Related papers: Conditions for Posterior Contraction in the Sparse…
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 consider the horseshoe estimator due to Carvalho, Polson and Scott (2010) for the multivariate normal mean model in the situation that the mean vector is sparse in the nearly black sense. We assume the frequentist framework where the…
Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional…
In astronomical observations, the estimation of distances from parallaxes is a challenging task due to the inherent measurement errors and the non-linear relationship between the parallax and the distance. This study leverages ideas from…
We consider a family of infinite dimensional product measures with tails between Gaussian and exponential, which we call $p$-exponential measures. We study their measure-theoretic properties and in particular their concentration. Our…
We consider a class of linear ill-posed inverse problems arising from inversion of a compact operator with singular values which decay exponentially to zero. We adopt a Bayesian approach, assuming a Gaussian prior on the unknown function.…
Sparse convex clustering is to cluster observations and conduct variable selection simultaneously in the framework of convex clustering. Although a weighted $L_1$ norm is usually employed for the regularization term in sparse convex…
In recent years, a rich variety of shrinkage priors have been proposed that have great promise in addressing massive regression problems. In general, these new priors can be expressed as scale mixtures of normals, but have more complex…
We develop a framework to study posterior contraction rates in sparse high dimensional generalized linear models (GLM). We introduce a new family of GLMs, denoted by clipped GLM, which subsumes many standard GLMs and makes minor…
The paper discusses shrinkage priors which impose increasing shrinkage in a sequence of parameters. We review the cumulative shrinkage process (CUSP) prior of Legramanti et al. (2020), which is a spike-and-slab shrinkage prior where the…
We study predictive density estimation under Kullback-Leibler loss in $\ell_0$-sparse Gaussian sequence models. We propose proper Bayes predictive density estimates and establish asymptotic minimaxity in sparse models. A surprise is the…
In the present work, we consider variable selection and shrinkage for the Gaussian dynamic linear regression within a Bayesian framework. In particular, we propose a novel method that allows for time-varying sparsity, based on an extension…
Precision matrices are crucial in many fields such as social networks, neuroscience, and economics, representing the edge structure of Gaussian graphical models (GGMs), where a zero in an off-diagonal position of the precision matrix…
In various applications, we deal with high-dimensional positive-valued data that often exhibits sparsity. This paper develops a new class of continuous global-local shrinkage priors tailored to analyzing gamma-distributed observations where…
In the general signal+noise model we construct an empirical Bayes posterior which we then use for uncertainty quantification for the unknown, possibly sparse, signal. We introduce a novel excessive bias restriction (EBR) condition, which…
While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter…
We examine the effect of a prior that favours low values of fine-tuning on Bayesian multi-dimensional fits of the constrained minimal supersymmetric standard model (CMSSM or mSUGRA) to current data. The dark matter relic density, the…
Shrinkage prior has gained great successes in many data analysis, however, its applications mostly focus on the Bayesian modeling of sparse parameters. In this work, we will apply Bayesian shrinkage to model high dimensional parameter that…
Variable selection has received widespread attention over the last decade as we routinely encounter high-throughput datasets in complex biological and environment research. Most Bayesian variable selection methods are restricted to mixture…
We investigate the problem of deriving posterior concentration rates under different loss functions in nonparametric Bayes. We first provide a lower bound on posterior coverages of shrinking neighbourhoods that relates the metric or loss…