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We consider the problem of subspace estimation in situations where the number of available snapshots and the observation dimension are comparable in magnitude. In this context, traditional subspace methods tend to fail because the…

Deep Ensembles, as a type of Bayesian Neural Networks, can be used to estimate uncertainty on the prediction of multiple neural networks by collecting votes from each network and computing the difference in those predictions. In this paper,…

Robust tracking of a target in a clutter environment is an important and challenging task. In recent years, the nearest neighbor methods and probabilistic data association filters were proposed. However, the performance of these methods…

Bayesian clustering methods have the widely touted advantage of providing a probabilistic characterization of uncertainty in clustering through the posterior distribution. An amazing variety of priors and likelihoods have been proposed for…

Bayesian inference is central to modern cosmology. While parameter estimation is achievable with unnormalised posteriors traditionally obtained via MCMC methods, comprehensive model comparison and tension quantification require Bayesian…

Bayesian likelihood-free inference, which is used to perform Bayesian inference when the likelihood is intractable, enjoys an increasing number of important scientific applications. However, many aspects of a Bayesian analysis become more…

We provide a general solution to a fundamental open problem in Bayesian inference, namely poor uncertainty quantification, from a frequency standpoint, of Bayesian methods in misspecified models. While existing solutions are based on…

The transductive inference is an effective technique in the few-shot learning task, where query sets update prototypes to improve themselves. However, these methods optimize the model by considering only the classification scores of the…

This study presents a Bayesian hierarchical model for analyzing spatially correlated functional data and handling irregularly spaced observations. The model uses Bernstein polynomial (BP) bases combined with autoregressive random effects,…

In this paper, we develop a graphical modeling framework for the inference of networks across multiple sample groups and data types. In medical studies, this setting arises whenever a set of subjects, which may be heterogeneous due to…

One way to incorporate systematic uncertainties into the calculation of confidence intervals is by integrating over probability density functions parametrizing the uncertainties. In this note we present a development of this method which…

This paper introduces a novel uncertainty quantification framework for regression models where the response takes values in a separable metric space, and the predictors are in a Euclidean space. The proposed algorithms can efficiently…

We propose a method for testing whether hierarchically ordered groups of potentially correlated variables are significant for explaining a response in a high-dimensional linear model. In presence of highly correlated variables, as is very…

We apply Bayesian statistics to the estimation of correlation functions. We give the probability distributions of auto- and cross-correlations as functions of the data. Our procedure uses the measured data optimally and informs about the…

Stochastic simulation is widely used to study complex systems composed of various interconnected subprocesses, such as input processes, routing and control logic, optimization routines, and data-driven decision modules. In practice, these…

While neural networks have demonstrated impressive performance across various tasks, accurately quantifying uncertainty in their predictions is essential to ensure their trustworthiness and enable widespread adoption in critical systems.…

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…

Causal inference on populations embedded in social networks poses technical challenges, since the typical no interference assumption frequently does not hold. Existing methods developed in the context of network interference rely upon the…

Unnormalized (or energy-based) models provide a flexible framework for capturing the characteristics of data with complex dependency structures. However, the application of standard Bayesian inference methods has been severely limited…

First principles microphysics models are essential to the design and analysis of high energy density physics experiments. Using experimental data to investigate the underlying physics is also essential, particularly when simulations and…