School of Medicine Publications and Presentations

Document Type


Publication Date



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.


© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication Title



10.3390/ a14100296

Academic Level


Mentor/PI Department

Office of Human Genetics



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.