1,721,119 research outputs found
Erratum to “Rudolf Daniel wins the 2010 information-based complexity Young Researcher Award” [J. Complexity 26 (2010) 575]
No full text
Explicit error bounds for lazy reversible Markov chain Monte Carlo
No full textAbstractWe prove explicit, i.e., non-asymptotic, error bounds for Markov Chain Monte Carlo methods, such as the Metropolis algorithm. The problem is to compute the expectation (or integral) of f with respect to a measure π which can be given by a density ϱ with respect to another measure. A straight simulation of the desired distribution by a random number generator is in general not possible. Thus it is reasonable to use Markov chain sampling with a burn-in. We study such an algorithm and extend the analysis of Lovasz and Simonovits [L. Lovász, M. Simonovits, Random walks in a convex body and an improved volume algorithm, Random Structures Algorithms 4 (4) (1993) 359–412] to obtain an explicit error bound
Rudolf Daniel: The Violin and the Horse. Historical analysis of the manuscript with regard to social acitivities of the author in the post-war Romani ethno-emancipatory movement in Czechoslovakia
No full textThis thesis focuses on the manuscript entitled The Violin and the Horse, and pursues two approaches: one is based on the Romani studies, the other on the methods of the history science. Its aim is to verify historical facts contained in the manuscript. The main presumption of the thesis is the attribution of the text to Rudolf Daniel - the thesis verifies autobiographical data and its cultural and social context. The paper systematically concentrates on the figure of Rudolf Daniel (born 1911 in Oslavany - died in 1978 in Brno) and his biography (entirely unknown so far). The context of the manuscript The Violin and the Horse is framed by the post-war Roma ethno-emancipatory movement, and Rudolf Daniel is a newly discovered figure of its history. Keywords: the Roma, horse trade, the Holocaust, ethno-emancipatory movement, history of the Rom
Rudolf Daniel: The Violin and the Horse. Historical analysis of the manuscript with regard to social acitivities of the author in the post-war Romani ethno-emancipatory movement in Czechoslovakia
No full textThis thesis focuses on the manuscript entitled The Violin and the Horse, and pursues two approaches: one is based on the Romani studies, the other on the methods of the history science. Its aim is to verify historical facts contained in the manuscript. The main presumption of the thesis is the attribution of the text to Rudolf Daniel - the thesis verifies autobiographical data and its cultural and social context. The paper systematically concentrates on the figure of Rudolf Daniel (born 1911 in Oslavany - died in 1978 in Brno) and his biography (entirely unknown so far). The context of the manuscript The Violin and the Horse is framed by the post-war Roma ethno-emancipatory movement, and Rudolf Daniel is a newly discovered figure of its history. Keywords: the Roma, horse trade, the Holocaust, ethno-emancipatory movement, history of the Rom
Dimension-independent spectral gap of polar slice sampling
Full text linkPolar slice sampling, a Markov chain construction for approximate sampling,
performs, under suitable assumptions on the target and initial distribution,
provably independent of the state space dimension. We extend the aforementioned
result of Roberts & Rosenthal (2002) by developing a theory which identifies
conditions, in terms of a generalized level set function, that imply an
explicit lower bound on the spectral gap even in a general slice sampling
context. Verifying the identified conditions for polar slice sampling yields a
lower bound of 1/2 on the spectral gap for arbitrary dimension if the target
density is rotationally invariant, log-concave along rays emanating from the
origin and sufficiently smooth. The general theoretical result is potentially
applicable beyond the polar slice sampling framework.Comment: 14 pages, 2 figure
The minimal spherical dispersion
No full textWe prove upper and lower bounds on the minimal spherical dispersion, improving upon previous estimates obtained by Rote and Tichy [Spherical dispersion with an application to polygonal approximation of curves, Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 132 (1995), 3--10]. In particular, we see that the inverse of the minimal spherical dispersion is, for fixed , linear in the dimension of the ambient space. We also derive upper and lower bounds on the expected dispersion for points chosen independently and uniformly at random from the Euclidean unit sphere. In terms of the corresponding inverse , our bounds are optimal with respect to the dependence on
Convergence of hybrid slice sampling via spectral gap
No full textIt is known that the simple slice sampler has very robust convergence
properties, however the class of problems where it can be implemented is
limited. In contrast, we consider hybrid slice samplers which are easily
implementable and where another Markov chain approximately samples the uniform
distribution on each slice. Under appropriate assumptions on the Markov chain
on the slice we show a lower bound and an upper bound of the spectral gap of
the hybrid slice sampler in terms of the spectral gap of the simple slice
sampler. An immediate consequence of this is that spectral gap and geometric
ergodicity of the hybrid slice sampler can be concluded from spectral gap and
geometric ergodicity of its simple version which is very well understood. These
results indicate that robustness properties of the simple slice sampler are
inherited by (appropriately designed) easily implementable hybrid versions and
provide the first theoretical underpinning of their use in applications. We
apply the developed theory and analyse a number of specific algorithms such as
the stepping-out shrinkage slice sampling, hit-and-run slice sampling on very
general multidimensional targets and an easily implementable combination of
both procedures on fairly general and realistic multidimensional bimodal
densities
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