Related papers: Exact Bayesian Analysis of Mixtures
As for other latent-variable problems, exact Bayesian analysis is typically not practicable for mixture problems and approximate methods have been developed. Variational Bayes tends to produce approximate posterior distributions for…
We propose a new method for conducting Bayesian prediction that delivers accurate predictions without correctly specifying the unknown true data generating process. A prior is defined over a class of plausible predictive models. After…
In this paper, we study the accuracy of values aggregated over classes predicted by a classification algorithm. The problem is that the resulting aggregates (e.g., sums of a variable) are known to be biased. The bias can be large even for…
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…
A natural Bayesian approach for mixture models with an unknown number of components is to take the usual finite mixture model with Dirichlet weights, and put a prior on the number of components---that is, to use a mixture of finite mixtures…
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…
We focus on Bayesian inverse problems with Gaussian likelihood, linear forward model, and priors that can be formulated as a Gaussian mixture. Such a mixture is expressed as an integral of Gaussian density functions weighted by a mixing…
Making inferences from data streams is a pervasive problem in many modern data analysis applications. But it requires to address the problem of continuous model updating and adapt to changes or drifts in the underlying data generating…
Bayesian models quantify uncertainty and facilitate optimal decision-making in downstream applications. For most models, however, practitioners are forced to use approximate inference techniques that lead to sub-optimal decisions due to…
In many applications, a finite mixture is a natural model, but it can be difficult to choose an appropriate number of components. To circumvent this choice, investigators are increasingly turning to Dirichlet process mixtures (DPMs), and…
Many statistical problems involve data from thousands of parallel cases. Each case has some associated effect size, and most cases will have no effect. It is often important to estimate the effect size and the local or tail-area false…
Exponential families are the workhorses of parametric modelling theory. One reason for their popularity is their associated inference theory, which is very clean, both from a theoretical and a computational point of view. One way in which…
We consider estimating the parameters of a Gaussian mixture density with a given number of components best representing a given set of weighted samples. We adopt a density interpretation of the samples by viewing them as a discrete Dirac…
Nonparametric Bayesian approaches based on Gaussian processes have recently become popular in the empirical learning community. They encompass many classical methods of statistics, like Radial Basis Functions or various splines, and are…
We discuss Bayesian inference for a known-mean Gaussian model with a compound symmetric variance-covariance matrix. Since the space of such matrices is a linear subspace of that of positive definite matrices, we utilize the methods of…
Mixture models are widely used in modeling heterogeneous data populations. A standard approach of mixture modeling assumes that the mixture component takes a parametric kernel form. In many applications, making parametric assumptions on the…
This study explores the classification error of Mixture Discriminant Analysis (MDA) in scenarios where the number of mixture components exceeds those present in the actual data distribution, a condition known as overspecification. We use a…
For two vast families of mixture distributions and a given prior, we provide unified representations of posterior and predictive distributions. Model applications presented include bivariate mixtures of Gamma distributions labelled as…
Finite mixtures of regression models offer a flexible framework for investigating heterogeneity in data with functional dependencies. These models can be conveniently used for unsupervised learning on data with clear regression…
Informally, "Information Inconsistency" is the property that has been observed in many Bayesian hypothesis testing and model selection procedures whereby the Bayesian conclusion does not become definitive when the data seems to become…