The problem of preferential sampling in geostatistics arises when the choise of location to be sampled is made with information about the phenomena in the study. The geostatistical model under preferential sampling deals with this problem, but parameter estimation is challenging because the likelihood function has no closed form. We developed an MCEM and an SAEM algorithm for finding the maximum likelihood estimators of parameters of the model and compared our methodology with the existing ones: Monte Carlo likelihood approximation and Laplace approximation. Simulated studies were realized to assess the quality of the proposed methods and showed good parameter estimation and prediction in preferential sampling. Finally, we illustrate our findings on the well known moss data from Galicia.

翻译：地理统计学的优先抽样问题出现时,要抽样的地点的粗略位置与研究中的现象有关的信息。在优先抽样下的地理统计模型处理这一问题,但参数估计具有挑战性,因为可能性功能没有封闭形式。我们开发了MCEM和SAEM算法,以找到模型参数的最大可能性估计器,并将我们的方法与现有的方法(蒙特卡洛概率近似和拉普尔近似)进行比较。我们进行了模拟研究,以评估拟议方法的质量,并在优惠抽样中显示良好的参数估计和预测。最后,我们展示了我们从加利西亚获得的众所周知的苔类数据的调查结果。