MCEM and SAEM Algorithms for Geostatistical Models under Preferential Sampling

TL;DR

This paper introduces MCEM and SAEM algorithms for parameter estimation in geostatistical models affected by preferential sampling, addressing the challenge of intractable likelihood functions and demonstrating their effectiveness through simulations and real data application.

Contribution

The paper develops and compares MCEM and SAEM algorithms for maximum likelihood estimation in preferential sampling models, improving over existing methods.

Findings

Proposed methods achieve accurate parameter estimation.

Algorithms show good prediction performance.

Validated on moss data from Galicia.

Abstract

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.