Related papers: Understanding Data Better with Bayesian and Global…
The Hubble constant, which measures the expansion rate, together with the total energy density of the Universe, sets the size of the observable Universe, its age, and its radius of curvature. Excellent progress has been made recently toward…
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of…
Different measurements of the Hubble constant ($H_{0}$) are not consistent and a tension between the CMB based methods and cosmic distance ladder based methods has been observed. Measurements from various distance based methods are also…
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…
Although cosmologists have been trying to determine the value of the Hubble constant for nearly 65 years, they have only succeeded in limiting the range of possibilities: most of the current observational determinations place the Hubble…
Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…
The potential of gravitational lenses for providing direct, physical measurements of the Hubble constant, free from systematic errors associated with the traditional distance ladder, has long been recognized. However, it is only recently…
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…
Estimation of time delays from a noisy and gapped data is one of the simplest data analysis problems in astronomy by its formulation. But as history of real experiments show, the work with observed data sets can be quite complex and…
Gravitational lensing is now widely and successfully used to study a range of astronomical phenomena, from individual objects, like galaxies and clusters, to the mass distribution on various scales, to the overall geometry of the Universe.…
This chapter provides a overview of Bayesian inference, mostly emphasising that it is a universal method for summarising uncertainty and making estimates and predictions using probability statements conditional on observed data and an…
Astrometric calibration of images with a small field of view is often inferior to the internal accuracy of the source detections due to the small number of accessible guide stars. One important experiment with such challenges is the Hubble…
Incompatible observables can be approximated by compatible observables in joint measurement or measured sequentially, with constrained accuracy as implied by Heisenberg's original formulation of the uncertainty principle. Recently, Busch,…
Mathematical models connect theory with the real world through data, enabling us to interpret, understand, and predict complex phenomena. However, scientific knowledge often extends beyond what can be empirically measured, offering valuable…
The production of complex astronomical data is accelerating, especially with newer telescopes producing ever more large-scale surveys. The increased quantity, complexity, and variety of astronomical data demand a parallel increase in skill…
The Standard Cosmological Model has experienced tremendous success at reproducing observational data by assuming a universe dominated by a cosmological constant and dark matter in a flat geometry. However, several studies, based on local…
By introducing Crossing functions and hyper-parameters I show that the Bayesian interpretation of the Crossing Statistics [1] can be used trivially for the purpose of model selection among cosmological models. In this approach to falsify a…
The tightest and most robust cosmological results of the next decade will be achieved by bringing together multiple surveys of the Universe. This endeavor has to happen across multiple layers of the data processing and analysis, e.g.,…
Bayesian statistics is based on the subjective definition of probability as {\it ``degree of belief''} and on Bayes' theorem, the basic tool for assigning probabilities to hypotheses combining {\it a priori} judgements and experimental…
This perspective chapter briefly surveys: (1) past growth in the use of Bayesian methods in astrophysics; (2) current misconceptions about both frequentist and Bayesian statistical inference that hinder wider adoption of Bayesian methods by…