Related papers: Shape restricted regression with random Bernstein …

Maximum approximate Bernstein likelihood estimates of the baseline density function and the regression coefficients in the proportional hazard regression models based on interval-censored event time data are proposed. This results in not…

Besov priors are nonparametric priors that can model spatially inhomogeneous functions. They are routinely used in inverse problems and imaging, where they exhibit attractive sparsity-promoting and edge-preserving features. A recent line of…

Discrete mixture models are routinely used for density estimation and clustering. While conducting inferences on the cluster-specific parameters, current frequentist and Bayesian methods often encounter problems when clusters are placed too…

The Bayesian approach to inverse problems typically relies on posterior sampling approaches, such as Markov chain Monte Carlo, for which the generation of each sample requires one or more evaluations of the parameter-to-observable map or…

During the past decade, shrinkage priors have received much attention in Bayesian analysis of high-dimensional data. This paper establishes the posterior consistency for high-dimensional linear regression with a class of shrinkage priors,…

Shape constraints (such as non-negativity, monotonicity, convexity) play a central role in a large number of applications, as they usually improve performance for small sample size and help interpretability. However enforcing these shape…

We study full Bayesian procedures for high-dimensional linear regression. We adopt data-dependent empirical priors introduced in [1]. In their paper, these priors have nice posterior contraction properties and are easy to compute. Our paper…

This paper devises a regression-type model for the situation where both the response and covariates are extreme. The proposed approach is designed for the setting where both the response and covariates are themselves block maxima, and thus…

In many large-scale inverse problems, such as computed tomography and image deblurring, characterization of sharp edges in the solution is desired. Within the Bayesian approach to inverse problems, edge-preservation is often achieved using…

Spike-and-slab priors are popular Bayesian solutions for high-dimensional linear regression problems. Previous theoretical studies on spike-and-slab methods focus on specific prior formulations and use prior-dependent conditions and…

This paper proposes a CS scheme that exploits the representational power of restricted Boltzmann machines and deep learning architectures to model the prior distribution of the sparsity pattern of signals belonging to the same class. The…

We propose alternatives to Bayesian a priori distributions that are frequently used in the study of inverse problems. Our aim is to construct priors that have similar good edge-preserving properties as total variation or Mumford-Shah priors…

Segmenting images of low quality or with missing data is a challenging problem. Integrating statistical prior information about the shapes to be segmented can improve the segmentation results significantly. Most shape-based segmentation…

In this paper, we consider the so-called Shape Invariant Model which stands for the estimation of a function f0 submitted to a random translation of law g0 in a white noise model. We are interested in such a model when the law of the…

Consider a problem of predicting a response variable using a set of covariates in a linear regression model. If it is \emph{a priori} known or suspected that a subset of the covariates do not significantly contribute to the overall fit of…

In the present paper, we propose and analyze a novel method for estimating a univariate regression function of bounded variation. The underpinning idea is to combine two classical tools in nonparametric statistics, namely isotonic…

We develop a data-driven algorithm for automatically selecting the regularisation parameter in Bayesian inversion under random tree Besov priors. One of the key challenges in Bayesian inversion is the construction of priors that are both…

Discrete Markov random fields are undirected graphical models that capture complex conditional dependencies between discrete variables. Conducting exact posterior inference in these models is often computationally challenging because…

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

We propose to use L\'evy {\alpha}-stable distributions for constructing priors for Bayesian inverse problems. The construction is based on Markov fields with stable-distributed increments. Special cases include the Cauchy and Gaussian…