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Current analysis of astronomical data are confronted with the daunting task of modeling the awkward features of astronomical data, among which heteroscedastic (point-dependent) errors, intrinsic scatter, non-ignorable data collection…
The principles of measuring the shapes of galaxies by a model-fitting approach are discussed in the context of shape-measurement for surveys of weak gravitational lensing. It is argued that such an approach should be optimal, allowing…
Markov Chain Monte Carlo based Bayesian data analysis has now become the method of choice for analyzing and interpreting data in almost all disciplines of science. In astronomy, over the last decade, we have also seen a steady increase in…
Astronomers are often confronted with funky populations and distributions of objects: brighter objects are more likely to be detected; targets are selected based on colour cuts; imperfect classification yields impure samples. Failing to…
The application of Bayesian methods in cosmology and astrophysics has flourished over the past decade, spurred by data sets of increasing size and complexity. In many respects, Bayesian methods have proven to be vastly superior to more…
We believe that a wide range of physical processes conspire to shape the observed galaxy population but we remain unsure of their detailed interactions. The semi-analytic model (SAM) of galaxy formation uses multi-dimensional…
In these lectures I cover a number of topics in cosmological data analysis. I concentrate on general techniques which are common in cosmology, or techniques which have been developed in a cosmological context. In fact they have very general…
This review article considers some of the most common methods used in astronomy for regressing one quantity against another in order to estimate the model parameters or to predict an observationally expensive quantity using trends between…
The goal of this thesis is twofold; introduce the fundamentals of Bayesian inference and computation focusing on astronomical and cosmological applications, and present recent advances in probabilistic computational methods developed by the…
In many inference problems, the evaluation of complex and costly models is often required. In this context, Bayesian methods have become very popular in several fields over the last years, in order to obtain parameter inversion, model…
These notes aim at presenting an overview of Bayesian statistics, the underlying concepts and application methodology that will be useful to astronomers seeking to analyse and interpret a wide variety of data about the Universe. The level…
Over the past 30 years, numerous large-scale photometric astronomical surveys have been conducted, including SDSS, Pan-STARRS, Gaia,2MASS, WISE, and others. These surveys provide extensive photometric measurements that can be used to infer…
We present a comparative analysis of estimators and Bayesian methods for determining the number count dipole from cosmological surveys. The increase in discordance between the number count dipole and the CMB's kinematic dipole has presented…
The body of photometric and astrometric data on stars in the Galaxy has been growing very fast in recent years (Hipparcos/Tycho, OGLE-3, 2-Mass, DENIS, UCAC2, SDSS, RAVE, Pan Starrs, Hermes, ...) and in two years ESA will launch the Gaia…
Modern astronomy has been rapidly increasing our ability to see deeper into the universe, acquiring enormous samples of cosmic populations. Gaining astrophysical insights from these datasets requires a wide range of sophisticated…
Analyzes of next-generation galaxy data require accurate treatment of systematic effects such as the bias between observed galaxies and the underlying matter density field. However, proposed models of the phenomenon are either numerically…
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,…
Demographic studies of cosmic populations must contend with measurement errors and selection effects. We survey some of the key ideas astronomers have developed to deal with these complications, in the context of galaxy surveys and 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…
This paper presents a systematic literature review focusing on the application of machine learning techniques for deriving observational constraints in cosmology. The goal is to evaluate and synthesize existing research to identify…