Related papers: Asymptotically Log-Optimal Bayes-Assisted Confiden…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

The decreasing cost and improved sensor and monitoring system technology (e.g. fiber optics and strain gauges) have led to more measurements in close proximity to each other. When using such spatially dense measurement data in Bayesian…

Despite much research targeted at enabling conventional machine learning models to continually learn tasks and data distributions sequentially without forgetting the knowledge acquired, little effort has been devoted to account for more…

Predictive uncertainty quantification is crucial for reliable decision-making in various applied domains. Bayesian neural networks offer a powerful framework for this task. However, defining meaningful priors and ensuring computational…

The role played by the composite analogue of the log likelihood ratio in hypothesis testing and in setting confidence regions is not as prominent as it is in the canonical likelihood setting, since its asymptotic distribution depends on the…

Quantile estimation and regression within the Bayesian framework is challenging as the choice of likelihood and prior is not obvious. In this paper, we introduce a novel Bayesian nonparametric method for quantile estimation and regression…

Modern regression analyses are often undermined by covariate measurement error, misspecification of the regression model, and misspecification of the measurement error distribution. We present, to the best of our knowledge, the first…

Estimation of finite mixture models when the mixing distribution support is unknown is an important problem. This paper gives a new approach based on a marginal likelihood for the unknown support. Motivated by a Bayesian Dirichlet prior…

Complex simulator-based models are now routinely used to perform inference across the sciences and engineering, but existing inference methods are often unable to account for outliers and other extreme values in data which occur due to…

A novel data-driven methodology is presented for the joint selection of prior parameters for both fixed and random effects in Linear Mixed Models (LMMs). This approach facilitates the estimation of complex random-effects structures, as well…

This paper considers a semiparametric approach within the general Bayesian linear model where the innovations consist of a stationary, mean zero Gaussian time series. While a parametric prior is specified for the linear model coefficients,…

Comparing competing mathematical models of complex natural processes is a shared goal among many branches of science. The Bayesian probabilistic framework offers a principled way to perform model comparison and extract useful metrics for…

Linear programming is widely used for decision-making in science, engineering, and operations research, yet in many modern applications the coefficients entering the constraints and objective are not known exactly and must be learned from…

An empirical Bayes approach to the estimation of possibly sparse sequences observed in Gaussian white noise is set out and investigated. The prior considered is a mixture of an atom of probability at zero and a heavy-tailed density \gamma,…

The construction of confidence intervals for the mean of a bounded random variable is a classical problem in statistics with numerous applications in machine learning and virtually all scientific fields. In particular, obtaining the…

Although large language models (LLMs) are becoming increasingly capable of solving challenging real-world tasks, accurately quantifying their uncertainty remains a critical open problem--one that limits their applicability in high-stakes…

Foundational image-language models have generated considerable interest due to their efficient adaptation to downstream tasks by prompt learning. Prompt learning treats part of the language model input as trainable while freezing the rest,…

Since the turn of the century, approximate Bayesian inference has steadily evolved as new computational techniques have been incorporated to handle increasingly complex and large-scale predictive problems. The recent success of deep neural…

The problem is that of sequential probability forecasting for finite-valued time series. The data is generated by an unknown probability distribution over the space of all one-way infinite sequences. It is known that this measure belongs to…

Bayesian optimal experimental design is a sub-field of statistics focused on developing methods to make efficient use of experimental resources. Any potential design is evaluated in terms of a utility function, such as the (theoretically…