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Despite centuries of close association, statistics and astronomy are surprisingly distant today. Most observational astronomical research relies on an inadequate toolbox of methodological tools. Yet the needs are substantial: astronomy…
Strong gravitational lensing at the galaxy scale is a valuable tool for various applications in astrophysics and cosmology. The primary uses of galaxy-scale lensing are to study elliptical galaxies' mass structure and evolution, constrain…
Gaussian random fields have been one of the most popular tools for analyzing spatial data. However, many geophysical and environmental processes often display non-Gaussian characteristics. In this paper, we propose a new class of spatial…
The characteristics and determinants of health and disease are often organised in space, reflecting our spatially extended nature. Understanding the influence of such factors requires models capable of capturing spatial relations. Though a…
This is a review article for The Review of Particle Physics 2020 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters at the end of 2019. Topics included are Parametrizing the Universe;…
This is a review article for The Review of Particle Physics 2022 (aka the Particle Data Book). It forms a compact review of knowledge of the cosmological parameters near the end of 2021. Topics included are Parametrizing the Universe;…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…
This paper describes several applications in astronomy and cosmology that are addressed using probabilistic modelling and statistical inference.
We estimate how clustering in large-scale redshift surveys can constrain various cosmological parameters. Depth and sky coverage of modern redshift surveys are greater than ever, opening new possibilities for statistical analysis. We have…
Current and upcoming cosmological surveys will produce unprecedented amounts of high-dimensional data, which require complex high-fidelity forward simulations to accurately model both physical processes and systematic effects which describe…
Environmental and climate processes are often distributed over large space-time domains. Their complexity and the amount of available data make modelling and analysis a challenging task. Statistical modelling of environment and climate data…
Wavelets are widely used in various disciplines to analyse signals both in space and scale. Whilst many fields measure data on manifolds (i.e., the sphere), often data are only observed on a partial region of the manifold. Wavelets are a…
Experimental sciences have come to depend heavily on our ability to organize and interpret high-dimensional datasets. Natural laws, conservation principles, and inter-dependencies among observed variables yield geometric structure, with…
We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift,…
Multi-object spectroscopy has been a key technique contributing to the current era of 'precision cosmology'. From the first exploratory surveys of the large-scale structure and evolution of the universe to the current generation of superbly…
Astronomical data does not always use Cartesian coordinates. Both all-sky observational data and simulations of rotationally symmetric systems, such as accretion and protoplanetary discs, may use spherical polar or other coordinate systems.…
Cosmological solutions of the equations with scalar interaction are being studied. It is shown, that the scalar field can effectively change the equation of state of statistical system, that leads to series of cosmological consequences.
Homology-based invariants can be used to characterize the geometry of datasets and thereby gain some understanding of the processes generating those datasets. In this work we investigate how the geometry of a dataset changes when it is…
Many systems of interest in general relativistic astrophysics, including neutron stars, accreting compact objects in X-ray binaries and active galactic nuclei, core collapse, and collapsars, are assumed to be approximately spherically…
We define an optimal basis system into which cosmological observables can be decomposed. The basis system can be optimised for a specific cosmological model or for an ensemble of models, even if based on drastically different physical…