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The unprecedented amount and the excellent quality of lensing data that the upcoming ground- and space-based surveys will produce represent a great opportunity to shed light on the questions that still remain unanswered concerning our…
Large-scale structures originate from coherent motions induced by inhomogeneities in the primeval gravitational potential. Here, we investigate the two-point statistics of the second derivative of the potential, the tidal shear, under the…
Preferential sampling is a common feature in geostatistics and occurs when the locations to be sampled are chosen based on information about the phenomena under study. In this case, point pattern models are commonly used as the probability…
The excursion set of a $C^2$ smooth random field carries relevant information in its various geometric measures. From a computational viewpoint, one never has access to the continuous observation of the excursion set, but rather to…
Studying the statistical properties of the large-scale structure in the Universe with weak gravitational lensing is a prime goal of several current and forthcoming galaxy surveys. The power that weak lensing has to constrain cosmological…
This paper presents a new derivation of the Generalized Poisson distribution. This distribution provides a good fit to the evolved, counts-in-cells distribution measured in numerical simulations of hierarchical clustering from Poisson…
Data analysis in high-dimensional spaces aims at obtaining a synthetic description of a data set, revealing its main structure and its salient features. We here introduce an approach providing this description in the form of a topography of…
Algorithmic Gaussianization is a phenomenon that can arise when using randomized sketching or sampling methods to produce smaller representations of large datasets: For certain tasks, these sketched representations have been observed to…
In the Excursion Set approach, halo abundances and clustering are closely related. This relation is exploited in many modern methods which seek to constrain cosmological parameters on the basis of the observed spatial distribution of…
We explore various Bayesian approaches to estimate partial Gaussian graphical models. Our hierarchical structures enable to deal with single-output as well as multiple-output linear regressions, in small or high dimension, enforcing either…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We present a sampling-based trajectory optimization method derived from the maximum entropy formulation of Differential Dynamic Programming with Tsallis entropy. This method is a generalization of the legacy work with Shannon entropy, which…
Smooth random Gaussian functions play an important role in mathematical physics, a main example being the random plane wave model conjectured by Berry to give a universal description of high-energy eigenfunctions of the Laplacian on generic…
We present a method, based on the correlation function of excursion sets above a given threshold, to test the Gaussianity of the CMB temperature fluctuations in the sky. In particular, this method can be applied to discriminate between…
We study differentially private ordinary least squares (DP-OLS) with bounded data $(X,Y)$ via sketching-based mechanisms. While Gaussian sketching approaches have been explored for DP-OLS \citep{sheffet2017differentially}, they are…
We consider the problem of high-dimensional Gaussian graphical model selection. We identify a set of graphs for which an efficient estimation algorithm exists, and this algorithm is based on thresholding of empirical conditional…
A new fast Bayesian approach is introduced for the detection of discrete objects immersed in a diffuse background. This new method, called PowellSnakes, speeds up traditional Bayesian techniques by: i) replacing the standard form of the…
Using the two-point Edgeworth series up to second order we construct the weakly nonlinear conditional probability distribution function for the density field around an overdense region. This requires calculating the two-point analogues of…
Recently, we provided a simple but accurate formula which closely approximates the first crossing distribution associated with random walks having correlated steps. The approximation is accurate for the wide range of barrier shapes of…
The ConflUent System of Peak trajectories (CUSP) is a rigorous formalism in the framework of the peak theory that allows one to derive from first principles andno free parameters the typical halo properties from the statistics of peaks in…