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Structured variational inference constitutes a core methodology in modern statistical applications. Unlike mean-field variational inference, the approximate posterior is assumed to have interdependent structure. We consider the natural…

Extraordinary amounts of data are being produced in many branches of science. Proven statistical methods are no longer applicable with extraordinary large data sets due to computational limitations. A critical step in big data analysis is…

In recent years, denoising problems have become intertwined with the development of deep generative models. In particular, diffusion models are trained like denoisers, and the distribution they model coincide with denoising priors in the…

Count data with zero inflation and large outliers are ubiquitous in many scientific applications. However, posterior analysis under a standard statistical model, such as Poisson or negative binomial distribution, is sensitive to such…

Approximate Bayesian computation (ABC) is a set of techniques for Bayesian inference when the likelihood is intractable but sampling from the model is possible. This work presents a simple yet effective ABC algorithm based on the…

We present prompt distribution learning for effectively adapting a pre-trained vision-language model to address downstream recognition tasks. Our method not only learns low-bias prompts from a few samples but also captures the distribution…

Bayesian A/B testing investigates metric changes using the joint posterior distribution of two (or more) experimentally-derived datasets. The construction of said joint posterior is often a time-consuming process requiring specialized…

In an indirect Gaussian sequence space model lower and upper bounds are derived for the concentration rate of the posterior distribution of the parameter of interest shrinking to the parameter value $\theta^\circ$ that generates the data.…

Variable selection in ultra-high dimensional linear regression is often preceded by a screening step to significantly reduce the dimension. Here we develop a Bayesian variable screening method (BITS) guided by the posterior model…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

Inference of the marginal probability distribution is defined as the calculation of the probability of a subset of the variables and is relevant for handling missing data and hidden variables. While inference of the marginal probability…

Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…

Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…

Clinical decisions to treat and diagnose patients are affected by implicit biases formed by racism, ableism, sexism, and other stereotypes. These biases reflect broader systemic discrimination in healthcare and risk marginalizing already…

Inductive Conformal Prediction (ICP) is a set of distribution-free and model agnostic algorithms devised to predict with a user-defined confidence with coverage guarantee. Instead of having point predictions, i.e., a real number in the case…

We propose a Bayesian inference framework to estimate uncertainties in inverse scattering problems. Given the observed data, the forward model and their uncertainties, we find the posterior distribution over a finite parameter field…

We propose a new model selection method, the posterior averaging information criterion, for Bayesian model assessment from a predictive perspective. The theoretical foundation is built on the Kullback-Leibler divergence to quantify the…

Posterior sampling is a task of central importance in Bayesian inference. For many applications in Bayesian meta-analysis and Bayesian transfer learning, the prior distribution is unknown and needs to be estimated from samples. In practice,…

Recently, deep generative models have been used for posterior inference in inverse problems, including high-stakes applications in medical imaging and scientific discovery, where the uncertainty of a prediction can matter as much as the…

We propose a novel approach to Bayesian analysis that is provably robust to outliers in the data and often has computational advantages over standard methods. Our technique is based on splitting the data into non-overlapping subgroups,…