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Thomas Hotz

  1. Sticky central limit theorems on open books.

    Втр, 02/21/2012 - 15:01 — SomNambul
    Authors: Jonathan C. Mattingly, Ezra Miller, Thomas Hotz, Stephan Huckemann, James Nolen, Huiling Le, J. Stephen Marron, Megan Owen, Vic Patrangenaru, Sean Skwerer
    Subjects: Probability
    Abstract

    Given a probability distribution on an open book (a metric space obtained by
    gluing a disjoint union of copies of a half-space along their boundary
    hyperplanes), we define a precise concept of when the Fr\'echet mean
    (barycenter) is "sticky". This non-classical phenomenon is quantified by a law
    of large numbers (LLN) stating that the empirical mean eventually almost surely
    lies on the (codimension 1 and hence measure 0) "spine" that is the glued
    hyperplane, and a central limit theorem (CLT) stating that the limiting
    distribution is Gaussian and supported on the spine.

  2. Intrinsic Means on the Circle: Uniqueness, Locus and Asymptotics.

    Чт, 08/11/2011 - 15:01 — SomNambul
    Authors: Thomas Hotz, Stephan Huckemann
    Subjects: Methodology
    Abstract

    This paper gives a comprehensive treatment of local uniqueness, asymptotics
    and numerics for intrinsic means on the circle. It turns out that local
    uniqueness as well as rates of convergence are governed by the distribution
    near the antipode. In a nutshell, if the distribution there is locally less
    than uniform, we have local uniqueness and asymptotic normality with a rate of
    1 / \surdn. With increased proximity to the uniform distribution the rate can
    be arbitrarly slow, and in the limit, local uniqueness is lost. Further, we
    give general distributional conditions, e.g.

  3. Locally adaptive image denoising by a statistical multiresolution criterion.

    Пнд, 02/01/2010 - 16:01 — SomNambul
    Authors: Axel Munk, Zakhar Kabluchko, Thomas Hotz, Philipp Marnitz, Rahel Stichtenoth, Laurie Davies
    Subjects: Methodology
    Abstract

    We demonstrate how one can choose the smoothing parameter in image denoising
    by a statistical multiresolution criterion, both globally and locally. Using
    inhomogeneous diffusion and total variation regularization as examples for
    localized regularization schemes, we present an efficient method for locally
    adaptive image denoising. As expected, the smoothing parameter serves as an
    edge detector in this framework. Numerical examples illustrate the usefulness
    of our approach. We also present an application in confocal microscopy.

Math-arch

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