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The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either chosen heuristically ...
How can we discern whether the covariance operator of a stochastic pro-cess is of reduced rank, and if so, what its precise rank is? And how can we do so at a given level of confidence? This question is central to a great deal of methods for functional dat ...
Measurements of large-scale structure (LSS), as performed on the largest 3D map of over two million extragalactic sources from the Sloan Digital Sky Survey, together with measurements of the cosmic microwave background (CMB) anisotropies, are in complete a ...
Traditional approaches to analysing functional data typically follow a two-step procedure, consisting in first smoothing and then carrying out a functional principal component analysis. The idea underlying this procedure is that functional data are well ap ...
Statistical analysis of alignments of large numbers of protein sequences has revealed sectors of collectively coevolving amino acids in several protein families. Here, we show that selection acting on any functional property of a protein, represented by an ...
We derive sharp probability bounds on the tails of a product of symmetric non-negative random variables using only information about their first two moments. If the covariance matrix of the random variables is known exactly, these bounds can be computed nu ...
Aims. We investigate the contribution of shot-noise and sample variance to uncertainties in the cosmological parameter constraints inferred from cluster number counts, in the context of the Euclid survey. Methods. By analysing 1000 Euclid-like light cones, ...
We test general relativity (GR) at the effective redshift (z) over tilde similar to 1.5 by estimating the statistic E-G, a probe of gravity, on cosmological scales 19 - 190 h(-1)Mpc. This is the highest redshift and largest scale estimation of E-G so far. ...
Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuatio ...
Uncertainty estimation in large deep-learning models is a computationally challenging task, where it is difficult to form even a Gaussian approximation to the posterior distribution. In such situations, existing methods usually resort to a diagonal approxi ...
