Extending Morris method: identification of the interaction graph using cycle-equitable designs

Abstract

The paper presents designs that allow detection of mixed effects when performing preliminary screening of the inputs of a scalar function of d input factors, in the spirit of Morris' Elementary Effects approach. We introduce the class of -cycle equitable designs as those that enable computation of exactly c second-order effects on all possible pairs of input factors. Using these designs, we propose a fast Mixed Effects screening method, that enables efficient identification of the interaction graph of the input variables. Design definition is formally supported on the establishment of an isometry between sub-graphs of the unit cube equipped of the Manhattan metric, and a set of polynomials in on which a convenient inner product is defined. In the paper we present systems of equations that recursively define these -cycle equitable designs for generic values of , from which direct algorithmic implementations are derived. Application cases are presented, illustrating the application of the proposed designs to the estimation of the interaction graph of specific functions.

Keywords:

• sensitivity analysis
• interaction graph
• Morris method
• elementary effects
• clustered designs
• second-order effects

AMS Subject Classification::

• 62K99
• 05B30
• 05C75
• 05C90

Acknowledgements

The authors acknowledge fruitful discussions with other colleagues during the SAMO 2013 meeting, and thank the reviewers for their careful reading and comments, that helped to considerably improve the original manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Notation denotes the Kroenecker symbol, begin equal to one if proposition a is true and zero otherwise.

Additional information

Funding

This work was partially funded by the ANR through project DESIRE (Designs for Spatial Random Fields), contract ANR 1-IS01-0001. Project web-site : www.i3s.unice.fr/desire.