Related papers: The Needlet CMB Trispesctrum
We compute the cosmic microwave background temperature bispectrum generated by nonlinearities at recombination on all scales. We use CosmoLib$2^{\rm nd}$, a numerical Boltzmann code at second-order to compute CMB bispectra on the full sky.…
To probe cosmological fields beyond the Gaussian level, three-point statistics can be used, all of which are related to the bispectrum. Hence, measurements of CMB anisotropies, galaxy clustering, and weak gravitational lensing alike have to…
Higher-order spectra (Brillinger's polyspectra) offer powerful methods for solving critical problems in signal processing and data analysis. Despite their significant potential, their practical use has remained limited due to unresolved…
The trispectrum of the cosmic microwave background can be used to assess the level of non-Gaussianity on cosmological scales. It probes the fourth order moment, as a function of angular scale, of the probability distribution function of…
We present a method for accelerating the calculation of CMB power spectra, matter power spectra and likelihood functions for use in cosmological parameter estimation. The algorithm, called CosmoNet, is based on training a multilayer…
The nonlinear parameter measures the amplitude of primordial non-Gaussianity in the cosmic microwave background radiation (CMB), offering a crucial test of early universe models. While standard single field inflation predicts nearly…
We develop the first algorithm able to jointly compute the maximum {\it a posteriori} estimate of the Cosmic Microwave Background (CMB) temperature and polarization fields, the gravitational potential by which they are lensed, and…
Polarization data will soon provide the best avenue for measurements of the CMB lensing potential, although it is potentially sensitive to several instrumental effects including beam asymmetry, polarization angle uncertainties, sky…
This paper reviews the application of a novel methodology for analysing the isotropy of the universe by probing the alignment of local structures in the CMB. The strength of the proposed methodology relies on the steerable wavelet filtering…
Inflation gives rise to a nearly scale-invariant spectrum of tensor perturbations (gravitational waves), their contribution to the Cosmic Background Radiation (CBR) anisotropy depends upon the present cosmological parameters as well as…
The search for primordial gravitational waves in the Cosmic Microwave Background (CMB) will soon be limited by our ability to remove the lensing contamination to $B$-mode polarization. The often-used quadratic estimator for lensing is known…
The lensing effect of the cosmic microwave background (CMB) is a powerful tool for our study of the distribution of matter in the universe. Currently, the quadratic estimator (EQ) method, which is widely used to reconstruct lensing…
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
The volume of a brain lesion (e.g. infarct or tumor) is a powerful indicator of patient prognosis and can be used to guide the therapeutic strategy. Lesional volume estimation is usually performed by segmentation with deep convolutional…
In recent years the goal of estimating different cosmological parameters precisely has set new challenges in the effort to accurately measure the angular power spectrum of CMB. This has required removal of foreground contamination as well…
The statistical analysis of the soon to come Planck satellite CMB data will help set tighter bounds on major cosmological parameters. On the way, a number of practical difficulties need to be tackled, notably that several other…
Parameter estimation in a class of heteroscedastic time series models is investigated. The existence of conditional least-squares and conditional likelihood estimators is proved. Their consistency and their asymptotic normality are…
Nonparametric regression is a standard statistical tool with increased importance in the Big Data era. Boundary points pose additional difficulties but local polynomial regression can be used to alleviate them. Local linear regression, for…
Forthcoming high-resolution observations of the Cosmic Microwave Background (CMB) radiation will generate datasets many orders of magnitude larger than have been obtained to date. The size and complexity of such datasets presents a very…
We study reconstruction of the lensing potential power spectrum from CMB temperature data, with an eye to the Planck experiment. We work with the optimal quadratic estimator of Okamoto and Hu, which we characterize thoroughly in application…