Inequalities for Conditioned Normal Approximations

Exponential Models: Approximations for Probabilities

Welch & Peers (1963) used a root-information prior to obtain posterior probabilities for a scalar parameter exponential model and showed that these Bayes probabilities had the confidence property to second order asymptotically. An important undercurrent of this indicates that the constant information reparameterization provides location model structure, for which the confidence property ...

Ill-conditioned Convex Processes and Linear Inequalities

We prove the smallest possible norm of a linear perturbation making a closed convex process nonsurjective is the inverse of the norm of the inverse process. This generalizes the fundamental property of the condition number of a linear map. We then apply this result to strengthen a theorem of Renegar measuring the size of perturbation necessary to make an inequality system inconsistent.

Support Approximations Using Bonferroni-Type Inequalities

Discrete Sobolev-Poincaré Inequalities for Voronoi Finite Volume Approximations

We prove a discrete Sobolev-Poincaré inequality for functions with arbitrary boundary values on Voronoi finite volume meshes. We use Sobolev’s integral representation and estimate weakly singular integrals in the context of finite volumes. We establish the result for star shaped polyhedral domains and generalize it to the finite union of overlapping star shaped domains. In the appendix we prove...

Transport-Entropy inequalities and deviation estimates for stochastic approximations schemes

We obtain new transport-entropy inequalities and, as a by-product, new deviation estimates for the laws of two kinds of discrete stochastic approximation schemes. The first one refers to the law of an Euler like discretization scheme of a diffusion process at a fixed deterministic date and the second one concerns the law of a stochastic approximation algorithm at a given time-step. Our results ...