MCMC-CE: A Novel and Efficient Algorithm for Estimating Small Right-Tail Probabilities of Quadratic Forms with...

Area of Science:

• Statistics
• Genomics
• Bioinformatics

Background:

• Quadratic forms of multivariate normal variables are crucial in genomics.
• Computing small right-tail probabilities (p-values) for large-scale quadratic forms is computationally challenging.
• Existing methods face numerical constraints and computational burdens.

Purpose of the Study:

• To develop an efficient and accurate algorithm for estimating small p-values for large-scale quadratic forms.
• To address the computational challenges in statistical genomics and bioinformatics.

Main Methods:

• Proposed Markov chain Monte Carlo cross-entropy (MCMC-CE) algorithm.
• Integrated MCMC sampling with the cross-entropy (CE) method.
• Utilized leading eigenvalue extraction and Satterthwaite-type approximation techniques.

Main Results:

• MCMC-CE efficiently estimates small p-values for quadratic forms with ranks exceeding 10,000.
• Demonstrated advantageous numerical accuracy and computational reliability in simulations and genomic applications.
• Outperformed existing methods like Davies', Imhof's, Farebrother's, Liu-Tang-Zhang's, and saddlepoint approximations.

Conclusions:

• MCMC-CE provides a robust and scalable solution for computing small p-values.
• Facilitates more precise statistical inference in large-scale genomic studies.
• Enhances accuracy and reliability in bioinformatics and statistical genomics.