50,741 research outputs found
Multiple kernel contraction
This paper focuses on the extension of AGM that allows change for a belief
base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson
presented an axiomatic for Multiple Contraction and a construction based on the AGM
Partial Meet Contraction. We propose for their model another way to construct functions:
Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by
Hansson [Han94] to construct classical AGM contractions and belief base contractions.
This construction works out the unsolved problem pointed out by Hansson in [Han99, pp.
369].info:eu-repo/semantics/publishedVersio
Rates of contraction of posterior distributions based on Gaussian process priors
We derive rates of contraction of posterior distributions on nonparametric or
semiparametric models based on Gaussian processes. The rate of contraction is
shown to depend on the position of the true parameter relative to the
reproducing kernel Hilbert space of the Gaussian process and the small ball
probabilities of the Gaussian process. We determine these quantities for a
range of examples of Gaussian priors and in several statistical settings. For
instance, we consider the rate of contraction of the posterior distribution
based on sampling from a smooth density model when the prior models the log
density as a (fractionally integrated) Brownian motion. We also consider
regression with Gaussian errors and smooth classification under a logistic or
probit link function combined with various priors.Comment: Published in at http://dx.doi.org/10.1214/009053607000000613 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Scattering problems for symmetric systems with dissipative boundary conditions
We study symmetric systems with dissipative boundary conditions. The
solutions of the mixed problems for such systems are given by a contraction
semigroup . The solutions , where
is an eigenfunction of the generator with eigenvalue are called asymptotically disappearing (ADS). We prove that the
wave operators are not complete if there exist (ADS). This is the case for
Maxwell system with special boundary conditions in the exterior of the sphere.
We obtain a representation of the scattering kernel and we examine the inverse
back-scattering problem related to the leading term of the scattering kernel
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