305,227 research outputs found
A short history of algebraic statistics
No full textIn algebraic statistics, computational techniques from algebraic geometry
become tools to address statistical problems. This, in turn, may prompt research in
algebraic geometry. The basic ideas at the core of algebraic statistics will be presented.
In particular we shall consider application to contingency tables and to design of experiments
On the description and identifiability analysis of experiments with mixtures
No full textIn a mixture experiment the collinearity problems, implied by the sum to one functional relationship among the factors, have strong consequences on the identification and analysis of regression models for such designs. Here to address these problems, mixture designs are represented as sets of homogeneous polynomials. Techniques from computational commutative algebra are employed to deduce generalized confounding relationships on power products, and to determine families of identifiable models
An algebraic computational approach to the identifiability of Fourier Model
No full textComputer algebra and in particular Grobner bases are powerful tools in experimental design (Pistone and Wynn, 1996, Biometrika 83, 653-666). 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 Grobner bases over the complex rational numbers and other simple algebraic extensions of the rational numbers. Some examples are fully carried out
Replicated measurements and algebraic statistics
No full textA basic application of algebraic statistics to design and analysis of experiments considers a design as a zero-dimensional variety and identifies it with the ideal of the variety. Then, a subset of a standard basis of the design ideal is used as support for identifiable regression models. Estimation of the model parameter is performed by standard least squares techniques. We consider this identifiability problem in the case where more than one measurement is taken at a design point
Algebraic Statistics: Computational Commutative Algebra in Statistics
No full textWritten by pioneers in this exciting new field, Algebraic Statistics introduces the application of polynomial algebra to experimental design, discrete probability, and statistics. It begins with an introduction to Gröbner bases and a thorough description of their applications to experimental design. A special chapter covers the binary case with new application to coherent systems in reliability and two level factorial designs. The work paves the way, in the last two chapters, for the application of computer algebra to discrete probability and statistical modelling through the important concept of an algebraic statistical model.As the first book on the subject, Algebraic Statistics presents many opportunities for spin-off research and applications and should become a landmark work welcomed by both the statistical community and its relatives in mathematics and computer science
Arbitrato e Imprese
No full textDIECI ANNI DI SENTENZE E STATISTICHE DELLA CORTE D'APPELLO DI GENOVA IN MATERIA DI IMPUGNAZIONE DI LODI ARBITRAL
The causal manipulation and Bayesian estimation of chain event graphs
No full textDiscrete Bayesian Networks (BNs) have been very successful as
a framework both for inference and for expressing certain causal hypotheses. In this paper we present a class of graphical models called
the chain event graph (CEG) models, that generalises the class of discrete BN models. This class is suited for representing conditional independence and sample space structures of asymmetric models. It retains many useful properties of discrete BNs, in particular admitting
conjugate estimation. It provides a flexible and expressive framework
for representing and analysing the implications of causal hypotheses,
expressed in terms of the effects of a manipulation of the generating
underlying system.We prove that, as for a BN, identifiability analyses
of causal effects can be performed through examining the topology
of the CEG graph, leading to theorems analogous to the Backdoor
theorem for the BN
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