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In all areas of human knowledge, datasets are increasing in both size and complexity, creating the need for richer statistical models. This trend is also true for economic data, where high-dimensional and nonlinear/nonparametric inference…

In a variety of scientific applications we wish to characterize a physical system using measurements or observations. This often requires us to solve an inverse problem, which usually has non-unique solutions so uncertainty must be…

Fitting the multi-wavelength spectral energy distributions (SEDs) of galaxies is a widely used technique to extract information about the physical properties of galaxies. However, a major difficulty lies in the numerous uncertainties…

The Bayesian approach to data analysis provides a powerful way to handle uncertainty in all observations, model parameters, and model structure using probability theory. Probabilistic programming languages make it easier to specify and fit…

Bayesian analysis is increasingly popular for use in social science and other application areas where the data are observations from an informative sample. An informative sampling design leads to inclusion probabilities that are correlated…

Once upon a time, predictions for the accuracy of inference on gravitational-wave signals relied on computationally inexpensive but often inaccurate techniques. Recently, the approach has shifted to actual inference on noisy signals with…

BayesicFitting is a comprehensive, general-purpose toolbox for simple and standardized model fitting. Its fitting options range from simple least-squares methods, via maximum likelihood to fully Bayesian inference, working on a multitude of…

In recent years, methods for Bayesian inference have been widely used in many different problems in physics where detection and characterization are necessary. Data analysis in gravitational-wave astronomy is a prime example of such a case.…

Bayesian Networks (BNs) are used in various fields for modeling, prediction, and decision making. pgmpy is a python package that provides a collection of algorithms and tools to work with BNs and related models. It implements algorithms for…

Bayesian probabilistic numerical methods are a set of tools providing posterior distributions on the output of numerical methods. The use of these methods is usually motivated by the fact that they can represent our uncertainty due to…

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…

Bayesian methods are particularly effective for addressing inverse problems due to their ability to manage uncertainties inherent in the inference process. However, employing these methods with costly forward models poses significant…

Bayesian inference is used extensively to quantify the uncertainty in an inferred field given the measurement of a related field when the two are linked by a mathematical model. Despite its many applications, Bayesian inference faces…

Bayesian inference is an effective approach for solving statistical learning problems especially with uncertainty and incompleteness. However, inference efficiencies are physically limited by the bottlenecks of conventional computing…

Bayesian methods are useful for statistical inference. However, real-world problems can be challenging using Bayesian methods when the data analyst has only limited prior knowledge. In this paper we consider a class of problems, called…

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…

Bayesian estimation is a powerful theoretical paradigm for the operation of quantum sensors. However, the Bayesian method for statistical inference generally suffers from demanding calibration requirements that have so far restricted its…

This report introduces general ideas and some basic methods of the Bayesian probability theory applied to physics measurements. Our aim is to make the reader familiar, through examples rather than rigorous formalism, with concepts such as:…

Bayesian inference is used extensively to infer and to quantify the uncertainty in a field of interest from a measurement of a related field when the two are linked by a physical model. Despite its many applications, Bayesian inference…

We introduce a novel framework for the estimation of the posterior distribution over the weights of a neural network, based on a new probabilistic interpretation of adaptive optimisation algorithms such as AdaGrad and Adam. We demonstrate…