MAXIMUM LIKELIHOOD ESTIMATION OF GAUSSIAN COPULA MODELS FOR GEOSTATISTICAL COUNT DATA.

Area of Science:

• Statistics
• Computational Statistics
• Geostatistics

Background:

• Gaussian copula models are used for geostatistical count data.
• Computing maximum likelihood estimators (MLEs) is challenging due to high-dimensional integrals.
• Existing methods include Genz-Bretz and Geweke-Hajivassiliou-Keane (GHK) simulators.

Purpose of the Study:

• To investigate and compare computational methods for MLEs in Gaussian copula models.
• To evaluate a new data cloning algorithm alongside existing Monte Carlo methods.
• To identify the most statistically and computationally efficient method.

Main Methods:

• Review of Genz-Bretz and GHK Monte Carlo simulators.
• Investigation of a novel data cloning algorithm using Markov chain Monte Carlo (MCMC).
• Simulation study to compare statistical and computational performance.

Main Results:

• All three methods demonstrated similar statistical properties.
• The Geweke-Hajivassiliou-Keane simulator exhibited the least computational effort.
• The data cloning algorithm, while functional, was not superior in efficiency.

Conclusions:

• The Geweke-Hajivassiliou-Keane simulator is the recommended method for its computational efficiency.
• The study provides practical guidance for analyzing geostatistical count data with Gaussian copula models.
• A real-world application using Lansing Woods tree count data illustrates the methods.