Related papers: Can we trust Bayesian uncertainty quantification f…

Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…

This paper focuses on Bayesian shrinkage for covariance matrix estimation. We examine posterior properties and frequentist risks of Bayesian estimators based on new hierarchical inverse-Wishart priors. More precisely, we give the existence…

In this paper, we introduce the notion of Gaussian processes indexed by probability density functions for extending the Mat\'ern family of covariance functions. We use some tools from information geometry to improve the efficiency and the…

For the purpose of maximum likelihood estimation of static parameters, we apply a kernel smoother to the particles in the standard SIR filter for non-linear state space models with additive Gaussian observation noise. This reduces the Monte…

Uncertainty estimation is essential for robust decision-making in the presence of ambiguous or out-of-distribution inputs. Gaussian Processes (GPs) are classical kernel-based models that offer principled uncertainty quantification and…

Deep learning methods continue to have a decided impact on machine learning, both in theory and in practice. Statistical theoretical developments have been mostly concerned with approximability or rates of estimation when recovering…

In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

Complex-valued Gaussian processes are commonly used in Bayesian frequency-domain system identification as prior models for regression. If each realization of such a process were an $H_\infty$ function with probability one, then the same…

We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…

The kernel-based method has been successfully applied in linear system identification using stable kernel designs. From a Gaussian process perspective, it automatically provides probabilistic error bounds for the identified models from the…

Large Language Models (LLMs) have shown remarkable progress in multiple-choice question answering (MCQA), but their inherent unreliability, such as hallucination and overconfidence, limits their application in high-risk domains. To address…

We establish a general Bernstein--von Mises theorem for approximately linear semiparametric functionals of fractional posterior distributions based on nonparametric priors. This is illustrated in a number of nonparametric settings and for…

Among the various approaches for producing point distributions with blue noise spectrum, we argue for an optimization framework using Gaussian kernels. We show that with a wise selection of optimization parameters, this approach attains…

Gaussian processes are a natural way of defining prior distributions over functions of one or more input variables. In a simple nonparametric regression problem, where such a function gives the mean of a Gaussian distribution for an…

Gaussian Process Regression is a popular nonparametric regression method based on Bayesian principles that provides uncertainty estimates for its predictions. However, these estimates are of a Bayesian nature, whereas for some important…

A key factor in ensuring the accuracy of computer simulations that model physical systems is the proper calibration of their parameters based on real-world observations or experimental data. Inevitably, uncertainties arise, and Bayesian…

Tomographic reconstruction, despite its revolutionary impact on a wide range of applications, suffers from its ill-posed nature in that there is no unique solution because of limited and noisy measurements. Therefore, in the absence of…

We establish theoretical guarantees for the expected prediction error of the exponential weighting aggregate in the case of multivariate regression that is when the label vector is multidimensional. We consider the regression model with…

To the frequentist who computes posteriors, not all priors are useful asymptotically: in this paper Schwartz's 1965 Kullback-Leibler condition is generalised to enable frequentist interpretation of convergence of posterior distributions…

This study proposes a novel approach to quantifying uncertainties of constitutive relations inferred from noisy experimental data using inverse modelling. We focus on electrochemical systems in which charged species (e.g., Lithium ions) are…