34,833 research outputs found
On adaptive Bayesian inference
We study the rate of Bayesian consistency for hierarchical priors consisting
of prior weights on a model index set and a prior on a density model for each
choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained
general in-probability theorems on the rate of convergence of the resulting
posterior distributions. We extend their results to almost sure assertions. As
an application we study log spline densities with a finite number of models and
obtain that the Bayes procedure achieves the optimal minimax rate
of convergence if the true density of the
observations belongs to the H\"{o}lder space . This
strengthens a result in [1; 2]. We also study consistency of posterior
distributions of the model index and give conditions ensuring that the
posterior distributions concentrate their masses near the index of the best
model.Comment: Published in at http://dx.doi.org/10.1214/08-EJS244 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere
with various background R-symmetry gauge fields. We study free energy and
supersymmetric Renyi entropy using heat kernel method as well as localization
technique. We find that the universal contribution to the partition function in
the free field limit is the same as that in the strong coupling limit, which
implies that it may be protected by supersymmetry. Based on the fact that, the
conic sphere can be conformally mapped to and the R-symmetry
background fields can be supported by the R-charges of black hole, we propose
that the holographic dual of these theories are five-dimensional,
supersymmetric STU topological black holes. We demonstrate perfect agreement
between N=4 super-Yang-Mills theories in the planar limit and the STU
topological black holes.Comment: 1+48 pages, v2:typo fixed+references adde
- …