1,721,071 research outputs found
Algebraic geometry in experimental design and related fields.
No full textPhD thesis
Department of Statistics, The University of Warwick (UK
Rational non-commutative formal power series and iterated integral representation of a class of Ito processes
No full textIn 1982 and 1983 two articles [M. Fliess and F. Lamnabhi-Lagarrigue, J. Math. Phys. 23 (1982), no. 4, 495--502; F. Lamnabhi-Lagarrigue and M. Lamnabhi, in Computer algebra 55--67, Lecture Notes in Comput. Sci., 162, Springer, Berlin, 1983] were published in which the previous study is used to analyze the solution of stochastic differential equations in Stratonovich form. A formal power series is associated to the Volterra series with analytic kernels, of the analytic causal functional solution of some SDE. The purpose is to solve the SDE `by series'. Then, the statistics of the solution are deduced by the formal series properties.
In the present paper, starting from these ideas, we analyze this association for functionals for the Wiener process and we give a theorem of convergence, in suitable norm, for formal rational series. In Section 1 we recall some basic algebraic notions which are used in the sequel
The precision space of interpolatory cubature formulae
No full textMethods from Commutative Algebra and Numerical Analysis are combined to address
a problem common to many disciplines: the estimation of the expected value of a polynomial of a random vector using a linear combination of a finite number of its values. In this work we remark on the error estimation in cubature formulæ for polynomial functions and introduce the notion of a precision space for a cubature rule
STRUCTURAL IDENTIFIABILITY: A PREREQUISITE TO PARAMETER ESTIMATION IN STATE SPACE MODELLING
No full textOn error evaluation for interpolatory cubature formulae
No full textIn this work we remark on the error estimation in cubature formulae. Methods from Commutative Algebra and Orthogonal Polynomial Theory are combined to address a problem common to many disciplines: the estimation of the expected value of a polynomial of a random vector using a linear combination of a finite number of its values. We study in particular the error for a special class of nodes
AN ALGEBRAIC COMPUTATIONAL APPROACH TO THE IDENTIFIABILITY OF FOURIER MODELS
No full textComputer algebra and, in particular, Gröbner bases are powerful tools in experimental design [G. Pistone and H. P. Wynn, Biometrika 83 (1996), no. 3, 653--666 MR1423881 ]. This paper applies this algebraic methodology to the identifiability of Fourier models. The choice of the class of trigonometric models forces one to deal with complex entities and algebraic irrational numbers. By means of standard techniques we have implemented a version of the Buchberger algorithm that computes Gröbner bases over the complex rational numbers and other simple algebraic extensions of the rational numbers. Some examples are fully worked out
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