Shot noise Cox processes

By Jesper Møller. Advances in Applied Probability, 2003

180 citations recorded by the source corpus.

Subfields: Applied Mathematics, Artificial Intelligence, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/0a23381916e3cd1c45dc121a1e5836ac9aa380af

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Citations in the corpus

Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes (2013, methodology): “(iv) PCP2(ν, σ, α,mc, ζ 2, θ, ω): geometric anisotropic Poisson cluster processes, as defined in (iii) but with g(u, v) = g0 (√ uΣ−1ut, v ) , where u ∈ R2 is a row vector with transpose ut, the function g0 is such that g is locally integrable (see Møller and Toftager, 2012), Σ is a 2 × 2 symmetric p”
Lévy-based Cox point processes (2008, methodology): “shot noise Cox processes defined by means of generalized gamma measures [5], log Gaussian Cox processes [9], [33], and shot noise Cox processes [28].”
The permanental process (2006, methodology): “Examples are shot noise Cox processes [3], [23] and log Gaussian Cox processes”
Structured Spatio‐Temporal Shot‐Noise Cox Point Process Models, with a View to Modelling Forest Fires (2010, methodology): “…in the spatial case where the two main classes of models are log-Gaussian Cox processes and shot-noise Cox processes (Møller et al., 1998; Wolpert and Ickstadt, 1998; Brix, 1999; Møller, 2003; Diggle, 2003; Møller and Waagepetersen, 2004, 2007; Møller and Torrisi, 2005, Hellmund et al., 2008).”
Bayesian mixture modeling for spatial Poisson process intensities, with applications to extreme value analysis (2007, background): “processes are studied by Mller (2003) and Mller and Torrisi (2005), though the focus”
Residual analysis for spatial point processes (with discussion) (2005, methodology): “41/ The right-hand side can be estimated by Markov chain Monte Carlo methods (Møller et al., 1998; Møller, 2003; Møller and Waagepetersen, 2003a) so that the residuals can then be computed.”
Two‐step estimation for inhomogeneous spatial point processes (2009, background): “Shot-noise Cox processes provide a further extension where the fixed mean cluster size α is replaced by a random variable, see Møller (2003) and Waagepetersen and Schweder (2006).”
Handbook of Spatial Statistics (2008, methodology): “The log ratio of normalizing constants is approximated by evaluating the outer integral in (4.16) using e.g. the trapezoidal rule and the expectation using MCMC methods (Berthelsen and Møller, 2003; Møller and Waagepetersen, 2004).”
Perfect simulation of Hawkes processes (2005, methodology): “Assuming, for the moment, that F (the CDF for the length of a cluster) is known, the following algorithm for perfect simulation of the marked Hawkes process is similar to the algorithm for simulation of Poisson cluster processes without edge effects given in [6] (see also [17] and [21]).”
Order-Based Dependent Dirichlet Processes (2006, background): “Møller (2003) defined shot noise Cox processes that could generate a very wide class of potential forms for the autocorrelation function.”
Generalised shot noise Cox processes (2005, methodology): “Reduced Palm distributions and J -functions A simple description of the reduced Palm distribution of an SNCP was established in [31].”