Related papers: Adaptive density estimation based on a mixture of …
We develop constrained Bayesian estimation methods for small area problems: those requiring smoothness with respect to similarity across areas, such as geographic proximity or clustering by covariates; and benchmarking constraints,…
For extreme value estimation we propose to use a model with a Dirichlet process mixture of gamma densities in the center and generalized Pareto densities for the tails. Due to the randomness in the center and a heavy tailed density in the…
Mixture models are regularly used in density estimation applications, but the problem of estimating the mixing distribution remains a challenge. Nonparametric maximum likelihood produce estimates of the mixing distribution that are…
Shape restriction, like monotonicity or convexity, imposed on a function of interest, such as a regression or density function, allows for its estimation without smoothness assumptions. The concept of $k$-monotonicity encompasses a family…
Construction methods for prior densities are investigated from a predictive viewpoint. Predictive densities for future observables are constructed by using observed data. The simultaneous distribution of future observables and observed data…
Bayesian methods are a popular choice for statistical inference in small-data regimes due to the regularization effect induced by the prior. In the context of density estimation, the standard nonparametric Bayesian approach is to target the…
Gaussian distributions are widely used in Bayesian variational inference to approximate intractable posterior densities, but the ability to accommodate skewness can improve approximation accuracy significantly, when data or prior…
We consider density estimators based on the nearest neighbors method applied to discrete point distibutions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is…
While mixtures of Gaussian distributions have been studied for more than a century (Pearson, 1894), the construction of a reference Bayesian analysis of those models still remains unsolved, with a general prohibition of the usage of…
When modeling a probability distribution with a Bayesian network, we are faced with the problem of how to handle continuous variables. Most previous work has either solved the problem by discretizing, or assumed that the data are generated…
Bayesian predictive inference provides a coherent description of entire predictive uncertainty through predictive distributions. We examine several widely used sparsity priors from the predictive (as opposed to estimation) inference…
We study the well-known problem of estimating a sparse $n$-dimensional unknown mean vector $\theta = (\theta_1, ..., \theta_n)$ with entries corrupted by Gaussian white noise. In the Bayesian framework, continuous shrinkage priors which can…
Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering…
Non-parametric estimation of a multivariate density estimation is tackled via a method which combines traditional local smoothing with a form of global smoothing but without imposing a rigid structure. Simulation work delivers encouraging…
This paper builds on recent research that focuses on regression modeling of continuous bounded data, such as proportions measured on a continuous scale. Specifically, it deals with beta regression models with mixed effects from a Bayesian…
While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittle's Likelihood, involving the second order…
We revisit the problem of model-based object recognition for intensity images and attempt to address some of the shortcomings of existing Bayesian methods, such as unsuitable priors and the treatment of residuals with a non-robust error…
Finite mixture models provide a flexible framework for approximating and estimating multivariate probability densities. We study mixtures formed from translated and rescaled copies of a fixed density kernel and obtain explicit results for…
Finite mixture models are a useful statistical model class for clustering and density approximation. In the Bayesian framework finite mixture models require the specification of suitable priors in addition to the data model. These priors…
The authors consider the problem of estimating the density $g$ of independent and identically distributed variables $X\_i$, from a sample $Z\_1, ..., Z\_n$ where $Z\_i=X\_i+\sigma\epsilon\_i$, $i=1, ..., n$, $\epsilon$ is a noise…