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We consider the problem of predictive density estimation under Kullback-Leibler loss in a high-dimensional Gaussian model with exact sparsity constraints on the location parameters. We study the first order asymptotic minimax risk of Bayes…
Given a random sample from a distribution with density function that depends on an unknown parameter $\theta$, we are interested in accurately estimating the true parametric density function at a future observation from the same…
This paper addresses the weak instruments problem in linear instrumental variable models from a Bayesian perspective. The new approach has two components. First, a novel predictor-dependent shrinkage prior is developed for the many…
A spectral approach to Bayesian inference is presented. It pursues the emulation of the posterior probability density. The starting point is a series expansion of the likelihood function in terms of orthogonal polynomials. From this…
The method of Bayesian variable selection via penalized credible regions separates model fitting and variable selection. The idea is to search for the sparsest solution within the joint posterior credible regions. Although the approach was…
In a remarkable series of papers beginning in 1956, Charles Stein set the stage for the future development of minimax shrinkage estimators of a multivariate normal mean under quadratic loss. More recently, parallel developments have seen…
We consider the problem of estimating probability density functions based on sample data, using a finite mixture of densities from some component class. To this end, we introduce the $h$-lifted Kullback--Leibler (KL) divergence as a…
Positivity of the prior probability of Kullback-Leibler neighborhood around the true density, commonly known as the Kullback-Leibler property, plays a fundamental role in posterior consistency. A popular prior for Bayesian estimation is…
Modern applications routinely collect high-dimensional data, leading to statistical models having more parameters than there are samples available. A common solution is to impose sparsity in parameter estimation, often using penalized…
We introduce a density basis of the trigonometric polynomials that is suitable to mixture modelling. Statistical and geometric properties are derived, suggesting it as a circular analogue to the Bernstein polynomial densities. Nonparametric…
Modern approaches to perform Bayesian variable selection rely mostly on the use of shrinkage priors. That said, an ideal shrinkage prior should be adaptive to different signal levels, ensuring that small effects are ruled out, while keeping…
Based on independently distributed $X_1 \sim N_p(\theta_1, \sigma^2_1 I_p)$ and $X_2 \sim N_p(\theta_2, \sigma^2_2 I_p)$, we consider the efficiency of various predictive density estimators for $Y_1 \sim N_p(\theta_1, \sigma^2_Y I_p)$, with…
Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…
We study the problem of model selection type aggregation with respect to the Kullback-Leibler divergence for various probabilistic models. Rather than considering a convex combination of the initial estimators $f_1, \ldots, f_N$, our…
Accelerated algorithms for maximum likelihood image reconstruction are essential for emerging applications such as 3D tomography, dynamic tomographic imaging, and other high dimensional inverse problems. In this paper, we introduce and…
A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of $\xv$ are naturally associated with a tree structure. Important examples are when $\xv$…
Projected priors were originally introduced to accommodate parameter constraints, but have recently regained popularity due to their ability to assign probability mass to low-dimensional parameter sets, such as the spaces of sparse vectors,…
We propose a novel spike and slab prior specification with scaled beta prime marginals for the importance parameters of regression coefficients to allow for general effect selection within the class of structured additive distributional…
This paper focuses on $\alpha$-divergence minimisation methods for Variational Inference. More precisely, we are interested in algorithms optimising the mixture weights of any given mixture model, without any information on the underlying…
The first Bayesian results for the sparse normal means problem were proven for spike-and-slab priors. However, these priors are less convenient from a computational point of view. In the meanwhile, a large number of continuous shrinkage…