Related papers: A Gibbs Sampler for Multivariate Linear Regression

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…

The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…

Gibbs sampling is a widely popular Markov chain Monte Carlo algorithm that can be used to analyze intractable posterior distributions associated with Bayesian hierarchical models. There are two standard versions of the Gibbs sampler: The…

Gibbs sampling is a common procedure used to fit finite mixture models. However, it is known to be slow to converge when exploring correlated regions of a parameter space and so blocking correlated parameters is sometimes implemented in…

An energy efficient use of large scale sensor networks necessitates activating a subset of possible sensors for estimation at a fusion center. The problem is inherently combinatorial; to this end, a set of iterative, randomized algorithms…

We consider the question of Markov chain Monte Carlo sampling from a general stick-breaking Dirichlet process mixture model, with concentration parameter alpha. This paper introduces a Gibbs sampling algorithm that combines the slice…

Pre-trained diffusion models have been successfully used as priors in a variety of linear inverse problems, where the goal is to reconstruct a signal from noisy linear measurements. However, existing approaches require knowledge of the…

The use of Gaussian processes (GPs) is supported by efficient sampling algorithms, a rich methodological literature, and strong theoretical grounding. However, due to their prohibitive computation and storage demands, the use of exact GPs…

Within Bayesian nonparametrics, dependent Dirichlet process mixture models provide a highly flexible approach for conducting inference about the conditional density function. However, several formulations of this class make either rather…

Over the last decade, a large variety of clustering algorithms have been developed to detect coregulatory relationships among genes from microarray gene expression data. Model based clustering approaches have emerged as statistically well…

In this article, we present some specific aspects of symmetric Gamma process mixtures for use in regression models. We propose a new Gibbs sampler for simulating the posterior and we establish adaptive posterior rates of convergence related…

We consider the problem of sampling from a product-of-experts-type model that encompasses many standard prior and posterior distributions commonly found in Bayesian imaging. We show that this model can be easily lifted into a novel latent…

Multivariate density estimation is a popular technique in statistics with wide applications including regression models allowing for heteroskedasticity in conditional variances. The estimation problems become more challenging when…

Bayesian feature allocation models are a popular tool for modelling data with a combinatorial latent structure. Exact inference in these models is generally intractable and so practitioners typically apply Markov Chain Monte Carlo (MCMC)…

For many survey-based spatial modelling problems, responses are observed as spatially aggregated over survey regions due to limited resources. Covariates, from weather models and satellite imageries, can be observed at many different…

Gibbs sampling, as a model learning method, is known to produce the most accurate results available in a variety of domains, and is a de facto standard in these domains. Yet, it is also well known that Gibbs random walks usually have…

Non-Gaussian mixture models are gaining increasing attention for mixture model-based clustering particularly when dealing with data that exhibit features such as skewness and heavy tails. Here, such a mixture distribution is presented,…

The K-Mean and EM algorithms are popular in clustering and mixture modeling, due to their simplicity and ease of implementation. However, they have several significant limitations. Both coverage to a local optimum of their respective…

We present a Dirichlet process mixture model over discrete incomplete rankings and study two Gibbs sampling inference techniques for estimating posterior clusterings. The first approach uses a slice sampling subcomponent for estimating…

We propose a new method for clustering multivariate time-series data based on Dynamic Linear Models. Whereas usual time-series clustering methods obtain static membership parameters, our proposal allows each time-series to dynamically…