Related papers: Adaptive Bayesian Estimation of Mixed Discrete-Con…

We consider the problem of estimating the mixing density $f$ from $n$ i.i.d. observations distributed according to a mixture density with unknown mixing distribution. In contrast with finite mixtures models, here the distribution of the…

Discrete mixture models are one of the most successful approaches for density estimation. Under a Bayesian nonparametric framework, Dirichlet process location-scale mixture of Gaussian kernels is the golden standard, both having nice…

We study the rate of Bayesian consistency for hierarchical priors consisting of prior weights on a model index set and a prior on a density model for each choice of model index. Ghosal, Lember and Van der Vaart [2] have obtained general…

In the context of regressing a response $Y$ on a predictor $X$, we consider estimating the local modes of the distribution of $Y$ given $X=x$ when $X$ is prone to measurement error. We propose two nonparametric estimation methods, with one…

We propose a methodology for modeling and comparing probability distributions within a Bayesian nonparametric framework. Building on dependent normalized random measures, we consider a prior distribution for a collection of discrete random…

Linear mixed-effects models are a central analytical tool for modeling hierarchical and longitudinal data, as they allow simultaneous representation of fixed and random sources of variation. In practice, inference for such models is most…

In the sparse normal means model, coverage of adaptive Bayesian posterior credible sets associated to spike and slab prior distributions is considered. The key sparsity hyperparameter is calibrated via marginal maximum likelihood empirical…

Predicting extreme events is important in many applications in risk analysis. The extreme-value theory suggests modelling extremes by max-stable distributions. The Bayesian approach provides a natural framework for statistical prediction.…

This paper proposes a new Bayesian strategy for the smooth estimation of altimetric parameters. The altimetric signal is assumed to be corrupted by a thermal and speckle noise distributed according to an independent and non identically…

Compositional data, representing proportions constrained to the simplex, arise in diverse fields such as geosciences, ecology, genomics, and microbiome research. Existing nonparametric density estimation methods often rely on…

Determining the strength of non-linear statistical dependencies between two variables is a crucial matter in many research fields. The established measure for quantifying such relations is the mutual information. However, estimating mutual…

Hierarchical parametric models consisting of observable and latent variables are widely used for unsupervised learning tasks. For example, a mixture model is a representative hierarchical model for clustering. From the statistical point of…

We consider nonparametric Bayesian estimation of a probability density $p$ based on a random sample of size $n$ from this density using a hierarchical prior. The prior consists, for instance, of prior weights on the regularity of the…

Seemingly unrelated linear regression models are introduced in which the distribution of the errors is a finite mixture of Gaussian components. Identifiability conditions are provided. The score vector and the Hessian matrix are derived.…

Suppose that a compound Poisson process is observed discretely in time and assume that its jump distribution is supported on the set of natural numbers. In this paper we propose a non-parametric Bayesian approach to estimate the intensity…

The problem of nonparametric estimation of the conditional density of a response, given a vector of explanatory variables, is classical and of prominent importance in many prediction problems since the conditional density provides a more…

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 consider a binary unsupervised classification problem where each observation is associated with an unobserved label that we want to retrieve. More precisely, we assume that there are two groups of observation: normal and abnormal. The…

We study the sparse high-dimensional Gaussian mixture model when the number of clusters is allowed to grow with the sample size. A minimax lower bound for parameter estimation is established, and we show that a constrained maximum…

Mixture-of-experts models provide a flexible framework for learning complex probabilistic input-output relationships by combining multiple expert models through an input-dependent gating mechanism. These models have become increasingly…