Related papers: Shrinkage priors on complex-valued circular-symmet…
Bayesian predictive densities when the observed data $x$ and the target variable $y$ to be predicted have different distributions are investigated by using the framework of information geometry. The performance of predictive densities is…
We propose a novel adaptive importance sampling scheme for Bayesian inversion problems where the inference of the variables of interest and the power of the data noise is split. More specifically, we consider a Bayesian analysis for the…
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
We study the maximum likelihood estimator of density of $n$ independent observations, under the assumption that it is well approximated by a mixture with a large number of components. The main focus is on statistical properties with respect…
Effective uncertainty quantification is important for training modern predictive models with limited data, enhancing both accuracy and robustness. While Bayesian methods are effective for this purpose, they can be challenging to scale. When…
Recent advances in deep learning have brought to the fore models that can make multiple computational steps in the service of completing a task; these are capable of describ- ing long-term dependencies in sequential data. Novel recurrent…
We use a newly released version of the SuperBayeS code to analyze the impact of the choice of priors and the influence of various constraints on the statistical conclusions for the preferred values of the parameters of the Constrained MSSM.…
Most estimates for penalised linear regression can be viewed as posterior modes for an appropriate choice of prior distribution. Bayesian shrinkage methods, particularly the horseshoe estimator, have recently attracted a great deal of…
We study the behavior of the posterior distribution in high-dimensional Bayesian Gaussian linear regression models having $p\gg n$, with $p$ the number of predictors and $n$ the sample size. Our focus is on obtaining quantitative finite…
In the Bayes paradigm and for a given loss function, we propose the construction of a new type of posterior distributions, that extends the classical Bayes one, for estimating the law of an $n$-sample. The loss functions we have in mind are…
Some convergence results on the kernel density estimator are proven for a class of linear processes with cyclical effects. In particular we extend the results of Ho and Hsing (1996a) and Mielniczuk (1997) to the stationary processes for…
We introduce a new shrinkage prior on function spaces, called the functional horseshoe prior (fHS), that encourages shrinkage towards parametric classes of functions. Unlike other shrinkage priors for parametric models, the fHS shrinkage…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
This paper investigates sparse high-dimensional linear regression, particularly examining the properties of the posterior under conditions of random design and unknown error variance. We provide consistency results for the posterior and…
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…
The training of high-dimensional regression models on comparably sparse data is an important yet complicated topic, especially when there are many more model parameters than observations in the data. From a Bayesian perspective, inference…
We consider a Bayesian framework for estimating a high-dimensional sparse precision matrix, in which adaptive shrinkage and sparsity are induced by a mixture of Laplace priors. Besides discussing our formulation from the Bayesian…
We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric…
Simultaneous predictive distributions for independent Poisson observables are investigated. A class of improper prior distributions for Poisson means is introduced. The Bayesian predictive distributions based on priors from the introduced…