Related papers: Relabelling in Bayesian mixture models by pivotal …
Many inference problems involve inferring the number $N$ of components in some region, along with their properties $\{\mathbf{x}_i\}_{i=1}^N$, from a dataset $\mathcal{D}$. A common statistical example is finite mixture modelling. In the…
A well known identifiability issue in factor analytic models is the invariance with respect to orthogonal transformations. This problem burdens the inference under a Bayesian setup, where Markov chain Monte Carlo (MCMC) methods are used to…
Bayesian hierarchical modeling is a popular approach to capturing unobserved heterogeneity across individual units. However, standard estimation methods such as Markov chain Monte Carlo (MCMC) can be impracticable for modeling outcomes from…
A new approach for Bayesian model averaging (BMA) and selection is proposed, based on the mixture model approach for hypothesis testing in Kaniav et al., 2014. Inheriting from the good properties of this approach, it extends BMA to cases…
This work addresses the problem of segmentation in time series data with respect to a statistical parameter of interest in Bayesian models. It is common to assume that the parameters are distinct within each segment. As such, many Bayesian…
This paper deals with Bayesian inference of a mixture of Gaussian distributions. A novel formulation of the mixture model is introduced, which includes the prior constraint that each Gaussian component is always assigned a minimal number of…
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…
Based on an idea in [4] we propose a new iterative multiplicative filtering algorithm for label assignment matrices which can be used for the supervised partitioning of data. Starting with a row-normalized matrix containing the averaged…
Analysis of a Bayesian mixture model for the Matrix Langevin distribution on the Stiefel manifold is presented. The model exploits a particular parametrization of the Matrix Langevin distribution, various aspects of which are elaborated on.…
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…
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…
In this chapter, we address the challenge of exploring the posterior distributions of Bayesian inverse problems with computationally intensive forward models. We consider various multivariate proposal distributions, and compare them with…
The Bayesian approach to machine learning amounts to computing posterior distributions of random variables from a probabilistic model of how the variables are related (that is, a prior distribution) and a set of observations of variables.…
This paper introduces methodology for performing Bayesian inference sequentially on a sequence of posteriors on spaces of different dimensions. We show how this may be achieved through the use of sequential Monte Carlo (SMC) samplers (Del…
Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable…
A new method for the computation of the posterior distribution of the number k of components in a finite mixture is presented. Two aspects of prior specification are also studied: an argument is made for the use of a Poisson(1) distribution…
This paper outlines a Bayesian approach to estimate finite mixtures of Tobit models. The method consists of an MCMC approach that combines Gibbs sampling with data augmentation and is simple to implement. I show through simulations that the…
In large-scale genomic applications vast numbers of molecular features are scanned in order to find a small number of candidates which are linked to a particular disease or phenotype. This is a variable selection problem in the "large p,…
Reversible jump Markov chain Monte Carlo (RJMCMC) extends ordinary MCMC methods for use in Bayesian multimodel inference. We show that RJMCMC can be implemented as Gibbs sampling with alternating updates of a model indicator and a…
Bayesian mixture models are widely used for clustering of high-dimensional data with appropriate uncertainty quantification. However, as the dimension of the observations increases, posterior inference often tends to favor too many or too…