School of Medicine Publications and Presentations
Document Type
Article
Publication Date
10-14-2021
Abstract
Statistical analysis of multinomial data in complex datasets often requires estimation of the multivariate normal (MVN) distribution for models in which the dimensionality can easily reach 10–1000 and higher. Few algorithms for estimating the MVN distribution can offer robust and efficient performance over such a range of dimensions. We report a simulation-based comparison of two algorithms for the MVN that are widely used in statistical genetic applications. The venerable Mendell- Elston approximation is fast but execution time increases rapidly with the number of dimensions, estimates are generally biased, and an error bound is lacking. The correlation between variables significantly affects absolute error but not overall execution time. The Monte Carlo-based approach described by Genz returns unbiased and error-bounded estimates, but execution time is more sensitive to the correlation between variables. For ultra-high-dimensional problems, however, the Genz algorithm exhibits better scale characteristics and greater time-weighted efficiency of estimation.
Recommended Citation
Blondell, L.; Koz, M.Z.; Blangero, J.; Göring, H.H.H. Genz and Mendell-Elston Estimation of the High-Dimensional Multivariate Normal Distribution. Algorithms 2021, 14, 296. https://doi.org/10.3390/ a14100296
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Publication Title
Algorithms
DOI
10.3390/ a14100296
Academic Level
faculty
Mentor/PI Department
Office of Human Genetics
Comments
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.