Statistical Applications of Random Matrix Theory: Comparison of Two Populations
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We show how to deal with uncertainties on the Standard Model predictions in an agnostic new physics search strategy that exploits artificial neural networks. Our approach builds directly on the specific Maximum Likelihood ratio treatment of uncertainties a ...
We define a new statistic on Weyl groups called the atomic length and investigate its combinatorial and representation-theoretic properties. In finite types, we show a number of properties of the atomic length which are reminiscent of the properties of the ...
In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...
We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...
We consider two statistical problems at the intersection of functional and non-Euclidean data analysis: the determination of a Fréchet mean in the Wasserstein space of multivariate distributions; and the optimal registration of deformed random measures and ...
This thesis focuses on two kinds of statistical inference problems in signal processing and data science. The first problem is the estimation of a structured informative tensor from the observation of a noisy tensor in which it is buried. The structure com ...
Objectives To determine and compare the qualitative and quantitative diagnostic performance of a single sagittal fast spin echo (FSE) T2-weighted Dixon sequence in differentiating benign and malignant vertebral compression fractures (VCF), using multiple r ...
We propose a statistically optimal approach to construct data-driven decisions for stochastic optimization problems. Fundamentally, a data-driven decision is simply a function that maps the available training data to a feasible action. It can always be exp ...
Null models are useful for assessing whether a dataset exhibits a non-trivial property of interest. These models have recently gained interest in the neuroimaging community as means to explore dynamic properties of functional Magnetic Resonance Imaging (fM ...
The Internet of Things creates opportunities to develop data-driven design methodologies for smart cities. However, effects rather than causes are often measured in complex urban systems, requiring robust data-interpretation methodologies. Additionally, ef ...