Related papers: Bayesian astrostatistics: a backward look to the f…

The intuitive reasoning of physicists in conditions of uncertainty is closer to the Bayesian approach than to the frequentist ideas taught at University and which are considered the reference framework for handling statistical problems. The…

We present and implement a probabilistic (Bayesian) method for producing catalogs from images of stellar fields. The method is capable of inferring the number of sources N in the image and can also handle the challenges introduced by noise,…

Perhaps more than other physical sciences, astronomy is frequently statistical in nature. The objects under study are inaccessible to direct manipulation in the laboratory, so the astronomer is restricted to observing a few external…

This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…

In Bayesian statistics, one's prior beliefs about underlying model parameters are revised with the information content of observed data from which, using Bayes' rule, a posterior belief is obtained. A non-trivial example taken from the…

I discuss the effects of measurement error on regression and density estimation. I review the statistical methods that have been developed to correct for measurement error that are most popular in astronomical data analysis, discussing…

I present a critical review of techniques for estimating confidence intervals on binomial population proportions inferred from success counts in small-to-intermediate samples. Population proportions arise frequently as quantities of…

Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the…

Bayesian inference is a powerful tool in gravitational-wave astronomy. It enables us to deduce the properties of merging compact-object binaries and to determine how these mergers are distributed as a population according to mass, spin, and…

We describe and use two different statistical approaches to try and detect low-frequency solar oscillations in Sun-as-a-star data: a frequentist approach and a Bayesian approach. We have used frequentist statistics to search contemporaneous…

Star-galaxy classification is one of the most fundamental data-processing tasks in survey astronomy, and a critical starting point for the scientific exploitation of survey data. For bright sources this classification can be done with…

This expository paper discusses Bayesian decision analysis perspectives on problems of constrained forecasting. Foundational and pedagogic discussion contrasts decision analytic approaches with the traditional, but typically inappropriate,…

Building on a strong foundation of philosophy, theory, methods and computation over the past three decades, Bayesian approaches are now an integral part of the toolkit for most statisticians and data scientists. Whether they are dedicated…

This introduction to Bayesian statistics presents the main concepts as well as the principal reasons advocated in favour of a Bayesian modelling. We cover the various approaches to prior determination as well as the basis asymptotic…

Bayesian inference --- although becoming popular in physics and chemistry --- is hampered up to now by the vagueness of its notion of prior probability. Some of its supporters argue that this vagueness is the unavoidable consequence of the…

Photometric redshift estimation is becoming an increasingly important technique, although the currently existing methods present several shortcomings which hinder their application. Here it is shown that most of those drawbacks are…

Large scale astronomical surveys are going wider and deeper than ever before. However, astronomers, cosmologists and theorists continue to face the perennial issue that their data sets are often incomplete in magnitude space and must be…

Modern astronomy increasingly relies upon systematic surveys, whose dedicated telescopes continuously observe the sky across varied wavelength ranges of the electromagnetic spectrum; some surveys also observe non-electromagnetic…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…