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We marshall the arguments for preferring Bayesian hypothesis testing and confidence sets to frequentist ones. We define admissible solutions to inference problems, noting that Bayesian solutions are admissible. We give seven weaker…
Design of experiments has traditionally relied on the frequentist hypothesis testing framework where the optimal size of the experiment is specified as the minimum sample size that guarantees a required level of power. Sample size…
In large scale multiple testing problems, a two-class empirical Bayes approach can be used to control the false discovery rate (Fdr) for the entire array of hypotheses under study. A sample splitting step is incorporated to modify that…
Given the sensitivity of current ground-based Gravitational Wave (GW) detectors, any continuous-wave signal we can realistically expect will be at a level or below the background noise. Hence, any data analysis of detector data will need to…
It is argued that the Calibrated Bayesian (CB) approach to statistical inference capitalizes on the strength of Bayesian and frequentist approaches to statistical inference. In the CB approach, inferences under a particular model are…
Fuzzy data, prevalent in social sciences and other fields, capture uncertainties arising from subjective evaluations and measurement imprecision. Despite significant advancements in fuzzy statistics, a unified inferential regression-based…
The cleanest way to discover a new particle is generally the "bump-hunt" methodology: looking for a localised excess in a mass (or related) distribution. However, if the mass of the particle being discovered is not known the procedure of…
Anomalies drive scientific discovery -- they are associated with the cutting edge of the research frontier, and thus typically exploit data in the low signal-to-noise regime. In astronomy, the prevalence of systematics --- both "known…
A general analytical method is developed for describing crossover phenomena of arbitrary nature. The method is based on the algebraic self-similar renormalization of asymptotic series, with control functions defined by crossover conditions.…
Observational astrophysics consists of making inferences about the Universe by comparing data and models. The credible intervals placed on model parameters are often as important as the maximum a posteriori probability values, as the…
This paper describes a Bayesian method for combining an arbitrary mixture of observational and experimental data in order to learn causal Bayesian networks. Observational data are passively observed. Experimental data, such as that produced…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
We construct a "hyperparameter matrix" statistical method for performing the joint analyses of multiple correlated astronomical data sets, in which the weights of data sets are determined by their own statistical properties. This method is…
Finite mixture models have become a popular tool for clustering. Amongst other uses, they have been applied for clustering longitudinal data and clustering high-dimensional data. In the latter case, a latent Gaussian mixture model is…
In a network meta-analysis, some of the collected studies may deviate markedly from the others, for example having very unusual effect sizes. These deviating studies can be regarded as outlying with respect to the rest of the network and…
Binary observations are often repeated to improve data quality, creating technical replicates. Several scoring methods are commonly used to infer the actual individual state and obtain a probability for each state. The common practice of…
Boosting algorithms to simultaneously estimate and select predictor effects in statistical models have gained substantial interest during the last decade. This review article aims to highlight recent methodological developments regarding…
Emerging applications of sensor networks for detection sometimes suggest that classical problems ought be revisited under new assumptions. This is the case of binary hypothesis testing with independent - but not necessarily identically…
Realizing the full potential of interconnecting the large amounts of data created in physics experiments, phenomenological models and theory simulations requires robust tools for statistical inference. Here I review a particularly promising…
In this paper we review the concepts of Bayesian evidence and Bayes factors, also known as log odds ratios, and their application to model selection. The theory is presented along with a discussion of analytic, approximate and numerical…