25,012 research outputs found
Fully Bayesian Penalized Regression with a Generalized Bridge Prior
We consider penalized regression models under a unified framework. The
particular method is determined by the form of the penalty term, which is
typically chosen by cross validation. We introduce a fully Bayesian approach
that incorporates both sparse and dense settings and show how to use a type of
model averaging approach to eliminate the nuisance penalty parameters and
perform inference through the marginal posterior distribution of the regression
coefficients. We establish tail robustness of the resulting estimator as well
as conditional and marginal posterior consistency for the Bayesian model. We
develop a component-wise Markov chain Monte Carlo algorithm for sampling.
Numerical results show that the method tends to select the optimal penalty and
performs well in both variable selection and prediction and is comparable to,
and often better than alternative methods. Both simulated and real data
examples are provided
Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields
We discuss several enumerative results for irreducible polynomials of a given
degree and pairs of relatively prime polynomials of given degrees in several
variables over finite fields. Two notions of degree, the {\em total degree} and
the {\em vector degree}, are considered. We show that the number of
irreducibles can be computed recursively by degree and that the number of
relatively prime pairs can be expressed in terms of the number of irreducibles.
We also obtain asymptotic formulas for the number of irreducibles and the
number of relatively prime pairs. The asymptotic formulas for the number of
irreducibles generalize and improve several previous results by Carlitz, Cohen
and Bodin.Comment: 33 page
Association schemes from the action of fixing a nonsingular conic in PG(2,q)
The group has an embedding into such that it acts as
the group fixing a nonsingular conic in . This action affords a
coherent configuration on the set of non-tangent lines of the
conic. We show that the relations can be described by using the cross-ratio.
Our results imply that the restrictions and to the sets
of secant lines and to the set of exterior lines,
respectively, are both association schemes; moreover, we show that the elliptic
scheme is pseudocyclic.
We further show that the coherent configuration with even allow
certain fusions. These provide a 4-class fusion of the hyperbolic scheme
, and 3-class fusions and 2-class fusions (strongly regular graphs)
of both schemes and $R_{-}(q^2). The fusion results for the
hyperbolic case are known, but our approach here as well as our results in the
elliptic case are new.Comment: 33 page
Multiple wavemode scanning for near and far-side defect characterisation
The combination of ultrasonic inspections using different wavemodes can give more information than is available with single mode inspection. In this work, the response of shear and Rayleigh waves to surface-breaking defects propagating on the near-side and far-side of a sample is investigated. The directivity of shear waves generated by a racetrack coil electromagnetic acoustic transducer (EMAT) is identified and used to set an ideal separation for a pair of transmit-receive EMATs. Defects are indicated by a reduction in the transmitted Rayleigh wave amplitude, and by blocking of the shear wave. Used together, these can identify features in the bulk wave behaviour which are due to near-face surface-breaking defects, and give a full picture of both surfaces. By using a combination of the two wavemodes, the angle of propagation and length of any near-side defects can additionally be identified. A scanning method for samples is proposed
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