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We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…
We develop a Bayesian approach called Bayesian projected calibration to address the problem of calibrating an imperfect computer model using observational data from a complex physical system. The calibration parameter and the physical…
We consider the problem of statistical inference on parameters of a target population when auxiliary observations are available from related populations. We propose a flexible empirical Bayes approach that can be applied on top of any…
A method for sequential inference of the fixed parameters of a dynamic latent Gaussian models is proposed and evaluated that is based on the iterated Laplace approximation. The method provides a useful trade-off between computational…
Calibration error is commonly adopted for evaluating the quality of uncertainty estimators in deep neural networks. In this paper, we argue that such a metric is highly beneficial for training predictive models, even when we do not…
In this paper, we describe centering and noncentering methodology as complementary techniques for use in parametrization of broad classes of hierarchical models, with a view to the construction of effective MCMC algorithms for exploring…
We propose a new family of error distributions for model-based quantile regression, which is constructed through a structured mixture of normal distributions. The construction enables fixing specific percentiles of the distribution while,…
Recent advances in machine learning have significantly improved prediction accuracy in various applications. However, ensuring the calibration of probabilistic predictions remains a significant challenge. Despite efforts to enhance model…
We present a Bayesian nonparametric system reliability model which scales well and provides a great deal of flexibility in modeling. The Bayesian approach naturally handles the disparate amounts of component and subsystem data that may…
We study objective Bayesian inference for linear regression models with residual errors distributed according to the class of two-piece scale mixtures of normal distributions. These models allow for capturing departures from the usual…
We present a posteriori error estimates for inconsistent and non-hierarchical Galerkin methods for linear parabolic problems, allowing them to be used in conjunction with very general mesh modification for the first time. We treat schemes…
We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…
Quantifying uncertainty in word embeddings is crucial for reliable inference from textual data. However, existing Bayesian methods such as Hamiltonian Monte Carlo (HMC) and mean-field variational inference (MFVI) are either computationally…
The Bayesian paradigm has the potential to solve core issues of deep neural networks such as poor calibration and data inefficiency. Alas, scaling Bayesian inference to large weight spaces often requires restrictive approximations. In this…
We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss…
In a Bayesian inverse problem setting, the solution consists of a posterior measure obtained by combining prior belief, information about the forward operator, and noisy observational data. This measure is most often given in terms of a…
A key challenge in probabilistic regression is ensuring that predictive distributions accurately reflect true empirical uncertainty. Minimizing overall prediction error often encourages models to prioritize informativeness over calibration,…
The Bayesian Lasso is constructed in the linear regression framework and applies the Gibbs sampling to estimate the regression parameters. This paper develops a new sparse learning model, named the Bayesian Lasso Sparse (BLS) model, that…
In the sparse normal means model, convergence of the Bayesian posterior distribution associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…
We consider a Bayesian nonparametric approach to a family of linear inverse problems in a separable Hilbert space setting with Gaussian noise. We assume Gaussian priors, which are conjugate to the model, and present a method of identifying…