# Variance Components and Generalized Sobol' Indices

@article{Owen2012VarianceCA, title={Variance Components and Generalized Sobol' Indices}, author={Art B. Owen}, journal={SIAM/ASA J. Uncertain. Quantification}, year={2012}, volume={1}, pages={19-41} }

This paper introduces generalized Sobol' indices, compares strategies for their estimation, and makes a systematic search for efficient estimators. Of particular interest are contrasts, sums of squares and indices of bilinear form which allow a reduced number of function evaluations compared to alternatives. The bilinear framework includes some efficient estimators from Saltelli (2002) and Mauntz (2002) as well as some new estimators for specific variance components and mean dimensions. This…

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## References

SHOWING 1-10 OF 37 REFERENCES

### Asymptotic normality and efficiency of two Sobol index estimators

- Mathematics, Economics
- 2013

Many mathematical models involve input parameters, which are not precisely known. Global sensitivity analysis aims to identify the parameters whose uncertainty has the largest impact on the…

### Studies in crop variation. II. The manurial response of different potato varieties

- BiologyThe Journal of Agricultural Science
- 1923

It is not infrequently assumed that varieties of cultivated plants differ not only in their suitability to different climatic and soil conditions, but in their response to different manures, and this supposition affords a means of explaining discrepancies between the results of manurial experiments conducted with different varieties.

### Discovering additive structure in black box functions

- Computer ScienceKDD
- 2004

This paper presents a method that seeks not to display the behavior of a function, but to evaluate the importance of non-additive interactions within any set of variables, and displays of the output as a graphical model of the function for interpretation purposes.

### Valuation of mortgage-backed securities using Brownian bridges to reduce effective dimension

- Mathematics
- 1997

### Total interaction index: A variance-based sensitivity index for interaction screening

- Mathematics
- 2012

We consider the problem of investigating the interaction structure of a multivariate function, possibly containing high order interactions, through variance-based indices. By analogy with the total…

### Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates

- Mathematics
- 2001

### C. R. Rao's minque under four two‐way anova models

- Mathematics
- 1980

This paper presents C. R. RAO'S MINQUE along with their sample variances under four normal two-way ANOVA models. The resulting formulae are similar to the ANOVA sums of squares, equally easy to…

### Estimation of variance components and applications

- Mathematics
- 1988

Matrix Algebra. Asymptotic Distribution of Quadratic Statistics. Variance and Covariance Components Models. Identifiability and Estimability. Minimum Norm Quadratic Estimation. Pooling of Information…