1,721,061 research outputs found
Confidence bands for regression: the independence point method
No full textIn some circumstances for a linear model with ? parameters ? regression in Rd of the form ? one can find special points ? for which the usual least squares estimators ? of the expected response ? are uncorrelated, independent in the Gaussian case. Following Wynn (Biometrika, 1984) we use this to set up simple piecewise linear confidence bands in the case ?, namely the additive main effect model in multiple regression and some other cases.(this abstract contains LaTex markup that cannot be reproduced here; see the original paper for details)<br/
Cumulant varieties
No full textAbstractFor a discrete distribution in Rd on a finite support D probabilities and moments are algebraically related. If there are n=|D| support points then there are n probabilities p(x),x∈D and n basic moments. By suitable interpolation of the probabilities using a Gröbner basis method, high order moments can be express linearly in terms of n basic moments. A main result is that high order cumulants can also be expressed as polynomial functions of n low order moments and cumulants. This means that statistical models which can be expressed via an algebraically variety for the basic probabilities and moments, such as graphical models, induce a variety for the basic cumulants, which we shall call the “cumulant variety”. It is important to stress that the cumulant variety depends on the monomial ordering defining the original Gröbner basis
Grobner basis methods for structuring and analyzing complex industrial experiments
No full textINTERNATIONAL JOURNAL OF RELIABILITY, QUALITY, AND SAFETY ENGINEERIN
Circuits for robust designs
No full textThis paper continues the application of circuit theory to experimental design started by the first two authors. The theory gives a very special and detailed representation of the kernel of the design model matrix named circuit basis. This representation turns out to be an appropriate way to study the optimality criteria referred to as robustness: the sensitivity of the design to the removal of design points. Exploiting the combinatorial properties of the circuit basis, we show that high values of robustness are obtained by avoiding small circuits. Many examples are given, from classical combinatorial designs to two-level factorial designs including interactions. The complexity of the circuit representations is useful because the large range of options they offer, but conversely requires the use of dedicated software. Suggestions for speed improvement are made
GROBNER BASES AND FACTORISATION IN DISCRETE PROBABILITY AND BAYES
No full textGroebner bases, elimination theory and factorization may be used to perform calculations in elementary discrete probability and more complex areas such as Bayesian networks (influence diagrams). The paper covers the application of computational algebraic geometry to probability theory. The application to the Boolean algebra of events is straightforward (and essentially known). The extension into the probability superstructure is via the polynomial interpolation of densities and log densities and this is used naturally in the Bayesian application
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