Related papers: Bayesian astrostatistics: a backward look to the f…
A method is developed for fitting theoretically predicted astronomical spectra to an observed spectrum. Using a hierarchical Bayesian principle, the method takes both systematic and statistical measurement errors into account, which has not…
This paper describes several applications in astronomy and cosmology that are addressed using probabilistic modelling and statistical inference.
The concepts of Bayesian prediction, model comparison, and model selection have developed significantly over the last decade. As a result, the Bayesian community has witnessed a rapid growth in theoretical and applied contributions to…
Astronomy is entering a new era as multiple, large area, digital sky surveys are in production. The resulting datasets are truly remarkable in their own right; however, a revolutionary step arises in the aggregation of complimentary…
Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. As opposed to classical algorithms which return a single clustering solution, Bayesian nonparametric models provide a posterior over…
Cosmological experiments often employ Bayesian workflows to derive constraints on cosmological and astrophysical parameters from their data. It has been shown that these constraints can be combined across different probes such as Planck and…
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…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
A common concern with Bayesian methodology in scientific contexts is that inferences can be heavily influenced by subjective biases. As presented here, there are two types of bias for some quantity of interest: bias against and bias in…
Probability forecasting is common in the geosciences, the finance sector, and elsewhere. It is sometimes the case that one has multiple probability-forecasts for the same target. How is the information in these multiple forecast systems…
The original formulation of BEAMS - Bayesian Estimation Applied to Multiple Species - showed how to use a dataset contaminated by points of multiple underlying types to perform unbiased parameter estimation. An example is cosmological…
Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in…
Bayesian hypothesis testing is re-examined from the perspective of an a priori assessment of the test statistic distribution under the alternative. By assessing the distribution of an observable test statistic, rather than prior parameter…
In this study, we examine a Bayesian approach to analyze extreme daily rainfall amounts and forecast return-levels. Estimating the probability of occurrence and quantiles of future extreme events is important in many applications, including…
This article attempts to offer some perspectives on Bayesian inference for finite population quantities when the units in the population are assumed to exhibit complex dependencies. Beginning with an overview of Bayesian hierarchical…
Ising models originated in statistical physics and are widely used in modeling spatial data and computer vision problems. However, statistical inference of this model remains challenging due to intractable nature of the normalizing constant…
Inverse problems, where in broad sense the task is to learn from the noisy response about some unknown function, usually represented as the argument of some known functional form, has received wide attention in the general scientific…
Bayesian and frequentist methods differ in many aspects, but share some basic optimality properties. In practice, there are situations in which one of the methods is more preferred by some criteria. We consider the case of inference about a…
These lecture notes delve into field-level inference, a framework offering a robust way to extract more information and avoid biases compared to traditional methods for cosmological data analysis. The core idea is to analyse uncompressed…
This document is due to appear as a chapter of the forthcoming Handbook of Approximate Bayesian Computation (ABC) edited by S. Sisson, Y. Fan, and M. Beaumont. Since the earliest work on ABC, it has been recognised that using summary…