Perfect simulation and inference for point processes given noisy observations
The authors deal with the problem of exact simulation of an unobserved true point process conditional on a noise observation and focus on specific features of the proposed simulation technique. The paper starts with the presentation of a noise model which specifies the relation between the true and observed point pattern through such point process operations as thinning, displacement, censoring and superposition. This is followed by description of the posterior distribution of the true point process. The authors propose to apply a modification method called dominated coupling from the past (CFTP) to spatial birth-and-death process to produce an exact sample of the target posterior distribution. New aspects of the developed algorithm are the sampling of a market point process, the use of an augmented state space and the problem of specific optimisation of the coupling of the target chains. An optimised coupling makes the algorithm considerable faster than with the standard coupling used in dominated CFTP for point processes. The perfect simulations are used for inference and the results are compared to the ordinary Metropolis-Hastings sampler.
scientific article; zbMATH DE number 2169412