Related papers: Bayesian inference for higher order ordinary diffe…

In this paper, we propose a progressive Bayesian procedure, where the measurement information is continuously included into the given prior estimate (although we perform observations at discrete time steps). The key idea is to derive a…

Although linear regression models are fundamental tools in statistical science, the estimation results can be sensitive to outliers. While several robust methods have been proposed in frequentist frameworks, statistical inference is not…

We consider Bayesian inference in inverse regression problems where the objective is to infer about unobserved covariates from observed responses and covariates. We establish posterior consistency of such unobserved covariates in Bayesian…

Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings…

We introduce a new method of estimation of parameters in semiparametric and nonparametric models. The method is based on estimating equations that are $U$-statistics in the observations. The $U$-statistics are based on higher order…

In this paper several related estimation problems are addressed from a Bayesian point of view and optimal estimators are obtained for each of them when some natural loss functions are considered. Namely, we are interested in estimating a…

Variational autoencoder (VAE) is a very successful generative model whose key element is the so called amortized inference network, which can perform test time inference using a single feed forward pass. Unfortunately, this comes at the…

We propose a general framework for obtaining probabilistic solutions to PDE-based inverse problems. Bayesian methods are attractive for uncertainty quantification but assume knowledge of the likelihood model or data generation process. This…

Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…

This paper develops a methodology for approximating the posterior first two moments of the posterior distribution in Bayesian inference. Partially specified probability models, which are defined only by specifying means and variances, are…

We present two approaches to system identification, i.e. the identification of partial differential equations (PDEs) from measurement data. The first is a regression-based Variational System Identification procedure that is advantageous in…

The main challenge in Bayesian models is to determine the posterior for the model parameters. Already, in models with only one or few parameters, the analytical posterior can only be determined in special settings. In Bayesian neural…

Motivated by molecular biology, there has been an upsurge of research activities in directional statistics in general and its Bayesian aspect in particular. The central distribution for the circular case is von Mises distribution which has…

In recent years we have witnessed a growth in mathematics for deep learning, which has been used to solve inverse problems of partial differential equations (PDEs). However, most deep learning-based inversion methods either require paired…

In this paper we consider the estimation of unknown parameters in Bayesian inverse problems. In most cases of practical interest, there are several barriers to performing such estimation, This includes a numerical approximation of a…

Reliable predictive uncertainty estimation plays an important role in enabling the deployment of neural networks to safety-critical settings. A popular approach for estimating the predictive uncertainty of neural networks is to define a…

The hazard function is central to the formulation of commonly used survival regression models such as the proportional hazards and accelerated failure time models. However, these models rely on a shared baseline hazard, which, when…

We propose a semiparametric Bayesian methodology for estimating the average treatment effect (ATE) within the potential outcomes framework using observational data with high-dimensional nuisance parameters. Our method introduces a Bayesian…

Inverse problems are crucial for many applications in science, engineering and medicine that involve data assimilation, design, and imaging. Their solution infers the parameters or latent states of a complex system from noisy data and…

In this article a novel approach for training deep neural networks using Bayesian techniques is presented. The Bayesian methodology allows for an easy evaluation of model uncertainty and additionally is robust to overfitting. These are…