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Remarks on flat and differential K-theory
In this note we prove some results in flat and differential -theory. The
first one is a proof of the compatibility of the differential topological index
and the flat topological index by a direct computation. The second one is the
explicit isomorphisms between Bunke-Schick differential -theory and
Freed-Lott differential -theory.Comment: 9 pages. Comments are welcome. Final version. To appear in Annales
Mathematiques Blaise Pasca
A Bayes method for a monotone hazard rate via S-paths
A class of random hazard rates, which is defined as a mixture of an indicator
kernel convolved with a completely random measure, is of interest. We provide
an explicit characterization of the posterior distribution of this mixture
hazard rate model via a finite mixture of S-paths. A closed and tractable Bayes
estimator for the hazard rate is derived to be a finite sum over S-paths. The
path characterization or the estimator is proved to be a Rao--Blackwellization
of an existing partition characterization or partition-sum estimator. This
accentuates the importance of S-paths in Bayesian modeling of monotone hazard
rates. An efficient Markov chain Monte Carlo (MCMC) method is proposed to
approximate this class of estimates. It is shown that S-path characterization
also exists in modeling with covariates by a proportional hazard model, and the
proposed algorithm again applies. Numerical results of the method are given to
demonstrate its practicality and effectiveness.Comment: Published at http://dx.doi.org/10.1214/009053606000000047 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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