# Multivariate analysis

Multivariate analysis (MVA) is based on the principles of multivariate statistics, which involves observation and analysis of more than one statistical outcome variable at a time. Typically, MVA is used to address the situations where multiple measurements are made on each experimental unit and the relations among these measurements and their structures are important.[1] A modern, overlapping categorization of MVA includes[1]:

• Normal and general multivariate models and distribution theory
• The study and measurement of relationships
• Probability computations of multidimensional regions
• The exploration of data structures and patterns

Multivariate analysis can be complicated by the desire to include physics-based analysis to calculate the effects of variables for a hierarchical "system-of-systems". Often, studies that wish to use multivariate analysis are stalled by the dimensionality of the problem. These concerns are often eased through the use of surrogate models, highly accurate approximations of the physics-based code. Since surrogate models take the form of an equation, they can be evaluated very quickly. This becomes an enabler for large-scale MVA studies: while a Monte Carlo simulation across the design space is difficult with physics-based codes, it becomes trivial when evaluating surrogate models, which often take the form of response-surface equations.

## History

Anderson's 1958 textbook, An Introduction to Multivariate Statistical Analysis, educated a generation of theorists and applied statisticians; Anderson's book emphasizes hypothesis testing via likelihood ratio tests and the properties of power functions: Admissibility, unbiasedness and monotonicity.[2][3] MVA once solely stood in the statistical theory realms due to the size, complexity of underlying data set and high computational consumption. With the dramatic growth of computational power, MVA now plays an increasingly important role in data analysis and has wide application in OMICS fields.

## References

1. Olkin, I.; Sampson, A. R. (2001-01-01), Smelser, Neil J.; Baltes, Paul B., eds., Multivariate Analysis: Overview, Pergamon, pp. 10240–10247, ISBN 9780080430768, retrieved 2019-09-02
2. Sen, Pranab Kumar; Anderson, T. W.; Arnold, S. F.; Eaton, M. L.; Giri, N. C.; Gnanadesikan, R.; Kendall, M. G.; Kshirsagar, A. M. et al. (June 1986). "Review: Contemporary Textbooks on Multivariate Statistical Analysis: A Panoramic Appraisal and Critique". Journal of the American Statistical Association 81 (394): 560–564. doi:10.2307/2289251. ISSN 0162-1459. (Pages 560–561)
3. Schervish, Mark J. (November 1987). "A Review of Multivariate Analysis". Statistical Science 2 (4): 396–413. doi:10.1214/ss/1177013111. ISSN 0883-4237.