Alternative implementations of Monte Carlo EM algorithms for likelihood inferences.

Area of Science:

• Statistics
• Computational Statistics
• Quantitative Genetics

Background:

• Variance components are crucial for understanding variation in complex traits.
• Restricted maximum likelihood (REML) is a standard method for estimating variance components.
• The expectation-maximisation (EM) algorithm is often used with REML, but requires computationally intensive estimators.

Purpose of the Study:

• To review and compare existing Monte Carlo methods for REML variance component estimation.
• To propose a novel Monte Carlo approach for improved computational efficiency.
• To evaluate the performance of different methods using simulated datasets.

Main Methods:

• Review of two established Monte Carlo estimators for variance components via REML-EM.
• Development and introduction of a third, alternative Monte Carlo estimation strategy.
• Performance comparison of the three methods using simulated data.

Main Results:

• The study provides a comparative analysis of the computational performance and accuracy of the reviewed and proposed methods.
• Simulated data results indicate potential advantages of the suggested approach under specific conditions.
• Quantitative insights into the trade-offs between different Monte Carlo estimation techniques are presented.

Conclusions:

• The proposed Monte Carlo method offers a potentially more efficient alternative for variance component estimation in certain scenarios.
• Understanding the performance characteristics of different estimators is vital for selecting appropriate methods in statistical genetics and related fields.
• Further research may explore the application of these methods to real-world complex datasets.