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Exoplanet research is carried out at the limits of the capabilities of current telescopes and instruments. The studied signals are weak, and often embedded in complex systematics from instrumental, telluric, and astrophysical sources.…

The statistical procedure used in the search for the Higgs boson is investigated in this paper. A Bayesian hierarchical model is proposed that uses the information provided by the theory in the analysis of the data generated by the particle…

Frequentist (classical) and the Bayesian approaches to the construction of confidence limits are compared. Various examples which illustrate specific problems are presented. The Likelihood Principle and the Stopping Rule Paradox are…

Differential analysis is a routine procedure in the statistical analysis toolbox across many applied fields, including quantitative proteomics, the main illustration of the present paper. The state-of-the-art limma approach uses a…

Over the last few years lattice techniques have been used to investigate candidate theories of new physics beyond the Standard Model. This review gives a survey of results from these studies. Most of these investigations have been of…

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…

Conjoint analysis is a popular experimental design used to measure multidimensional preferences. Researchers examine how varying a factor of interest, while controlling for other relevant factors, influences decision-making. Currently,…

Clustering methods are a valuable tool for the identification of patterns in high dimensional data with applications in many scientific problems. However, quantifying uncertainty in clustering is a challenging problem, particularly when…

This textbook provides a systematic treatment of statistical machine learning for astronomical research through the lens of Bayesian inference, developing a unified framework that reveals connections between modern data analysis techniques…

Clustering objects into synthetic groups is a natural activity of any science. Astrophysics is not an exception and is now facing a deluge of data. For galaxies, the one-century old Hubble classification and the Hubble tuning fork are still…

Bayesian statistics plays a pivotal role in advancing medical science by enabling healthcare companies, regulators, and stakeholders to assess the safety and efficacy of new treatments, interventions, and medical procedures. The Bayesian…

The original frequentist approach for computing confidence intervals involves the construction of the confidence belt which provides a mapping of the observation in data into a subset of values for the parameter. There are different…

Searches for new physics by experimental collaborations represent a significant investment in time and resources. Often these searches are sensitive to a broader class of models than they were originally designed to test. We aim to extend…

We have developed a new Bayesian method to correct the flux densities of astronomical sources. The hybrid method combines a simulated likelihood to model survey selection together with an analytic source-count-based prior. The simulated…

The aim of this paper is to describe new statistical methods for determination of the correlations among and distributions of physical parameters from a multivariate data with general and arbitrary truncations and selection biases. These…

The ATLAS and CMS detectors can be used to search for heavy long-lived particles which might signal physics beyond the Standard Model. Such new states can be distinguished from Standard Model particles by exploiting their unique signatures,…

Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability…

Statistical analysis is an important tool to distinguish systematic from chance findings. Current statistical analyses rely on distributional assumptions reflecting the structure of some underlying model, which if not met lead to problems…

Statistical matching methods are widely used in the social and health sciences to estimate causal effects using observational data. Often the objective is to find comparable groups with similar covariate distributions in a dataset, with the…

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…