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The problem of preferential sampling in geostatistics arises when the choiseof location to be sampled is made with information about the phenomena in thestudy. The geostatistical model under preferential sampling deals with thisproblem, but parameter estimation is challenging because the likelihoodfunction has no closed form. We developed an MCEM and an SAEM algorithm forfinding the maximum likelihood estimators of parameters of the model andcompared our methodology with the existing ones: Monte Carlo likelihoodapproximation and Laplace approximation. Simulated studies were realized toassess the quality of the proposed methods and showed good parameter estimationand prediction in preferential sampling. Finally, we illustrate our findings onthe well known moss data from Galicia.

MCEM and SAEM Algorithms for Geostatistical Models under Preferential Sampling