Plackett-Burman Design: Hadamard Matrix

In course

Description

This lecture covers the Plackett-Burman Design, focusing on the construction and application of Hadamard matrices for efficient estimation of main effects without interactions. It explains the least squares fit for Hadamard matrices, the optimality of VIF, variance function, and de-aliazing techniques. The lecture also discusses the use of Hadamard designs in optimizing factors for a bicycle race.

Instructor

Official source

https://mediaspace.epfl.ch/media/0_sznlv9lf

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Related concepts (53)

Least squares

The method of least squares is a standard approach in regression analysis to approximate the solution of overdetermined systems (sets of equations in which there are more equations than unknowns) by minimizing the sum of the squares of the residuals (a residual being the difference between an observed value and the fitted value provided by a model) made in the results of each individual equation. The most important application is in data fitting.

Linear least squares

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Non-linear least squares

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Fractional factorial design

In statistics, fractional factorial designs are experimental designs consisting of a carefully chosen subset (fraction) of the experimental runs of a full factorial design. The subset is chosen so as to exploit the sparsity-of-effects principle to expose information about the most important features of the problem studied, while using a fraction of the effort of a full factorial design in terms of experimental runs and resources.

Factorial experiment

In statistics, a full factorial experiment is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose experimental units take on all possible combinations of these levels across all such factors. A full factorial design may also be called a fully crossed design. Such an experiment allows the investigator to study the effect of each factor on the response variable, as well as the effects of interactions between factors on the response variable.