Related papers: Cross Validated Non parametric Bayesianism by Mark…

Bayesian nonparametric methods are a popular choice for analysing survival data due to their ability to flexibly model the distribution of survival times. These methods typically employ a nonparametric prior on the survival function that is…

Empirical likelihood is a popular nonparametric statistical tool that does not require any distributional assumptions. In this paper, we explore the possibility of conducting variable selection via Bayesian empirical likelihood. We show…

We propose a novel approach to perform approximate Bayesian inference in complex models such as Bayesian neural networks. The approach is more scalable to large data than Markov Chain Monte Carlo, it embraces more expressive models than…

We consider Bayesian inverse problems arising in data assimilation for dynamical systems governed by partial and stochastic partial differential equations. The space-time dependent field is inferred jointly with static parameters of the…

The Metropolis-Hastings (MH) algorithm is one of the most widely used Markov Chain Monte Carlo schemes for generating samples from Bayesian posterior distributions. The algorithm is asymptotically exact, flexible and easy to implement.…

Undirected graphical models are widely used in statistics, physics and machine vision. However Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the…

Bayesian inference in deep neural networks is challenging due to the high-dimensional, strongly multi-modal parameter posterior density landscape. Markov chain Monte Carlo approaches asymptotically recover the true posterior but are…

We propose a novel Bayesian approach to the problem of variable selection in multiple linear regression models. In particular, we present a hierarchical setting which allows for direct specification of a-priori beliefs about the number of…

Bayesian statistics has gained popularity in psychological research due to its intuitive uncertainty quantification and convenient information-updating rules. In many applications, however, prior distributions are introduced merely as…

We study Bayesian methods for large-scale linear inverse problems, focusing on the challenging task of hyperparameter estimation. Typical hierarchical Bayesian formulations that follow a Markov Chain Monte Carlo approach are possible for…

We introduce a novel Bayesian approach for variable selection using Gaussian process regression, which is crucial for enhancing interpretability and model regularization. Our method employs nearest neighbor Gaussian processes, serving as…

We study Bayesian inference methods for solving linear inverse problems, focusing on hierarchical formulations where the prior or the likelihood function depend on unspecified hyperparameters. In practice, these hyperparameters are often…

We introduce a novel procedure for obtaining cross-validated predictive estimates for Bayesian hierarchical regression models (BHRMs). Bayesian hierarchical models are popular for their ability to model complex dependence structures and…

Probabilistic regression models typically use the Maximum Likelihood Estimation or Cross-Validation to fit parameters. These methods can give an advantage to the solutions that fit observations on average, but they do not pay attention to…

A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…

Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…

Bayesian inference and uncertainty quantification in a general class of non-linear inverse regression models is considered. Analytic conditions on the regression model $\{\mathscr G(\theta): \theta \in \Theta\}$ and on Gaussian process…

Bayesian nonparametric mixture models offer a rich framework for model based clustering. We consider the situation where the kernel of the mixture is available only up to an intractable normalizing constant. In this case, most of the…

In spite of the recent surge of interest in quantile regression, joint estimation of linear quantile planes remains a great challenge in statistics and econometrics. We propose a novel parametrization that characterizes any collection of…

Approximate Bayesian computation allows for inference of complicated probabilistic models with intractable likelihoods using model simulations. The Markov chain Monte Carlo implementation of approximate Bayesian computation is often…