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We describe a new method of overcoming problems inherent in peculiar velocity surveys by using data compression as a filter with which to separate large-scale, linear flows from small-scale noise that biases the results systematically. We…
Phenomenologically interesting scalar potentials are highly atypical in generic random landscapes. We develop the mathematical techniques to generate constrained random potentials, i.e. Slepian models, which can globally represent…
Multiple tracers of the cosmic density field, with different bias, number and luminosity evolution, can be used to measure the large-scale properties of the Universe. We show how an optimal combination of tracers can be used to detect…
We study non-Gaussian random fields constructed by the selection normal distribution, and we term them selection Gaussian random fields. The selection Gaussian random field can capture skewness, multi-modality, and to some extend heavy…
The forthcoming Stage-IV experiments aim to map the large scale structure of the Universe at high precision. The scales explored require a relativistic description, in addition to statistical tools for their analysis. In this thesis, we…
Direct detection of gravitational waves by pulsar timing arrays will become feasible over the next few years. In the low frequency regime ($10^{-7}$ Hz -- $10^{-9}$ Hz), we expect that a superposition of gravitational waves from many…
Single-spin quantum sensors, for example based on nitrogen-vacancy centres in diamond, provide nanoscale mapping of magnetic fields. In applications where the magnetic field may be changing rapidly, total sensing time is crucial and must be…
Fitting a theoretical model to experimental data in a Bayesian manner using Markov chain Monte Carlo typically requires one to evaluate the model thousands (or millions) of times. When the model is a slow-to-compute physics simulation,…
The $E_G$ statistic provides a valuable tool for evaluating predictions of General Relativity (GR) by probing the relationship between gravitational potential and galaxy clustering on cosmological scales within the observable universe. In…
Searches and analyses of strong gravitational lenses are challenging due to the rarity and image complexity of these astronomical objects. Next-generation surveys (both ground- and space-based) will provide more opportunities to derive…
The interpretation of cosmological observables requires the use of increasingly sophisticated theoretical models. Since these models are becoming computationally very expensive and display non-trivial uncertainties, the use of standard…
Nonlinear cosmological fields like galaxy density and lensing convergence can be approximately related to Gaussian fields via analytic point transforms. The lognormal transform (LN) has been widely used and is a simple example of a function…
The deflection of gamma-rays in Earth's gravitational field is tested in laser Compton scattering at high energy accelerators. Within a formalism connecting the bending angle to the photon's momentum it follows that detected gamma-ray…
This work considers the computation of risk measures for quantities of interest governed by PDEs with Gaussian random field parameters using Taylor approximations. While efficient, Taylor approximations are local to the point of expansion,…
Identifying the presence of a gravitational wave transient buried in non-stationary, non-Gaussian noise which can often contain spurious noise transients (glitches) is a very challenging task. For a given data set, transient gravitational…
Gaussian Mixture Models are a powerful tool in Data Science and Statistics that are mainly used for clustering and density approximation. The task of estimating the model parameters is in practice often solved by the Expectation…
Neighborhood selection is a widely used method used for estimating the support set of sparse precision matrices, which helps determine the conditional dependence structure in undirected graphical models. However, reporting only point…
Probing the relative speeds of gravitational waves and light acts as an important test of General Relativity and alternative theories of gravity. Measuring the arrival time of gravitational waves and electromagnetic counterparts can be used…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
Motivated by the problem of testing for the existence of a signal of known parametric structure and unknown ``location'' (as explained below) against a noisy background, we obtain for the maximum of a centered, smooth random field an…