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Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…
Spatial models are used in a variety research areas, such as environmental sciences, epidemiology, or physics. A common phenomenon in many spatial regression models is spatial confounding. This phenomenon takes place when spatially indexed…
Cosmology is undergoing an explosive period of activity, fueled both by new, accurate astrophysical data and by innovative theoretical developments. Cosmological parameters such as the total density of the Universe and the rate of…
We review the use of Bayesian Model Averaging in astrophysics. We first introduce the statistical basis of Bayesian Model Selection and Model Averaging. We discuss methods to calculate the model-averaged posteriors, including Markov Chain…
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…
Over the last 20 years, supernovae have become a key tool to constrain the expansion history of the Universe through the construction of Hubble diagrams, using luminosity distances to supernovae belonging to the "Ia" subtype. This technique…
Facing the advent of the next generation cosmological surveys we present a method to forecast knowledge gain on cosmological models. We propose this as a well defined and general tool to quantify the performance of different experiments in…
This is a summary of the `Astronomy Perspective' of the 4th meeting on 'Statistical Challenges in Modern Astronomy' held at Penn State University in June 2006. We comment on trends in the Astronomy community towards Bayesian methods and…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…
A common problem in natural sciences is the comparison of competing models in the light of observed data. Bayesian model comparison provides a statistically sound framework for this comparison based on the evidence each model provides for…
Data analysis methods have always been of critical importance for quantitative sciences. In astronomy, the increasing scale of current and future surveys is driving a trend towards a separation of the processes of low-level data reduction…
Cosmological inference becomes increasingly difficult when complex data-generating processes cannot be modeled by simple probability distributions. With the ever-increasing size of data sets in cosmology, there is increasing burden placed…
In modern cosmology, the discovery of the universe's accelerated expansion has significantly transformed our understanding of cosmic evolution and expansion history. The unknown properties of dark energy, the driver of this acceleration,…
Bayesian (Probabilistic) Machine Learning is used to probe the opacity of the Universe. It relies on a generative process where the model is the key object to generate the data involving the unknown parameters of the model, our prior…
The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis,…
We investigate the cosmology of a recently proposed deformation of Einstein gravity, emerging from quantum gravity heuristics. The theory is constructed to have de Sitter space as a vacuum solution, and thus to be relevant to the…
We present a Bayesian method for the identification and classification of objects from sets of astronomical catalogs, given a predefined classification scheme. Identification refers here to the association of entries in different catalogs…
Gravitational time delays, observed in strong lens systems where the variable background source is multiply-imaged by a massive galaxy in the foreground, provide direct measurements of cosmological distance that are very complementary to…
The gravitational field of a galaxy can act as a lens and deflect the light emitted by a more distant object such as a quasar. Strong gravitational lensing causes multiple images of the same quasar to appear in the sky. Since the light in…