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

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  • 1Vertex Pharmaceuticals, Boston MA 02210, USA, hanzifei1@gmail.com.

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Summary

This study compares Monte Carlo methods for Gaussian copula models. The Geweke-Hajivassiliou-Keane simulator is recommended for its computational efficiency in estimating parameters for geostatistical count data.

Keywords:
60G1060G6062M30Data cloningGaussian random fieldMarkov chain Monte CarloMultivariate normal integralSimulated likelihood

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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.