Related papers: Hierarchical Bayesian Modeling for Time-Dependent …

A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…

Turbulent flows have historically presented formidable challenges to predictive computational modeling. Traditional numerical simulations often require vast computational resources, making them infeasible for numerous engineering…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…

Calculation of Bayesian posteriors and model evidences typically requires numerical integration. Bayesian quadrature (BQ), a surrogate-model-based approach to numerical integration, is capable of superb sample efficiency, but its lack of…

Inverse problems are prevalent in both scientific research and engineering applications. In the context of Bayesian inverse problems, sampling from the posterior distribution can be particularly challenging when the forward models are…

Fast machine learning-based surrogate models are trained to emulate slow, high-fidelity engineering simulation models to accelerate engineering design tasks. This introduces uncertainty as the surrogate is only an approximation of the…

This paper is a note on the use of Bayesian nonparametric mixture models for continuous time series. We identify a key requirement for such models, and then establish that there is a single type of model which meets this requirement. As it…

We propose a novel hierarchical Bayesian model for learning with a large (possibly infinite) number of tasks/episodes, which suits well the few-shot meta learning problem. We consider episode-wise random variables to model episode-specific…

The identification of Linear Time-Varying (LTV) systems from input-output data is a fundamental yet challenging ill-posed inverse problem. This work introduces a unified Bayesian framework that models the system's impulse response, $h(t,…

We introduce a novel algorithm for controlling linear time invariant systems in a tracking problem. The controller is based on a Gaussian Process (GP) whose realizations satisfy a system of linear ordinary differential equations with…

We encounter time series data in many domains such as finance, physics, business, and weather. One of the main tasks of time series analysis, one that helps to take informed decisions under uncertainty, is forecasting. Time series are often…

Motivated by the analysis of extreme rainfall data, we introduce a general Bayesian hierarchical model for estimating the probability distribution of extreme values of intermittent random sequences, a common problem in geophysical and…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

In this work, we present a new class of models, called uncertain-input models, that allows us to treat system-identification problems in which a linear system is subject to a partially unknown input signal. To encode prior information about…

Supervised time-series classification garners widespread interest because of its applicability throughout a broad application domain including finance, astronomy, biosensors, and many others. In this work, we tackle this problem with hybrid…

In the framework of BEPU (Best Estimate plus Uncertainty) methodology, the uncertainties involved in the simulations must be quantified to prove that the investigated design is acceptable. The output uncertainties are usually calculated by…

Probabilistic neural networks are typically modeled with independent weight priors, which do not capture weight correlations in the prior and do not provide a parsimonious interface to express properties in function space. A desirable class…

This paper develops a Hierarchical Bayesian Modeling (HBM) framework for uncertainty quantification of Finite Element (FE) models based on modal information. This framework uses an existing Fast Fourier Transform (FFT) approach to identify…

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

Temporal modeling in complex systems requires capturing dependencies across multiple time scales while managing inherent uncertainties. We propose HierCVAE, a novel architecture that integrates hierarchical attention mechanisms with…