Related papers: Gaussian approximations of nonlinear statistics on…
We present a quantum algorithm for efficiently sampling transformed Gaussian random fields on $d$-dimensional domains, based on an enhanced version of the classical moving average method. Pointwise transformations enforcing boundedness are…
We present a novel approach for nonparametric regression using wavelet basis functions. Our proposal, $\texttt{waveMesh}$, can be applied to non-equispaced data with sample size not necessarily a power of 2. We develop an efficient proximal…
It is well known that the power spectrum is not able to fully characterize the statistical properties of non-Gaussian density fields. Recently, many different statistics have been proposed to extract information from non-Gaussian…
We study three kinetic Langevin samplers including the Euler discretization, the BU and the UBU splitting scheme. We provide contraction results in $L^1$-Wasserstein distance for non-convex potentials. These results are based on a carefully…
This paper investigates the Gaussian quasi-likelihood estimation of an exponentially ergodic multidimensional Markov process, which is expressed as a solution to a L\'{e}vy driven stochastic differential equation whose coefficients are…
A stochastic ordering approach is applied with Stein's method for approximation by the equilibrium distribution of a birth-death process. The usual stochastic order and the more general s-convex orders are discussed. Attention is focused on…
As a natural analog of Urysohn's inequality in Euclidean space, Gao, Hug, and Schneider showed in 2003 that in spherical or hyperbolic space, the total measure of totally geodesic hypersurfaces meeting a given convex body K is minimized…
Estimating the score, i.e., the gradient of log density function, from a set of samples generated by an unknown distribution is a fundamental task in inference and learning of probabilistic models that involve flexible yet intractable…
This paper deals with the numerical approximation of semilinear parabolic stochastic partial differential equation (SPDE) driven simultaneously by Gaussian noise and Poisson random measure, more realistic in modeling real world phenomena.…
We study the Stein equation associated with the one-dimensional Gamma distribution, and provide novel bounds, allowing one to effectively deal with test functions supported by the whole real line. We apply our estimates to derive new…
This paper deals with the problem of quantifying the approximation a probability measure by means of an empirical (in a wide sense) random probability measure, depending on the first n terms of a sequence of random elements. In Section 2,…
Directional Poisson wavelets, being directional derivatives of Poisson kernel, are introduced on $n$-dimensional spheres. It is shown that, slightly modified and together with another wavelet family, they are an admissible wavelet pair…
This paper is devoted to Gaussian interpolation inequalities with endpoint cases corresponding to the Gaussian Poincar\'e and the logarithmic Sobolev inequalities, seen as limits in large dimensions of Gagliardo-Nirenberg-Sobolev…
In a recent paper by the authors, a new approach--called the "embedding method"--was introduced, which allows to make use of exchangeable pairs for normal and multivariate normal approximation with Stein's method in cases where the…
We consider the problem of learning a Gaussian variational approximation to the posterior distribution for a high-dimensional parameter, where we impose sparsity in the precision matrix to reflect appropriate conditional independence…
The subject of this work is a new stochastic Galerkin method for second-order elliptic partial differential equations with random diffusion coefficients. It combines operator compression in the stochastic variables with tree-based spline…
Graph states are the backbone of measurement-based continuous-variable quantum computation. However, experimental realisations of these states induce Gaussian measurement statistics for the field quadratures, which poses a barrier to obtain…
A stochastic algorithm is proposed, finding some elements from the set of intrinsic $p$-mean(s) associated to a probability measure $\nu$ on a compact Riemannian manifold and to $p\in[1,\infty)$. It is fed sequentially with independent…
In this article, we investigate posterior convergence of nonparametric binary and Poisson regression under possible model misspecification, assuming general stochastic process prior with appropriate properties. Our model setup and objective…
We prove new concentration estimates for random variables that are functionals of a Poisson measure defined on a general measure space. Our results are specifically adapted to geometric applications, and are based on a pervasive use of a…