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Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
For a given target density, there exist an infinite number of diffusion processes which are ergodic with respect to this density. As observed in a number of papers, samplers based on nonreversible diffusion processes can significantly…
Diffusion models have recently shown considerable potential in solving Bayesian inverse problems when used as priors. However, sampling from the resulting denoising posterior distributions remains a challenge as it involves intractable…
Markov Chain Monte Carlo (MCMC) methods are a popular technique in Bayesian statistical modeling. They have long been used to obtain samples from posterior distributions, but recent research has focused on the scalability of these…
This paper introduces a novel Bayesian approach to detect changes in the variance of a Gaussian sequence model, focusing on quantifying the uncertainty in the change point locations and providing a scalable algorithm for inference. Such a…
We show that the stick-breaking construction of the beta process due to Paisley, et al. (2010) can be obtained from the characterization of the beta process as a Poisson process. Specifically, we show that the mean measure of the underlying…
This work delves into presenting a probabilistic method for analyzing linear process data with weakly dependent innovations, focusing on detecting change-points in the mean and estimating its spectral density. We develop a test for…
When working with multimodal Bayesian posterior distributions, Markov chain Monte Carlo (MCMC) algorithms have difficulty moving between modes, and default variational or mode-based approximate inferences will understate posterior…
We consider the sequential sampling of species, where observed samples are classified into the species they belong to. We are particularly interested in studying some quantities describing the sampling process when there is a new species…
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…
In this paper, we propose a MCMC algorithm based on elliptical slice sampling with the purpose to improve sampling efficiency. During sampling, a mixture distribution is fitted periodically to previous samples. The components of the mixture…
We present a new procedure for enhanced variable selection for component-wise gradient boosting. Statistical boosting is a computational approach that emerged from machine learning, which allows to fit regression models in the presence of…
We study existence and uniqueness of the fixed points solutions of a large class of non-linear variable discounted transfer operators associated to a sequential decision-making process. We establish regularity properties of these solutions,…
A sequence of random variables is exchangeable if its joint distribution is invariant under variable permutations. We introduce exchangeable variable models (EVMs) as a novel class of probabilistic models whose basic building blocks are…
The hierarchical Dirichlet process (HDP) has become an important Bayesian nonparametric model for grouped data, such as document collections. The HDP is used to construct a flexible mixed-membership model where the number of components is…
Flexible regression methods where interest centres on the way that the whole distribution of a response vector changes with covariates are very useful in some applications. A recently developed technique in this regard uses the…
The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which…
Measure-valued P\'{o}lya sequences (MVPS) are processes whose dynamics are governed by generalized P\'{o}lya urn schemes with infinitely many colors. Assuming a general reinforcement rule, exchangeable MVPSs can be viewed as extensions of…
Bayesian methods hold significant promise for improving the uncertainty quantification ability and robustness of deep neural network models. Recent research has seen the investigation of a number of approximate Bayesian inference methods…
Variable selection and classification are common objectives in the analysis of high-dimensional data. Most such methods make distributional assumptions that may not be compatible with the diverse families of distributions data can take. A…