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Explore the people, places, events, achievements, struggles and stories that shaped our journey.
Movements, leaders, victories and the continuing fight for equality.
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Katherine Johnson’s mathematical calculations helped guide some of America’s most important early space missions while she confronted the racial and gender barriers faced by Black women in twentieth-century America.
MORE →Reflects the personal views, recollections, and perspective of the author, Mike Davis.
This is a personal recollection on the Move fire on May 13, 1985
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became very useful because other methods available, such as the theoretical model, could be very cumbersome to use, time-consuming, inefficient, error-prone, and unreliable. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process.
Statistical approaches such as RSM can be employed in industry to maximize the output of a specific product by optimization of operational factors.
An easy way to estimate a first-degree polynomial model is to use a factorial experiment or a fractional factorial design. This is sufficient to determine which explanatory variables affect the response variable(s) of interest. Once it is suspected that only significant explanatory variables are left, then a more complicated design, such as a central composite design can be implemented to estimate a second-degree polynomial model, which is still only an approximation at best. However, the second-degree model can be used to optimize (maximize, minimize, or attain a specific target for) the response variable(s) of interest.
Cubic designs are discussed by Kiefer, by Atkinson, Donev, and Tobias and by Hardin and Sloane.
Spherical designs are discussed by Kiefer and by Hardin and Sloane.
Mixture experiments are discussed in many books on the design of experiments, and in the response-surface methodology textbooks of Box and Draper and of Atkinson, Donev and Tobias. An extensive discussion and survey appears in the advanced textbook by John Cornell.
Some extensions of response surface methodology deal with the multiple response problem. Multiple response variables create difficulty because what is optimal for one response may not be optimal for other responses. Other extensions are used to reduce variability in a single response while targeting a specific value, or attaining a near maximum or minimum while preventing variability in that response from getting too large.
Response surface methodology uses statistical models, and therefore practitioners need to be aware that even the best statistical model is an approximation to reality. In practice, both the models and the parameter values are unknown, and subject to uncertainty on top of ignorance. Of course, an estimated optimum point need not be optimum in reality, because of the errors of the estimates and of the inadequacies of the model.
Nonetheless, response surface methodology has an effective track-record of helping researchers improve products and services: For example, Box's original response-surface modeling enabled chemical engineers to improve a process that had been stuck at a saddle-point for years. The engineers had not been able to afford to fit a cubic three-level design to estimate a quadratic model, and their biased linear-models estimated the gradient to be zero. Box's design reduced the costs of experimentation so that a quadratic model could be fit, which led to a (long-sought) ascent direction.[1][2]
| Scientific method | |
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| Treatment and blocking | |
| Models and inference | |
| Designs Completely randomized | |
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| Correlation and dependence | |||||||||
| Regression analysis | |||||||||
| Regression as a statistical model |
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| Decomposition of variance | |||||||||
| Model exploration | |||||||||
| Background | |||||||||
| Design of experiments | |||||||||
| Numerical approximation | |||||||||
| Applications | |||||||||
Source: Wikipedia. Article content is retrieved live through the MediaWiki API.
In statistics, response surface methodology (RSM) explores the relationships between several explanatory variables and one or more response variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became very useful because other methods available, such as the theoretical model, could be very cumbersome to use, time-consuming, inefficient, error-prone, and unreliable. The method was introduced by George E. P. Box and K. B. Wilson in 1951. The main idea of RSM is to use a sequence of designed experiments to obtain an optimal response. Box and Wilson suggest using a second-degree polynomial model to do this. They acknowledge that this model is only an approximation, but they use it because such a model is easy to estimate and apply, even when little is known about the process. Statistical approaches such as RSM can be employed in industry to maximize the output of a specific product by optimization of operational factors.
Phenotypic response surfaces (PRS) is an artificial intelligence-guided personalized medicine platform that relies on combinatorial optimization principles to quantify drug interactions and efficacies to develop optimized combination therapies to treat a broad spectrum of illnesses. Phenotypic response surfaces fit a parabolic surface to a set of drug doses and biomarker values based on the understanding that the relationship between drugs, their interactions, and their effect on the measure biomarker can be modeled by quadric surfaces. The resulting surface allows for the omission of both in-vitro and in-silico screening of multi-drug combinations based on a patient's unique phenotypic response. This provides a method to utilize small data sets to create time-critical personalized therapies that is independent of the disease or drug mechanism. The adaptable nature of the platform allows it to tackle a wide range of applications from isolating novel combination therapies to predicting daily drug regimen adjustments to support in-patient treatments.
Christine Michaela Anderson-Cook (born 1966) is an American and Canadian statistician known for her work on the design of experiments, response surface methodology, reliability analysis in quality engineering, multiple objective optimization and decision-making, and the applications of statistics in nuclear forensics. She has published over 250 research articles in statistical, engineering and interdisciplinary journals. She has also written on misunderstandings caused by "hidden jargon": technical terms in statistics that are difficult to distinguish from colloquial English. Anderson-Cook is a project leader in the US National Technical Nuclear Forensics Center, a research scientist at the Los Alamos National Laboratory, and a former chair of the American Statistical Association Section of Quality and Productivity and of the American Society for Quality Statistics Division.
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. After the designed experiment is performed, linear regression is used, sometimes iteratively, to obtain results. Coded variables are often used when constructing this design.
Before the 1921 destruction of Tulsa’s Greenwood District, Black residents had created a remarkable center of business and community life. The district included stores, professional offices, entertainment venues and homes owned by Black citizens. Understanding Greenwood means learning what was built—not only what was burned.
MORE →Brown v. Board of Education in 1954.
