Efficient Monte Carlo algorithm for restricted maximum likelihood estimation of genetic parameters

Area of Science:

• Statistics
• Computational Biology
• Quantitative Genetics

Background:

• Monte Carlo (MC) methods are valuable for estimating variance parameters in complex models with large datasets.
• A key challenge with MC methods is the fluctuation in estimates, hindering convergence assessment.
• Newton-type algorithms are sensitive to gradient inaccuracies, exacerbating these fluctuations.

Purpose of the Study:

• To investigate the impact of reusing random numbers within MC samples to mitigate estimation fluctuations.
• To evaluate the performance of MC REML methods (EM, NR, AI, BM) with reused samples.
• To assess the trade-offs between reduced fluctuation and potential bias in variance component estimation.

Main Methods:

• Implemented a novel approach of reusing identical random numbers across MC samples.
• Applied four MC REML methods (Expectation-Maximization, Newton-Raphson, Average Information, Broyden's method) to simulated and field data.
• Analyzed data with varying numbers of variance components (6 and 96).

Main Results:

• Reusing MC samples effectively eliminated round-to-round fluctuations in all tested methods.
• Estimates from MC REML with reused samples showed larger deviations from analytical values than expected, particularly with fewer samples.
• While MC AI REML analyses indicated non-biased variance component estimates on average, a potential bias was observed with reused samples.
• Smooth convergence was achieved, facilitating the use of faster Newton-type algorithms.

Conclusions:

• Reusing MC samples stabilizes estimation and enables efficient use of Newton-type algorithms for variance component estimation.
• A sufficient number of MC samples is crucial to minimize potential bias and achieve acceptable accuracy.
• This technique offers a promising avenue for improving the computational efficiency of complex statistical models.