1,721,243 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
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
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
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 representation of Gaussian Markov combinations
No full textMarkov combinations for structural meta-analysis problems provide a way of constructing a statistical model that takes into account two or more marginal distributions by imposing conditional independence constraints between the variables that are not jointly observed. This paper considers Gaussian distributions and discusses how the covariance and concentration matrices of the different combinations can be found via matrix operations. In essence all these Markov combinations correspond to finding a positive definite completion of the covariance matrix over the set of random variables of interest and respecting the constraints imposed by each Markov combination. The paper further shows the potential of investigating the properties of the combinations via algebraic statistics tools. An illustrative application will motivate the importance of solving problems of this type
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