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We consider discrete nonparametric priors which induce Gibbs-type exchangeable random partitions and investigate their posterior behavior in detail. In particular, we deduce conditional distributions and the corresponding Bayesian…

Probability · Mathematics 2008-08-22 Antonio Lijoi , Igor Prünster , Stephen G. Walker

In this paper, we study the asymptotic posterior distribution of linear functionals of the density. In particular, we give general conditions to obtain a semiparametric version of the Bernstein-Von Mises theorem. We then apply this general…

Statistics Theory · Mathematics 2009-08-31 Vincent Rivoirard , Judith Rousseau

The prominent Bernstein -- von Mises (BvM) result claims that the posterior distribution after centering by the efficient estimator and standardizing by the square root of the total Fisher information is nearly standard normal. In…

Statistics Theory · Mathematics 2020-06-02 Vladimir Spokoiny , Maxim Panov

Prior specification for nonparametric Bayesian inference involves the difficult task of quantifying prior knowledge about a parameter of high, often infinite, dimension. Realistically, a statistician is unlikely to have informed opinions…

Methodology · Statistics 2012-05-01 David C. Kessler , Peter D. Hoff , David B. Dunson

Bayesian field theory denotes a nonparametric Bayesian approach for learning functions from observational data. Based on the principles of Bayesian statistics, a particular Bayesian field theory is defined by combining two models: a…

Data Analysis, Statistics and Probability · Physics 2007-05-23 J. C. Lemm

Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…

Methodology · Statistics 2023-03-22 Yifu Tang , Claudia Kirch , Jeong Eun Lee , Renate Meyer

A Bayesian nonparametric method for unimodal densities on the real line is provided by considering a class of species sampling mixture models containing random densities that are unimodal and not necessarily symmetric. This class of…

Statistics Theory · Mathematics 2007-06-13 Man-Wai Ho

State-of-the-art neural network-based methods for learning summary statistics have delivered promising results for simulation-based likelihood-free parameter inference. Existing approaches require density estimation as a post-processing…

By a mixture density is meant a density of the form $\pi_{\mu}(\cdot)=\int\pi_{\theta}(\cdot)\times\mu(d\theta)$, where $(\pi_{\theta})_{\theta\in\Theta}$ is a family of probability densities and $\mu$ is a probability measure on $\Theta$.…

Statistics Theory · Mathematics 2016-08-16 François Roueff , Tobias Rydén

In a Bayesian context, prior specification for inference on monotone densities is conceptually straightforward, but proving posterior convergence theorems is complicated by the fact that desirable prior concentration properties often are…

Statistics Theory · Mathematics 2020-07-28 Ryan Martin

The Whittle likelihood is widely used for Bayesian nonparametric estimation of the spectral density of stationary time series. However, the loss of efficiency for non-Gaussian time series can be substantial. On the other hand, parametric…

Methodology · Statistics 2017-01-19 Claudia Kirch , Matthew C. Edwards , Alexander Meier , Renate Meyer

We study nonparametric Bayesian models for reversible multi-dimensional diffusions with periodic drift. For continuous observation paths, reversibility is exploited to prove a general posterior contraction rate theorem for the drift…

Statistics Theory · Mathematics 2024-08-02 Matteo Giordano , Kolyan Ray

We discuss Bayesian nonparametric procedures for the regression analysis of compositional responses, that is, data supported on a multivariate simplex. The procedures are based on a modified class of multivariate Bernstein polynomials and…

Methodology · Statistics 2021-08-31 Claudia Wehrhahn , Andrés F. Barrientos , Alejandro Jara

Non-linear latent variable models have become increasingly popular in a variety of applications. However, there has been little study on theoretical properties of these models. In this article, we study rates of posterior contraction in…

Statistics Theory · Mathematics 2011-09-26 Debdeep Pati , Anirban Bhattacharya , David B. Dunson

The traditional kernel density estimator of an unknown density is by construction completely nonparametric, in the sense that it has no preferences and will work reasonably well for all shapes. The present paper develops a class of…

Methodology · Statistics 2026-05-05 Nils Lid Hjort , Ingrid Kristine Glad

Modeling structure in complex networks using Bayesian non-parametrics makes it possible to specify flexible model structures and infer the adequate model complexity from the observed data. This paper provides a gentle introduction to…

Machine Learning · Statistics 2013-12-23 Mikkel N. Schmidt , Morten Mørup

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…

Methodology · Statistics 2018-11-27 Alexander Meier , Claudia Kirch , Renate Meyer

We study the Bayesian density estimation of data living in the offset of an unknown submanifold of the Euclidean space. In this perspective, we introduce a new notion of anisotropic H\"older for the underlying density and obtain posterior…

Statistics Theory · Mathematics 2024-07-18 Clément Berenfeld , Paul Rosa , Judith Rousseau

Gaussian time-series models are often specified through their spectral density. Such models present several computational challenges, in particular because of the non-sparse nature of the covariance matrix. We derive a fast approximation of…

Computation · Statistics 2012-11-20 Nicolas Chopin , Judith Rousseau , Brunero Liseo

We study the rate of convergence of posterior distributions in density estimation problems for log-densities in periodic Sobolev classes characterized by a smoothness parameter p. The posterior expected density provides a nonparametric…

Statistics Theory · Mathematics 2009-09-29 Catia Scricciolo