22,355 research outputs found
Computational algebraic methods in efficient estimation
A strong link between information geometry and algebraic statistics is made
by investigating statistical manifolds which are algebraic varieties. In
particular it it shown how first and second order efficient estimators can be
constructed, such as bias corrected Maximum Likelihood and more general
estimators, and for which the estimating equations are purely algebraic. In
addition it is shown how Gr\"obner basis technology, which is at the heart of
algebraic statistics, can be used to reduce the degrees of the terms in the
estimating equations. This points the way to the feasible use, to find the
estimators, of special methods for solving polynomial equations, such as
homotopy continuation methods. Simple examples are given showing both equations
and computations. *** The proof of Theorem 2 was corrected by the latest
version. Some minor errors were also corrected.Comment: 21 pages, 5 figure
Covariant theory of asymptotic symmetries, conservation laws and central charges
Under suitable assumptions on the boundary conditions, it is shown that there
is a bijective correspondence between equivalence classes of asymptotic
reducibility parameters and asymptotically conserved n-2 forms in the context
of Lagrangian gauge theories. The asymptotic reducibility parameters can be
interpreted as asymptotic Killing vector fields of the background, with
asymptotic behaviour determined by a new dynamical condition. A universal
formula for asymptotically conserved n-2 forms in terms of the reducibility
parameters is derived. Sufficient conditions for finiteness of the charges
built out of the asymptotically conserved n-2 forms and for the existence of a
Lie algebra g among equivalence classes of asymptotic reducibility parameters
are given. The representation of g in terms of the charges may be centrally
extended. An explicit and covariant formula for the central charges is
constructed. They are shown to be 2-cocycles on the Lie algebra g. The general
considerations and formulas are applied to electrodynamics, Yang-Mills theory
and Einstein gravity.Comment: 86 pages Latex file; minor correction
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