Related papers: Non Gaussian extrema counts for CMB maps
Recent methods for estimating sparse undirected graphs for real-valued data in high dimensional problems rely heavily on the assumption of normality. We show how to use a semiparametric Gaussian copula--or "nonparanormal"--for high…
Considerable recent attention has focussed on the prospects to use the cosmic microwave background (CMB) trispectrum to probe the physics of the early universe. Here we evaluate the probability distribution function (PDF) for the standard…
ABRIDGED: We introduce and analyze a method for testing statistical isotropy and Gaussianity and apply it to the WMAP CMB foreground reduced, temperature maps, and cross-channel difference maps. We divide the sky into regions of varying…
This paper provides the relevant literature with a complete toolkit for conducting robust estimation and inference about the parameters of interest involved in a high-dimensional panel data framework. Specifically, (1) we allow for…
Estimating copulas with discrete marginal distributions is challenging, especially in high dimensions, because computing the likelihood contribution of each observation requires evaluating $2^{J}$ terms, with $J$ the number of discrete…
We analyze statistical properties of the separate multipole moments of the CMB temperature maps and find that the distribution tails are slightly non-Gaussian. Moreover, the deviation from Gaussianity peaks sharply at around $l\sim45\pm10$.…
We generalize the maximum likelihood method to non-Gaussian distribution functions by means of the multivariate Edgeworth expansion. We stress the potential interest of this technique in all those cosmological problems in which the…
An incremental approach for computation of convex hull for data points in two-dimensions is presented. The algorithm is not output-sensitive and costs a time that is linear in the size of data points at input. Graham's scan is applied only…
A description of CMB temperature fluctuations beyond the power spectrum is important for verifying models of structure formation, especially in view of forthcoming high-resolution observations. We argue that higher-order statistics of…
The forthcoming Planck experiment will provide high sensitivity polarization measurements that will allow us to further tighten the f_NL bounds from the temperature data. Monte Carlo simulations of non-Gaussian CMB maps have been used as a…
These notes were written for the mini-course "Extrema of log-correlated random variables: Principles and Examples" at the Introductory School held in January 2015 at the Centre International de Rencontres Math\'ematiques in Marseille. There…
This paper studies the joint tail asymptotics of extrema of the multi-dimensional Gaussian process over random intervals defined as $$ P(u):=\mathbb{P}\left\{\cap_{i=1}^n \left(\sup_{t\in[0,\mathcal{T}_i]} ( X_{i}(t) +c_i t )>a_i u…
We describe an elementary method to get non-asymptotic estimates for the moments of Hermitian random matrices whose elements are Gaussian independent random variables. As the basic example, we consider the GUE matrices. Immediate…
We have obtained some upper bounds for the probability distribution of extremes of a self-similar Gaussian random field with stationary rectangular increments that are defined on the compact spaces. The probability distributions of extremes…
We discuss the Full Counting Statistics of non-commuting variables with the measurement of successive spin counts in non-collinear directions taken as an example. We show that owing to an irreducible detector back-action, the FCS in this…
We develop adaptive estimation and inference methods for high-dimensional Gaussian copula regression that achieve the same performance without the knowledge of the marginal transformations as that for high-dimensional linear regression.…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
In this paper we demonstrate an efficient method for including both CMB temperature and polarisation data in optimal non-Gaussian estimators. The method relies on orthogonalising the multipoles of the temperature and polarisation maps and…
This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions…
Doubly intractable distributions arise in many settings, for example in Markov models for point processes and exponential random graph models for networks. Bayesian inference for these models is challenging because they involve intractable…