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We study Bayesian estimation of mixture models and argue in favor of fitting the marginal posterior distribution over component assignments directly, rather than Gibbs sampling from the joint posterior on components and parameters as is…

This paper presents a new Markov chain Monte Carlo method to sample from the posterior distribution of conjugate mixture models. This algorithm relies on a flexible split-merge procedure built using the particle Gibbs sampler. Contrary to…

Monte Carlo methods are essential tools for Bayesian inference. Gibbs sampling is a well-known Markov chain Monte Carlo (MCMC) algorithm, extensively used in signal processing, machine learning, and statistics, employed to draw samples from…

Solving ill-posed inverse problems by Bayesian inference has recently attracted considerable attention. Compared to deterministic approaches, the probabilistic representation of the solution by the posterior distribution can be exploited to…

Bayesian regression remains a simple but effective tool based on Bayesian inference techniques. For large-scale applications, with complicated posterior distributions, Markov Chain Monte Carlo methods are applied. To improve the well-known…

In this paper we consider Bayesian estimation for the parameters of inverse Gaussian distribution. Our emphasis is on Markov Chain Monte Carlo methods. We provide complete implementation of the Gibbs sampler algorithm. Assuming an…

Denoising diffusion models have driven significant progress in the field of Bayesian inverse problems. Recent approaches use pre-trained diffusion models as priors to solve a wide range of such problems, only leveraging inference-time…

This paper derives two new optimization-driven Monte Carlo algorithms inspired from variable splitting and data augmentation. In particular, the formulation of one of the proposed approaches is closely related to the alternating direction…

Bayesian hierarchical Poisson models are an essential tool for analyzing count data. However, designing efficient algorithms to sample from the posterior distribution of the target parameters remains a challenging task for this class of…

Approximate Bayesian computation methods are useful for generative models with intractable likelihoods. These methods are however sensitive to the dimension of the parameter space, requiring exponentially increasing resources as this…

In general, the statistical simulation approaches are referred to as the Monte Carlo methods as a whole. The broad class of the Monte Carlo methods involves the Markov chain Monte Carlo (MCMC) techniques that attract the attention of…

A new technique is explored for the Monte Carlo sampling of complex-valued distributions. The method is based on a heat bath approach where the conditional probability is replaced by a positive representation of it on the complex plane.…

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…

This survey covers state-of-the-art Bayesian techniques for the estimation of mixtures. It complements the earlier Marin, Mengersen and Robert (2005) by studying new types of distributions, the multinomial, latent class and t distributions.…

Diffusion models enable the synthesis of highly accurate samples from complex distributions and have become foundational in generative modeling. Recently, they have demonstrated significant potential for solving Bayesian inverse problems by…

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 particle Gibbs sampler is a Markov chain Monte Carlo (MCMC) algorithm to sample from the full posterior distribution of a state-space model. It does so by executing Gibbs sampling steps on an extended target distribution defined on the…

Finite mixture models are frequently used to uncover latent structures in high-dimensional datasets (e.g.\ identifying clusters of patients in electronic health records). The inference of such structures can be performed in a Bayesian…

We study the convergence properties of the Gibbs Sampler in the context of posterior distributions arising from Bayesian analysis of conditionally Gaussian hierarchical models. We develop a multigrid approach to derive analytic expressions…

In this paper, we study Bayesian approach for solving large scale linear inverse problems arising in various scientific and engineering fields. We propose a fused $L_{1/2}$ prior with edge-preserving and sparsity-promoting properties and…