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A Class of Non-Parametric Statistical Manifolds modelled on Sobolev SpaceAug 20 2018Jan 01 2019We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on $R^d$. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports the Fisher-Rao ... More

A Class of Non-Parametric Statistical Manifolds modelled on Sobolev SpaceAug 20 2018Mar 07 2019We construct a family of non-parametric (infinite-dimensional) manifolds of finite measures on $R^d$. The manifolds are modelled on a variety of weighted Sobolev spaces, including Hilbert-Sobolev spaces and mixed-norm spaces. Each supports the Fisher-Rao ... More

Optimal Cheeger cuts and bisections of random geometric graphsMay 22 2018Let $d \geq 2$. The Cheeger constant of a graph is the minimum surface-to-volume ratio of all subsets of the vertex set with relative volume at most 1/2. There are several ways to define surface and volume here: the simplest method is to count boundary ... More

Elements of the Kopula (eventological copula) theoryFeb 17 2018New in the probability theory and eventology theory, the concept of Kopula (eventological copula) is introduced. The theorem on the characterization of the sets of events by Kopula is proved, which serves as the eventological pre-image of the well-known ... More

Frechet bounds of the 1-st kind for sets of half-rare eventsFeb 10 2018Frechet bounds of the 1-st kind for sets of events and its main properties are considered. The lemma on not more than two nonzero values of lower Frechet-bounds of the 1-st kind for a set of half-rare events is proved with the corollary on the analogous ... More

Postulating the theory of experience and chance as a theory of co~events (co~beings)Jan 17 2018The paper aim is the axiomatic justification of the theory of experience and chance, one of the dual halves of which is the Kolmogorov probability theory. The author's main idea was the natural inclusion of Kolmogorov's axiomatics of probability theory ... More

Capturing, Ordering and Gaussianity in 2DJan 19 2016We collect various facts related loosely to random Gaussian quadrilaterals in the plane. For example, a side of a degenerate quadrilateral (one point inside three others) has a density that is non-Rayleigh.

Expected n-Step Product for Gaussian ToursDec 17 2015Supplements to Mehta & Normand (1997) are given, with regard to integrals involving Euclidean distances between n+1 random points in d-dimensional space, each visited once.

Moments and Classification for Conjugation-Invariant Rotations and Fake Uniformity in the Stochastic Radon TransformMar 06 2012We consider a generalisation of the stochastic Radon transform, introduced for an inverse problem in tomography by Panaretos. Specifically, we allow the distribution of the three-dimensional rotation in the statistical model of that work to be different ... More

On the structure and probabilistic interpretation of Askey-Wilson densities and polynomials with complex parametersNov 06 2010May 03 2011We give equivalent forms of the Askey-Wilson polynomials expressing them with the help of the Al-Salam-Chihara polynomials. After restricting parameters of the Askey-Wilson polynomials to complex conjugate pairs we expand the Askey-Wilson weight function ... More

Affinely invariant matching methods with discriminant mixtures of proportional ellipsoidally symmetric distributionsNov 09 2006In observational studies designed to estimate the effects of interventions or exposures, such as cigarette smoking, it is desirable to try to control background differences between the treated group (e.g., current smokers) and the control group (e.g., ... More