19,740 research outputs found
Optimal compromise between incompatible conditional probability distributions, with application to Objective Bayesian Kriging
Models are often defined through conditional rather than joint distributions,
but it can be difficult to check whether the conditional distributions are
compatible, i.e. whether there exists a joint probability distribution which
generates them. When they are compatible, a Gibbs sampler can be used to sample
from this joint distribution. When they are not, the Gibbs sampling algorithm
may still be applied, resulting in a "pseudo-Gibbs sampler". We show its
stationary probability distribution to be the optimal compromise between the
conditional distributions, in the sense that it minimizes a mean squared misfit
between them and its own conditional distributions. This allows us to perform
Objective Bayesian analysis of correlation parameters in Kriging models by
using univariate conditional Jeffreys-rule posterior distributions instead of
the widely used multivariate Jeffreys-rule posterior. This strategy makes the
full-Bayesian procedure tractable. Numerical examples show it has near-optimal
frequentist performance in terms of prediction interval coverage
On Homogeneous Decomposition Spaces and Associated Decompositions of Distribution Spaces
A new construction of decomposition smoothness spaces of homogeneous type is
considered. The smoothness spaces are based on structured and flexible
decompositions of the frequency space . We
construct simple adapted tight frames for that can be used
to fully characterise the smoothness norm in terms of a sparseness condition
imposed on the frame coefficients. Moreover, it is proved that the frames
provide a universal decomposition of tempered distributions with convergence in
the tempered distributions modulo polynomials. As an application of the general
theory, the notion of homogeneous -modulation spaces is introduced.Comment: 27 page
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