Related papers: Multilevel linear models, Gibbs samplers and multi…
This work presents a tractable approach to multi-object posterior computation under a generic measurement likelihood function. While filtering is a popular solution, valuable historical information is discarded. Posterior inference, which…
Gibbs sampling is one of the most popular Markov chain Monte Carlo algorithms because of its simplicity, scalability, and wide applicability within many fields of statistics, science, and engineering. In the labeled random finite sets…
Generative diffusions are a powerful class of Monte Carlo samplers that leverage bridging Markov processes to approximate complex, high-dimensional distributions, such as those found in image processing and language models. Despite their…
We introduce non-stationary Mat\'ern field priors with stochastic partial differential equations, and construct correlation length-scaling with hyperpriors. We model both the hyperprior and the Mat\'ern prior as continuous-parameter random…
A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…
Bayesian nonparametric mixtures and random partition models are powerful tools for probabilistic clustering. However, standard independent mixture models can be restrictive in some applications such as inference on cell lineage due to the…
One of the fundamental tasks of science is to find explainable relationships between observed phenomena. One approach to this task that has received attention in recent years is based on probabilistic graphical modelling with sparsity…
We consider the problem of learning a conditional Gaussian graphical model in the presence of latent variables. Building on recent advances in this field, we suggest a method that decomposes the parameters of a conditional Markov random…
It is common practice to use Laplace approximations to compute marginal likelihoods in Bayesian versions of generalised linear models (GLM). Marginal likelihoods combined with model priors are then used in different search algorithms to…
We introduce a class of scalable Bayesian hierarchical models for the analysis of massive geostatistical datasets. The underlying idea combines ideas on high-dimensional geostatistics by partitioning the spatial domain and modeling the…
The MC$^3$ (Madigan and York, 1995) and Gibbs (George and McCulloch, 1997) samplers are the most widely implemented algorithms for Bayesian Model Averaging (BMA) in linear regression models. These samplers draw a variable at random in each…
Cognitive diagnosis models (CDMs) are useful statistical tools to provide rich information relevant for intervention and learning. As a popular approach to estimate and make inference of CDMs, the Markov chain Monte Carlo (MCMC) algorithm…
In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex…
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…
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…
Analyzing and understanding the structure of complex relational data is important in many applications including analysis of the connectivity in the human brain. Such networks can have prominent patterns on different scales, calling for a…
We consider various versions of adaptive Gibbs and Metropolis-within-Gibbs samplers, which update their selection probabilities (and perhaps also their proposal distributions) on the fly during a run by learning as they go in an attempt to…
In Bayesian inverse problems, the posterior distribution is used to quantify uncertainty about the reconstructed solution. In practice, Markov chain Monte Carlo algorithms often are used to draw samples from the posterior distribution.…
A novel computationally efficient Markov chain Monte Carlo (MCMC) scheme for latent Gaussian models (LGMs) is proposed in this paper. The sampling scheme is a two block Gibbs sampling scheme designed to exploit the model structure of LGMs.…
A new algorithm is developed to tackle the issue of sampling non-Gaussian model parameter posterior probability distributions that arise from solutions to Bayesian inverse problems. The algorithm aims to mitigate some of the hurdles faced…