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Due to increased awareness of data protection and corresponding laws many data, especially involving sensitive personal information, are not publicly accessible. Accordingly, many data collecting agencies only release aggregated data, e.g.…
We present a Bayesian approach to identify optimal transformations that map model input points to low dimensional latent variables. The "projection" mapping consists of an orthonormal matrix that is considered a priori unknown and needs to…
We present a software framework for statistical data analysis, called HistFitter, that has been used extensively by the ATLAS Collaboration to analyze big datasets originating from proton-proton collisions at the Large Hadron Collider at…
In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by…
Count outcomes in longitudinal studies are frequent in clinical and engineering studies. In frequentist and Bayesian statistical analysis, methods such as Mixed linear models allow the variability or correlation within individuals to be…
I describe a framework for adaptive scientific exploration based on iterating an Observation--Inference--Design cycle that allows adjustment of hypotheses and observing protocols in response to the results of observation on-the-fly, as data…
The experimental problem of converting a measured binomial quantity, the fraction of events in a sample that pass a cut, into a physical binomial quantity, the fraction of events originating from a signal source, is described as a system of…
Nested sampling is a Bayesian sampling technique developed to explore probability distributions lo- calised in an exponentially small area of the parameter space. The algorithm provides both posterior samples and an estimate of the evidence…
The fundamental task of classification given a limited number of training data samples is considered for physical systems with known parametric statistical models. The standalone learning-based and statistical model-based classifiers face…
Selection bias arises when the probability that an observation enters a dataset depends on variables related to the quantities of interest, leading to systematic distortions in estimation and uncertainty quantification. For example, in…
Least-squares fits are an important tool in many data analysis applications. In this paper, we review theoretical results, which are relevant for their application to data from counting experiments. Using a simple example, we illustrate the…
Approximate Bayesian computation is a statistical framework that uses numerical simulations to calibrate and compare models. Instead of computing likelihood functions, Approximate Bayesian computation relies on numerical simulations, which…
Decision-making often involves ranking and selection. For example, to assemble a team of political forecasters, we might begin by narrowing our choice set to the candidates we are confident rank among the top 10% in forecasting ability.…
Bayesian evidence is a standard tool used for comparing the ability of different models to fit available data and is used extensively in cosmology. However, since the evidence calculation involves performing an integral of the likelihood…
We introduce NIFTY, "Numerical Information Field Theory", a software package for the development of Bayesian signal inference algorithms that operate independently from any underlying spatial grid and its resolution. A large number of…
Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a…
There has been a tremendous methodological development of Bayes factors for hypothesis testing in the social and behavioral sciences, and related fields. This development is due to the flexibility of the Bayes factor for testing multiple…
The Bayesian evidence, crucial ingredient for model selection, is arguably the most important quantity in Bayesian data analysis: at the same time, however, it is also one of the most difficult to compute. In this paper we present a…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a…