Pseudolikelihood for Exponential Family Models of Spatial Point Processes

By Jens Ledet Jensen, J. Møller. 1991

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Citations in the corpus

Determinantal Point Processes for Machine Learning (2012, methodology): “…attention has been paid to approximate inference algorithms for Markov point processes, employing pseudolikelihood [Besag, 1977, Besag et al., 1982, Jensen and Moller, 1991, Ripley, 1991], Markov chain Monte Carlo methods [Ripley and Kelly, 1977, Besag and Green, 1993, Häggström et al., 1999,…”
An efficient Markov chain Monte Carlo method for distributions with intractable normalising constants (2006, unknown): “Maximum likelihood and maximum pseudo likelihood estimation for spatial point processes and particularly the Strauss process is well established (Besag, 1977; Jensen and Møller, 1991; Geyer and Møller, 1994; Geyer, 1999; Baddeley and Turner, 2000; Møller and Waagepetersen, 2003a,b).”
Logistic regression for spatial Gibbs point processes (2014, background): “(9) Thus, if the last term in (8) is replaced by its integral compensator the score of the pseudolikelihood is obtained (Jensen & Møller, 1991).”
Spatial Point Processes and their Applications (2007, background): “Powerful advantages of the pseudolikelihood are that it avoids the normalising constant present in the likelihood, that it is usually easy to compute and maximise, and that it retains good properties such as consistency and asymptotic normality in a large-sample limit [25, 24].”
Gibbs point processes for studying the development of spatial-temporal stochastic processes (2001, methodology): “The parameters of the pair potential functions can be estimated using, for example, maximum likelihood (ML) (Ogata and Tanemura, 1985; Penttinen, 1984; Geyer and Thompson, 1992; Geyer and MHller, 1994), or maximum pseudo-likelihood (MPL) (Jensen and MHller, 1991; S, arkk, a, 1993; Goulard et al., 19”
spatstat: An R Package for Analyzing Spatial Point Patterns (2005, background): “Disadvantages of maximum pseudolikelihood (MPL) include its small-sample bias and in-eﬃciency Besag (1977); Jensen and Møller (1991); Jensen and K¨unsch (1994) relative to maximum likelihood estimators (MLE).”
Handbook of Spatial Statistics (2008, methodology): “35 and rC = 2.45 (distances are measured in ft), which are given by the observed minimum interpoint distances in the two types of point patterns. Using positive hard cores rM and rC may be viewed as an ad hoc approach to obtain a model which is well-defined for all real values of the parameters βM ,”
Model-Based Multiple Instance Learning (2017, background): “On the other hand, disadvantages of MPL (relative to ML) such as small-sample bias and inefficiency [44], [46] become less significant with large data.”
Residual analysis for spatial point processes (with discussion) (2005, background): “…of the log-pseudolikelihood of the point process that is defined by log{PL.θ, x/}= ∑ xi∈x log{λθ.xi, x/}− ∫ W λθ.u, x/du .12/ (Besag, 1978; Jensen and Møller, 1991) since the pseudoscore can be written @ @θ log{PL.θ, x/}= ∫ W @ @θ log{λθ.u, x/}dIθ.u/: .13/ Applying formula (8) to h.u,…”
Bayesian Analysis of Markov Point Processes (2006, methodology): “We introduce an auxiliary variable x defined on the same space as the state space of y. Assume that x has a normalised conditional density f(x|θ, y), so that the joint density of (θ, x, y) is given by π(θ, x, y) = f(x|θ, y)π(y|θ)π(θ).”
A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns (2000, background): “For Markov processes of finite range, maximum pseudo-likelihoodestimators are consistent (Jensen and Møller (1991)).”