Using coupling with the Gibbs sampler to assess convergence in animal models

Area of Science:

• Statistics
• Computational Biology
• Animal Genetics

Background:

• Assessing Markov chain convergence is crucial for reliable statistical inferences.
• Traditional methods for Gibbs sampler convergence assessment can be computationally intensive or require post-analysis.

Purpose of the Study:

• To investigate the coupling method for assessing Gibbs sampler convergence in animal models.
• To evaluate the efficiency and applicability of the coupling method under different model assumptions.

Main Methods:

• The study employed the coupling method, which utilizes two Markov chains with distinct starting points but identical conditional deviates.
• The method was applied to an animal model for marginal inferences.
• Convergence rates were analyzed with known and unknown variance components.

Main Results:

• The coupling method demonstrated exponential convergence for the Gibbs sampler when variance components are known.
• Convergence rates were consistent across all model variables and linked to the largest eigenvalue of a derived matrix.
• Approximately exponential convergence was observed even when variance components were treated as unknowns.

Conclusions:

• The coupling method provides an iterative estimation of Gibbs sampler convergence, negating the need for post-Gibbs analysis.
• It is computationally more efficient than multiple chain methods, requiring only two chains.
• The coupling method offers a robust and less demanding approach to assessing convergence in complex statistical models like animal models.