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# Response surface methodology

In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. [1]

In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is not any other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below.

## Bias (statistics)

Statistical bias is a feature of a statistical technique or of its results whereby the expected value of the results differs from the true underlying quantitative parameter being estimated.

## Box–Behnken design

In statistics, Box–Behnken designs are experimental designs for response surface methodology, devised by George E. P. Box and Donald Behnken in 1960, to achieve the following goals.

## C. R. Rao

Calyampudi Radhakrishna Rao, FRS known as C R Rao (born 10 September 1920) is an Indian-American mathematician and statistician.

## Central composite design

In statistics, a central composite design is an experimental design, useful in response surface methodology, for building a second order (quadratic) model for the response variable without needing to use a complete three-level factorial experiment.

## Charles Sanders Peirce

Charles Sanders Peirce ("purse"; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".

## Degree of a polynomial

The degree of a polynomial is the highest degree of its monomials (individual terms) with non-zero coefficients.

## Dependent and independent variables

In mathematical modeling, statistical modeling and experimental sciences, the values of dependent variables depend on the values of independent variables.

## Design of experiments

The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe or explain the variation of information under conditions that are hypothesized to reflect the variation.

## 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.

## 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.

## George E. P. Box

George Edward Pelham Box FRS (18 October 1919 – 28 March 2013) was a British statistician, who worked in the areas of quality control, time-series analysis, design of experiments, and Bayesian inference.

Gradient-Enhanced Kriging (GEK) is a surrogate modeling technique used in engineering.

## Invariant estimator

In statistics, the concept of being an invariant estimator is a criterion that can be used to compare the properties of different estimators for the same quantity.

## IOSO

IOSO (Indirect Optimization on the basis of Self-Organization) is a multiobjective, multidimensional nonlinear optimization technology.

## Jack Kiefer (statistician)

Jack Carl Kiefer (January 25, 1924 – August 10, 1981) was an American statistician.

## Joseph Diez Gergonne

Joseph Diez Gergonne (19 June 1771 at Nancy, France – 4 May 1859 at Montpellier, France) was a French mathematician and logician.

## Journal of the Royal Statistical Society

The Journal of the Royal Statistical Society is a peer-reviewed scientific journal of statistics.

## Lawrence D. Brown

Lawrence David Brown (16 December 1940 – 21 February 2018) was Miers Busch Professor and Professor of Statistics at the Wharton School of the University of Pennsylvania in Philadelphia, Pennsylvania.

## Linear regression

In statistics, linear regression is a linear approach to modelling the relationship between a scalar response (or dependent variable) and one or more explanatory variables (or independent variables).

## Neil Sloane

Neil James Alexander Sloane (born October 10, 1939) is a British-American mathematician.

## Optimal design

In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion.

## Plackett–Burman design

Plackett–Burman designs are experimental designs presented in 1946 by Robin L. Plackett and J. P. Burman while working in the British Ministry of Supply.

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.

## Polynomial and rational function modeling

In statistical modeling (especially process modeling), polynomial functions and rational functions are sometimes used as an empirical technique for curve fitting.

## Polynomial regression

In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. Polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted E(y |x), and has been used to describe nonlinear phenomena such as the growth rate of tissues, the distribution of carbon isotopes in lake sediments, and the progression of disease epidemics.

## Probabilistic design

Probabilistic design is a discipline within engineering design.

## Society for Industrial and Applied Mathematics

The Society for Industrial and Applied Mathematics (SIAM) is an academic association dedicated to the use of mathematics in industry.

## Spherical design

A spherical design, part of combinatorial design theory in mathematics, is a finite set of N points on the d-dimensional unit ''d''-sphere Sd such that the average value of any polynomial f of degree t or less on the set equals the average value of f on the whole sphere (that is, the integral of f over Sd divided by the area or measure of Sd).

## Stephen Stigler

Stephen Mack Stigler (born August 10, 1941) is Ernest DeWitt Burton Distinguished Service Professor at the Department of Statistics of the University of Chicago.

## Surrogate model

A surrogate model is an engineering method used when an outcome of interest cannot be easily directly measured, so a model of the outcome is used instead.

## References

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