Markov Point Processes and Their Applications

By V. Lieshout. 2000

399 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, background): “The Gibbs point process provides such an approach, offering a general framework for incorporating correlations among selected items [Preston, 1976, Ripley and Kelly, 1977, Ripley, 1991, Van Lieshout, 2000, Møller and Waagepetersen, 2004, 2007, Daley and Vere-Jones, 2008].”
A non-model-based approach to bandwidth selection for kernel estimators of spatial intensity functions (2018, methodology): “Throughout this paper, let be a point process in Rd , d 1, observed within some nonempty open and bounded observation window W ⊆ Rd (Daley & Vere-Jones, 2008; Diggle, 2014; Illian et al., 2008; van Lieshout, 2000).”
Residual analysis for spatial point processes (with discussion) (2005, methodology): “For Markov point processes (Ripley and Kelly, 1977; van Lieshout, 2000) it is convenient to model X by λ rather than by f , since λ plays the same role as the local characteristics do for Markov random fields when specifying local Markov properties.”
Generalised shot noise Cox processes (2005, background): “The results in Section 3.2 on reduced Palm distributions and J -functions may, to some extent, be useful for statistical applications [34], [47], [48].”
Logistic regression for spatial Gibbs point processes (2014, background): “Spatial Gibbs and Markov point processes are important classes of models for spatial depen- 25 dence in point patterns (van Lieshout, 2000) with a broad range of applications (e.g. Harkness & Isham, 1983; Stoyan & Penttinen, 2000; Mattfeldt et al., 2007; Funwi-Gabga & Mateu, 2012).”
Model-Based Multiple Instance Learning (2017, background): “ributed with mean (A), if A 1;:::;A m ˆXare disjoint (compact) sets, then the random variables N (A 1 );:::;N m are independent. In general the probability density of a point process may not exist [28], [29]. To ensure that probability densities are available, we restrict ourselves to ﬁnite point p”
A J-function for inhomogeneous point processes (2010, neutral): “For further details, see for example [10, 12, 16].”
Mapping local density of young Eucalyptus plantations by individual tree detection in high spatial resolution satellite images (2013, methodology): “As the reader can find abundant literature on the subject from the mathematical point of view (e.g. Stoyan et al., 1995; van Lieshout, 2000; Jacobsen, 2006), or from an image processing point of view (Descombes, 2012), we present here only the basics of marked point process modeling along with…”
Determinantal Point Processes (2016, background): “[9], [10], [16], [16], [29], [23], [18] and [32].”
spatstat: An R Package for Analyzing Spatial Point Patterns (2005, background): “…a large body of techniques for analysing spatial point patterns (e.g. Bartlett (1975); Cliﬀ and Ord (1981); Cressie (1991); Diggle (2003); van Lieshout (2000); Mat´ern (1986); Møller and Waagepetersen (2003); Moore (2001); Ripley (1981, 1988); Stoyan, Kendall, and Mecke (1995); Stoyan and…”
Ecological information from spatial patterns of plants: insights from point process theory (2009, methodology): “Choosing an appropriate point-process model requires detailed knowledge of available modelling approaches such as those discussed in van Lieshout (2000) and Møller & Waagepetersen (2004).”
Sequential Monte Carlo methods for multitarget filtering with random finite sets (2005, methodology): “Then vΥ defines a (unitless) measure on the Borel subsets of E, and is called the intensity measure of Υ [8], [43], [44].”
On Estimation of the Intensity Function of a Point Process (2011, neutral): “Consequently, by the Nguyen–Zessin formula (see e.g. Van Lieshout 2000; Stoyan et al. 1995), To do so, write (cid:2) d − 1 for sets of d − 1 distinct points in (cid:2) .”
Modern Statistics for Spatial Point Processes * (2007, methodology): “In short, ‘Modern statistics for spatial point processes’, where recent textbooks include Van Lieshout (2000), Diggle (2003), Møller & Waagepetersen (2003b), and Baddeley et al. (2006).”
The permanental process (2006, background): “…Boson process; Cox process; density of spatial point process; determinantal process; factorial moment measure; fermion process; Gaussian process; infinite divisibility; simulation; spatio-temporal process; weighted permanent 2000 Mathematics Subject Classification: Primary 60G55 Secondary 62M30”