Markov Point Processes

By B. D. Ripley, Frank P. Kelly. 1977

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, methodology): “The Gibbs point process provides such an approach, offering a general framework for incorporating correlations among selected items [33, 107, 108, 120, 124, 125, 148].”
A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns (2000, background): “Pairwise interaction processes (Ripley and Kelly (1977); Ripley (1977); Diggle et al. (1994)) can incorporate varying degrees of spatial regularity and provide reasonable empirical models.”
An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants (2006, background): “…probability distributions with intractable normalising constants arise in a number of statistical problems, including the definition of Gibbs distributions such as Markov random fields (Besag, 1974; Cressie, 1993) and Markov point processes (Ripley and Kelly, 1977; Møller and Waagepetersen, 2003b).”
Properties of residuals for spatial point processes (2008, background): “In applications we often consider the special case of a Markov point process (Ripley and Kelly 1977) of finite interaction range R ∞.”
Characterization results and Markov chain Monte Carlo algorithms including exact simulation for some spatial point processes (1999, methodology): “The Ripley and Kelly (1977) Markov point processes as well as certain Poisson cluster processes (Daley and Vere-Jones 1988) are special cases of (2.5); cf. Baddeley et al .”
Model distortions in Bayesian MAP reconstruction (2007, background): “Markov random models [8, 49, 23, 35, 9, 20, 30, 3] concentrate on the local characteristics of X , namely the distribution for each pixel xi conditionally to its neighbors xj , j ∈ Ni: fX(xi ∣”
Residual analysis for spatial point processes (with discussion) (2005, background): “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): “As in van Lieshout and Baddeley [22] suppose that Φcent is a finite Markov (or Gibbs) point process [1, 20, 33, 39, 40] defined on a bounded Borel set B ⊂ R.”
Point process limits of lattice processes (1982, background): “Ripley and Kelly (1977) mention but do not exploit possible connections between pairwise-interaction lattice models and point processes.”
Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns (2000, methodology): “…ds ðt2 identical to that of the inhomogeneous Poisson process with intensity function ë. 3 Thinned Markov point process 3.1 Introduction The class of Markov point processes (Ripley and Kelly, 1977, Baddeley and MÖller, 1989) allows for parametric modelling of clustering or repulsion between points.”
On the toric algebra of graphical models (2006, methodology): “The factorization of distributions according to exponential models is well studied (e.g., [2, 4, 5, 24 ]).”