, maximum l...

#1Jesper MøllerH-Index: 59

#2Morten NielsenH-Index: 18

Last.Ege Holger RubakH-Index: 7

view all 4 authors...

Functional summary statistics for point processes on the sphere with an application to determinantal point processes

#1Jesper Møller (AAU: Aalborg University)H-Index: 59

#2Ege Holger Rubak (AAU: Aalborg University)H-Index: 7

Abstract We study point processes on S d , the d -dimensional unit sphere S d , considering both the isotropic and the anisotropic case, and focusing mostly on the spherical case d = 2 . The first part studies reduced Palm distributions and functional summary statistics, including nearest neighbour functions, empty space functions, and Ripley’s and inhomogeneous K -functions. The second part partly discusses the appealing properties of determinantal point process (DPP) models on the sphere and p...

Mechanistic spatio-temporal point process models for marked point processes, with a view to forest stand data

#1Jesper Møller (AAU: Aalborg University)H-Index: 59

#2Mohammad Ghorbani (AAU: Aalborg University)H-Index: 4

Last.Ege Holger Rubak (AAU: Aalborg University)H-Index: 7

view all 3 authors...

type="main" xml:lang="en"> We show how a spatial point process, where to each point there is associated a random quantitative mark, can be identified with a spatio-temporal point process specified by a conditional intensity function. For instance, the points can be tree locations, the marks can express the size of trees, and the conditional intensity function can describe the distribution of a tree (i.e., its location and size) conditionally on the larger trees. This enable us to construct param...

#1Adrian Baddeley (Curtin University)H-Index: 35

#2Rolf Turner (University of Auckland)H-Index: 13

Last.Ege Holger Rubak (AAU: Aalborg University)H-Index: 7

view all 3 authors...

We investigate an analogue of the likelihood ratio test for spatial Gibbs point process models fitted by maximum pseudolikelihood or maximum composite likelihood. The test statistic must be adjusted in order to obtain an asymptotic χ2 distribution under the null hypothesis. Adjustments developed for composite likelihoods of finite systems of random variables are adapted to the point process setting. Recent results in point process theory are used to estimate the composite information J and sensi...

#1Jesper MøllerH-Index: 59

#2Ege Holger RubakH-Index: 7

#1Adrian Baddeley (Curtin University)H-Index: 35

#2Ege Holger Rubak (AAU: Aalborg University)H-Index: 7

Last.Rolf Turner (University of Auckland)H-Index: 13

view all 3 authors...

BASICS Introduction Point patterns Statistical methodology for point patterns About this book Software Essentials Introduction to RR Packages for R Introduction to spatstat Getting started with spatstat FAQ Collecting and Handling Point Pattern Data Surveys and experiments Data handling Entering point pattern data into spatstat Data errors and quirks Windows in spatstat Pixel images in spatstat Line segment patterns Collections of objects Interactive data entry in spatstat Reading GIS file forma...

#1Frédéric Lavancier (University of Nantes)H-Index: 13

#2Jesper Møller (AAU: Aalborg University)H-Index: 59

Last.Ege Holger Rubak (AAU: Aalborg University)H-Index: 7

view all 3 authors...

type="main" xml:id="rssb12096-abs-0001"> Statistical models and methods for determinantal point processes (DPPs) seem largely unexplored. We demonstrate that DPPs provide useful models for the description of spatial point pattern data sets where nearby points repel each other. Such data are usually modelled by Gibbs point processes, where the likelihood and moment expressions are intractable and simulations are time consuming. We exploit the appealing probabilistic properties of DPPs to develop ...

12