Likelihood and Non‐parametric Bayesian MCMC Inference for Spatial Point Processes Based on Perfect Simulation and Path Sampling

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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).”
Bayesian Inference and Model Assessment for Spatial Point Patterns Using Posterior Predictive Samples (2017, background): “Alternatively, Berthelsen and Møller (2002, 2003) develop a perfect simulation algorithm to simulate from spatial point processes such as Strauss processes.”
Modern Statistics for Spatial Point Processes * (2007, methodology): “Stoyan & Stoyan (1998), Kerscher (2000), Boots, Okabe & Thomas (2003), Diggle (2003) and Ballani (2006).”
Markov chain Monte Carlo for a Spatial-Temporal Autologistic Regression Model (2008, methodology): “More recently, Berthelsen and Møller (2003) used path sampling to approximate the ratio of unknown normalizing constants in spatial point processes, but the amount of computation involved can be rather large (see also Gelman and Meng 1998; Zhu et al. 2008).”
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).”