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Uncertainty quantification is essential when dealing with ill-conditioned inverse problems due to the inherent nonuniqueness of the solution. Bayesian approaches allow us to determine how likely an estimation of the unknown parameters is…

In indirect measurements, the measurand is determined by solving an inverse problem which requires a model of the measurement process. Such models are often approximations and introduce systematic errors leading to a bias of the posterior…

Bayesian methods have been very successful in quantifying uncertainty in physics-based problems in parameter estimation and prediction. In these cases, physical measurements y are modeled as the best fit of a physics-based model…

We consider the inverse reinforcement learning problem, that is, the problem of learning from, and then predicting or mimicking a controller based on state/action data. We propose a statistical model for such data, derived from the…

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary…

Bayesian calibration of black-box computer models offers an established framework to obtain a posterior distribution over model parameters. Traditional Bayesian calibration involves the emulation of the computer model and an additive model…

Bayesian interpretations of neural processing require that biological mechanisms represent and operate upon probability distributions in accordance with Bayes' theorem. Many have speculated that synaptic failure constitutes a mechanism of…

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…

Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. They are often used to describe complex real-world phenomena, and as such can often be misspecified in practice.…

Affordances are fundamental descriptors of relationships between actions, objects and effects. They provide the means whereby a robot can predict effects, recognize actions, select objects and plan its behavior according to desired goals.…

We study probit regression from a Bayesian perspective and give an alternative form for the posterior distribution when the prior distribution for the regression parameters is the uniform distribution. This new form allows simple Monte…

Bayes factor, defined as the ratio of the marginal likelihood functions of two competing models, is the natural Bayesian procedure for model selection. Marginal likelihoods are usually computationally demanding and complex. This scenario is…

We study a nonparametric Bayesian approach to linear inverse problems under discrete observations. We use the discrete Fourier transform to convert our model into a truncated Gaussian sequence model, that is closely related to the classical…

Recent developments in statistical regression methodology shift away from pure mean regression towards distributional regression models. One important strand thereof is that of conditional transformation models (CTMs). CTMs infer the entire…

Pimentel et al. (2020) recently analysed probing from an information-theoretic perspective. They argue that probing should be seen as approximating a mutual information. This led to the rather unintuitive conclusion that representations…

For a Bayesian, the task to define the likelihood can be as perplexing as the task to define the prior. We focus on situations when the parameter of interest has been emancipated from the likelihood and is linked to data directly through a…

The recent literature on deep learning offers new tools to learn a rich probability distribution over high dimensional data such as images or sounds. In this work we investigate the possibility of learning the prior distribution over neural…

In many application areas, data are collected on a categorical response and high-dimensional categorical predictors, with the goals being to build a parsimonious model for classification while doing inferences on the important predictors.…

The objective of Bayesian inference is often to infer, from data, a probability measure for a random variable that can be used as input for Monte Carlo simulation. When datasets for Bayesian inference are small, a principle challenge is…

Neural networks make accurate predictions but often fail to provide reliable uncertainty estimates, especially under covariate distribution shifts between training and testing. To address this problem, we propose a Bayesian framework for…