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The theory of two projections is utilized to study two-component Gibbs samplers. Through this theory, previously intractable problems regarding the asymptotic variances of two-component Gibbs samplers are reduced to elementary matrix…

We present a Gibbs sampler for the Dempster-Shafer (DS) approach to statistical inference for Categorical distributions. The DS framework extends the Bayesian approach, allows in particular the use of partial prior information, and yields…

We consider a general class of regression models with normally distributed covariates, and the associated nonconvex problem of fitting these models from data. We develop a general recipe for analyzing the convergence of iterative algorithms…

Herding is a technique to sequentially generate deterministic samples from a probability distribution. In this work, we propose a continuous herded Gibbs sampler that combines kernel herding on continuous densities with the Gibbs sampling…

Gibbs sampling is one of the most commonly used Markov Chain Monte Carlo (MCMC) algorithms due to its simplicity and efficiency. It cycles through the latent variables, sampling each one from its distribution conditional on the current…

We present the Gaussian process density sampler (GPDS), an exchangeable generative model for use in nonparametric Bayesian density estimation. Samples drawn from the GPDS are consistent with exact, independent samples from a distribution…

Surrogate models have become ubiquitous in science and engineering for their capability of emulating expensive computer codes, necessary to model and investigate complex phenomena. Bayesian emulators based on Gaussian processes adequately…

High dimensional data analysis is known to be as a challenging problem. In this article, we give a theoretical analysis of high dimensional classification of Gaussian data which relies on a geometrical analysis of the error measure. It…

Gibbs sampling methods are standard tools to perform posterior inference for mixture models. These have been broadly classified into two categories: marginal and conditional methods. While conditional samplers are more widely applicable…

The popularity of Adaptive MCMC has been fueled on the one hand by its success in applications, and on the other hand, by mathematically appealing and computationally straightforward optimisation criteria for the Metropolis algorithm…

In this paper, we present the Bayesian inference procedures for the parameters of the multivariate random effects model derived under the assumption of an elliptically contoured distribution when the Berger and Bernardo reference and the…

Uncertainty quantification for large-scale inverse problems remains a challenging task. For linear inverse problems with additive Gaussian noise and Gaussian priors, the posterior is Gaussian but sampling can be challenging, especially for…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Boson sampling devices are a prime candidate for exhibiting quantum supremacy, yet their application for solving problems of practical interest is less well understood. Here we show that Gaussian boson sampling (GBS) can be used for dense…

Sampling from matrix generalized inverse Gaussian (MGIG) distributions is required in Markov Chain Monte Carlo (MCMC) algorithms for a variety of statistical models. However, an efficient sampling scheme for the MGIG distributions has not…

High-dimensional and complex discrete distributions often exhibit multimodal behavior due to inherent discontinuities, posing significant challenges for sampling. Gradient-based discrete samplers, while effective, frequently become trapped…

We propose a generative model for the spatio-temporal distribution of high dimensional categorical observations. These are commonly produced by robots equipped with an imaging sensor such as a camera, paired with an image classifier,…

The Bayesian lasso is well-known as a Bayesian alternative for Lasso. Although the advantage of the Bayesian lasso is capable of full probabilistic uncertain quantification for parameters, the corresponding posterior distribution can be…

Variable selection in Gaussian processes (GPs) is typically undertaken by thresholding the inverse lengthscales of automatic relevance determination kernels, but in high-dimensional datasets this approach can be unreliable. A more…

We study general coordinate-wise MCMC schemes (such as Metropolis-within-Gibbs samplers), which are commonly used to fit Bayesian non-conjugate hierarchical models. We relate their convergence properties to the ones of the corresponding…