Factorial Sampling Plans for Preliminary Computational Experiments

TLDR

Computational models are deterministic programs that map many inputs to outputs, and their complexity makes classical analytical methods impractical. The study seeks to design experiments that identify which inputs have significant effects on a model’s output. The authors use randomized one‑factor‑at‑a‑time designs and analyze the resulting elementary effects to assess input importance. This approach offers advantages by not requiring assumptions of input sparsity, output monotonicity, or low‑order polynomial adequacy.

Abstract

A computational model is a representation of some physical or other system of interest, first expressed mathematically and then implemented in the form of a computer program; it may be viewed as a function of inputs that, when evaluated, produces outputs. Motivation for this article comes from computational models that are deterministic, complicated enough to make classical mathematical analysis impractical and that have a moderate-to-large number of inputs. The problem of designing computational experiments to determine which inputs have important effects on an output is considered. The proposed experimental plans are composed of individually randomized one-factor-at-a-time designs, and data analysis is based on the resulting random sample of observed elementary effects, those changes in an output due solely to changes in a particular input. Advantages of this approach include a lack of reliance on assumptions of relative sparsity of important inputs, monotonicity of outputs with respect to inputs, or adequacy of a low-order polynomial as an approximation to the computational model.