Related papers: Halfspace depth does not characterize probability …
We study the maximum likelihood degree of linear concentration models in algebraic statistics. We relate the geometry of the reciprocal variety to that of semidefinite programming. We show that the Zariski closure in the Grassmanian of the…
Level statistics is a crucial tool in the exploration of localization physics. The level spacing distribution of the disordered localized phase follows Poisson statistics, and many studies naturally apply it to the quasiperiodic localized…
In this paper we study the (strong) Leibniz property of centered moments of bounded random variables. We shall answer a question raised by M. Rieffel on the non-commutative standard deviation.
We introduce a new class of multivariate elliptically symmetric distributions including elliptically symmetric logistic distributions and Kotz type distributions. We investigate the various probabilistic properties including marginal…
This article is a continuation of a previous article which concerned the splitting problem for subspaces of superspaces. We begin with a general account of projective superspaces. Subsequently, we specialise to subvarieties of `positive'…
In dealing with asymptotic approximation of possibly divergent nets of probability distributions, we are led to study uniform structures on the set of distributions. This paper identifies a class of such uniform structures that may be…
It is shown that probability densities of finite-time Lyapunov exponents, corresponding to chimera states, have a characteristic shape. Such distributions could be used as a signature of chimera states, particularly in systems for which the…
Polarization quasi-probability distribution (PQPD) is defined in the Stokes space, and it enables the calculation of mean values and higher-order moments for polarization observables using simple algebraic averaging. It can be reconstructed…
We give a highly efficient "semi-agnostic" algorithm for learning univariate probability distributions that are well approximated by piecewise polynomial density functions. Let $p$ be an arbitrary distribution over an interval $I$ which is…
In this paper we have obtained two more characterizations of nearly pseudocompact spaces.
Considering discrete models, the univariate framework has been studied in depth compared to the multivariate one. This paper first proposes two criteria to define a sensu stricto multivariate discrete distribution. It then introduces the…
We derive a simple and precise approximation to probability density functions in sampling distributions based on the Fourier cosine series. After clarifying the required conditions, we illustrate the approximation on two examples: the…
In this paper we show that in systems where the probability distribution of the the overlap is non trivial in the infinity volume limit, the property of ultrametricity can be proved in general starting from two very simple and natural…
Let H be a finite dimensional semisimple Hopf algebra over an algebraically closed field of characteristic zero. In this note we give a short proof of the fact that a Hopf subalgebra of H is a depth two subalgebra if and only if it is…
We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…
It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…
The gaussian spread regression model for the calibration of site specific ensemble temperature forecasts depends on the apparently restrictive assumption that the uncertainty around temperature forecasts is normally distributed. We…
We survey results on the distribution of zeros of random polynomials and of random holomorphic sections of line bundles, especially for large classes of probability measures on the spaces of holomorphic sections. We provide furthermore some…
A probability space is a pair ($\mathcal{A},\phi $) where $\mathcal{A}$ is an algebra and $\phi $ a state on the algebra. In classical probability $\mathcal{A}$ is the algebra of linear combinations of indicator functions on the sample…
We study optimization problems whereby the optimization variable is a probability measure. Since the probability space is not a vector space, many classical and powerful methods for optimization (e.g., gradients) are of little help. Thus,…