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We present novel lower bounds on the localization error using a network of satellites randomly deployed on a sphere around Earth. Our new analysis approach characterizes the localization performance by its asymptotic behavior as the number…
A model is developed for an idealised spherical galaxy evolving from a uniform mass distribution at the epoch of galactic separation until attaining an equilibrium state through gravitational collapse. The final theoretical radial surface…
In random parameter estimation, Bayesian lower bounds (BLBs) for the mean-square error have been noticed to not be tight in a number of cases, even when the sample size, or the signal-to-noise ratio, grow to infinity. In this paper, we…
Incorporating atomistic and molecular information into models of cellular behaviour is challenging because of a vast separation of spatial and temporal scales between processes happening at the atomic and cellular levels. Multiscale or…
A new framework of compressive sensing (CS), namely statistical compressive sensing (SCS), that aims at efficiently sampling a collection of signals that follow a statistical distribution and achieving accurate reconstruction on average, is…
In semantic segmentation, the accuracy of models heavily depends on the high-quality annotations. However, in many practical scenarios, such as medical imaging and remote sensing, obtaining true annotations is not straightforward and…
Robustly determining the optimal number of clusters in a data set is an essential factor in a wide range of applications. Cluster enumeration becomes challenging when the true underlying structure in the observed data is corrupted by…
This paper deals with the Gaussian and bootstrap approximations to the distribution of the max statistic in high dimensions. This statistic takes the form of the maximum over components of the sum of independent random vectors and its…
In the present work, we show how the generalized Cram\'er-Rao inequality for the estimation of a parameter, presented in a recent paper, can be extended to the mutidimensional case with general norms on $\mathbb{R}^{n}$, and to a wider…
In Bayesian inference, predictive distributions are typically in the form of samples generated via Markov chain Monte Carlo (MCMC) or related algorithms. In this paper, we conduct a systematic analysis of how to make and evaluate…
The entropy computation of Gaussian mixture distributions with a large number of components has a prohibitive computational complexity. In this paper, we propose a novel approach exploiting the sphere decoding concept to bound and…
We study the Small Ball Probabilities (SBPs) of Gaussian rough paths. While many works on rough paths study the Large Deviations Principles (LDPs) for stochastic processes driven by Gaussian rough paths, it is a noticeable gap in the…
A point source on a plane constantly emits particles which rapidly diffuse and then stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The…
The discovery of the "hidden population", whose size and membership are unknown, is made possible by assuming that its members are connected in a social network by their relationships. We explore these groups by a chain-referral sampling…
A generic modular array architecture is proposed, featuring uniform/non-uniform subarray layouts that allows for flexible deployment. The bistatic near-field sensing system is considered, where the target is located in the near-field of the…
Spatial-sign covariance matrix (SSCM) is an important substitute of sample covariance matrix (SCM) in robust statistics. This paper investigates the SSCM on its asymptotic spectral behaviors under high-dimensional elliptical populations,…
In this paper, we introduce a new probability distribution, the Lasso distribution. We derive several fundamental properties of the distribution, including closed-form expressions for its moments and moment-generating function.…
The one-point probability distribution function (pdf) is computed for the $25\hmpc$-smoothed density field of rich clusters of galaxies in the Abell/\aco\ catalogs. The observed pdf is compared to the pdf s drawn similarly from mock…
In this paper we develop a new approach to nonlinear stochastic partial differential equations with Gaussian noise. Our aim is to provide an abstract framework which is applicable to a large class of SPDEs and includes many important cases…
We establish higher-order nonasymptotic expansions for a difference between probability distributions of sums of i.i.d. random vectors in a Euclidean space. The derived bounds are uniform over two classes of sets: the set of all Euclidean…