9,270 research outputs found
On the posterior distribution of the number of components in a finite mixture
The posterior distribution of the number of components k in a finite mixture
satisfies a set of inequality constraints. The result holds irrespective of the
parametric form of the mixture components and under assumptions on the prior
distribution weaker than those routinely made in the literature on Bayesian
analysis of finite mixtures. The inequality constraints can be used to perform
an ``internal'' consistency check of MCMC estimates of the posterior
distribution of k and to provide improved estimates which are required to
satisfy the constraints. Bounds on the posterior probability of k components
are derived using the constraints. Implications on prior distribution
specification and on the adequacy of the posterior distribution of k as a tool
for selecting an adequate number of components in the mixture are also
explored.Comment: Published at http://dx.doi.org/10.1214/009053604000000788 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Employment of Airships for the Transport of Passengers
It was a conclusion of this detailed study of the practicality of using airships for carrying passengers that, although slow, airships are capable of carrying useful loads over long distances. However, it is noted that there is a certain limit to the advantages of large cubature. Beyond a certain point, the maximum altitude of the airship goes on decreasing, in spite of the fact that the range of action in the horizontal plane and the useful load go on increasing. The possibility of rapid climb is an essential factor of security in aerial navigation in the case of storms, as is velocity. To rise above and run ahead of storms are ways of avoiding them. However, high altitude and high speed are antithetical. This investigation concluded that a maximum velocity of 120 km/h is as far as we ought to go. This figure can only be exceeded by excessive reduction of the altitude of ceiling, range of flight, and useful load. The essential requisites of a public transport service are discussed, as are flight security, regularity of service, competition with other forms of passenger transportation, and the choice between rigid and semi-rigid airships
Sparse approximation of multilinear problems with applications to kernel-based methods in UQ
We provide a framework for the sparse approximation of multilinear problems
and show that several problems in uncertainty quantification fit within this
framework. In these problems, the value of a multilinear map has to be
approximated using approximations of different accuracy and computational work
of the arguments of this map. We propose and analyze a generalized version of
Smolyak's algorithm, which provides sparse approximation formulas with
convergence rates that mitigate the curse of dimension that appears in
multilinear approximation problems with a large number of arguments. We apply
the general framework to response surface approximation and optimization under
uncertainty for parametric partial differential equations using kernel-based
approximation. The theoretical results are supplemented by numerical
experiments
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