Related papers: Interval estimation in the presence of nuisance pa…

We present an algorithm which allows a fast numerical computation of Feldman-Cousins confidence intervals for Poisson processes, even when the number of background events is relatively large. This algorithm incorporates an appropriate…

Many real world problems exhibit patterns that have periodic behavior. For example, in astrophysics, periodic variable stars play a pivotal role in understanding our universe. An important step when analyzing data from such processes is the…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…

Model explanations can be valuable for interpreting and debugging predictive models. We study a specific kind called Concept Explanations, where the goal is to interpret a model using human-understandable concepts. Although popular for…

Bayesian inference is often implemented using approximations, which can yield interval estimates that are too narrow, not fully capturing the uncertainty in the posterior distribution. We address the question of how to adjust these…

Many recently developed Bayesian methods have focused on sparse signal detection. However, much less work has been done addressing the natural follow-up question: how to make valid inferences for the magnitude of those signals after…

This paper focuses on the superset model problem that arises in the context of regression. To address this problem, we take the Bayesian approach to measure its uncertainty. An illustrative example with the real dataset is provided.

Data-driven risk analysis involves the inference of probability distributions from measured or simulated data. In the case of a highly reliable system, such as the electricity grid, the amount of relevant data is often exceedingly limited,…

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources…

Deep neural networks have achieved impressive results on a wide variety of tasks. However, quantifying uncertainty in the network's output is a challenging task. Bayesian models offer a mathematical framework to reason about model…

We describe some recent approaches to likelihood based inference in the presence of nuisance parameters. Our approach is based on plotting the likelihood function and the $p$-value function, using recently developed third order…

In this paper we focus on the parameter estimation of dynamic load models with stochastic terms, in particular, load models where protection settings are uncertain, such as in aggregated air conditioning units. We show how the uncertainty…

We propose a construction of frequentist confidence intervals that is effective near unphysical regions and unifies the treatment of two-sided and upper limit intervals. It is rigorous, has coverage, is computationally simple and avoids the…

We construct uncertainty intervals for weak Poisson signals in the presence of background. We consider the case where a primary experiment yields a realization of the signal plus background, and a second experiment yields a realization of…

Accurate quantification of model uncertainty has long been recognized as a fundamental requirement for trusted AI. In regression tasks, uncertainty is typically quantified using prediction intervals calibrated to a specific operating point,…

Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…

The Bayesian statistical paradigm uses the language of probability to express uncertainty about the phenomena that generate observed data. Probability distributions thus characterize Bayesian analysis, with the rules of probability used to…

We study the problem of designing interval-valued observers that simultaneously estimate the system state and learn an unknown dynamic model for partially unknown nonlinear systems with dynamic unknown inputs and bounded noise signals.…

The ranking problem is to order a collection of units by some unobserved parameter, based on observations from the associated distribution. This problem arises naturally in a number of contexts, such as business, where we may want to rank…

The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…