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We consider a non-parametric Bayesian model for conditional densities. The model is a finite mixture of normal distributions with covariate dependent multinomial logit mixing probabilities. A prior for the number of mixture components is…

Statistics Theory · Mathematics 2016-01-21 Andriy Norets , Debdeep Pati

Consider a nonparametric regression model with one-sided errors and regression function in a general H\"older class. We estimate the regression function via minimization of the local integral of a polynomial approximation. We show uniform…

Methodology · Statistics 2016-10-12 Holger Drees , Natalie Neumeyer , Leonie Selk

Motivated by the need to analyze large, decentralized datasets, distributed Bayesian inference has become a critical research area across multiple fields, including statistics, electrical engineering, and economics. This paper establishes…

Statistics Theory · Mathematics 2025-07-08 Bohan Wu , César A. Uribe

Consider binary observations whose response probability is an unknown smooth function of a set of covariates. Suppose that a prior on the response probability function is induced by a Gaussian process mapped to the unit interval through a…

Statistics Theory · Mathematics 2007-06-13 Subhashis Ghosal , Anindya Roy

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…

Methodology · Statistics 2022-06-01 Mario Beraha , Jim E. Griffin

This paper develops goodness of fit statistics that can be used to formally assess Markov random field models for spatial data, when the model distributions are discrete or continuous and potentially parametric. Test statistics are formed…

Statistics Theory · Mathematics 2012-05-29 Mark S. Kaiser , Soumendra N. Lahiri , Daniel J. Nordman

This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on a Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an…

Applications · Statistics 2015-11-02 Isabell M. Franck , P. S. Koutsourelakis

We study full Bayesian procedures for high-dimensional linear regression under sparsity constraints. The prior is a mixture of point masses at zero and continuous distributions. Under compatibility conditions on the design matrix, the…

Statistics Theory · Mathematics 2015-10-15 Ismaël Castillo , Johannes Schmidt-Hieber , Aad van der Vaart

We derive rates of contraction of posterior distributions on nonparametric models resulting from sieve priors. The aim of the paper is to provide general conditions to get posterior rates when the parameter space has a general structure,…

Statistics Theory · Mathematics 2016-05-03 Julyan Arbel , Ghislaine Gayraud , Judith Rousseau

We study nonparametric Bayesian statistical inference for the parameters governing a pure jump process of the form $$Y_t = \sum_{k=1}^{N(t)} Z_k,~~~ t \ge 0,$$ where $N(t)$ is a standard Poisson process of intensity $\lambda$, and $Z_k$ are…

Statistics Theory · Mathematics 2019-10-02 Richard Nickl , Jakob Söhl

It is well-known that the posterior density of linear inverse problems with Gaussian prior and Gaussian likelihood is also Gaussian, hence completely described by its covariance and expectation. Sampling from a Gaussian posterior may be…

Numerical Analysis · Mathematics 2025-02-11 Daniela Calvetti , Erkki Somersalo

Joint models for longitudinal and time-to-event data are widely used in many disciplines. Nonetheless, existing model comparison criteria do not indicate whether a model adequately fits the data or which components may be misspecified. We…

Methodology · Statistics 2026-01-27 Dimitris Rizopoulos , Jeremy M. G. Taylor , Isabella Kardys

In this paper, we consider the inverse problem of determining some coefficients within a coupled nonlinear parabolic system, through boundary observation of its non-negative solutions. In the physical setup, the non-negative solutions…

Analysis of PDEs · Mathematics 2024-04-23 Hongyu Liu , Catharine W. K. Lo

We present a new approach to semiparametric inference using corrected posterior distributions. The method allows us to leverage the adaptivity, regularization and predictive power of nonparametric Bayesian procedures to estimate…

Methodology · Statistics 2023-06-21 Andrew Yiu , Edwin Fong , Chris Holmes , Judith Rousseau

Testing hypotheses of goodness-of-fit about mixture distributions on the basis of independent but not necessarily identically distributed random vectors is considered. The hypotheses are given by a specific distribution or by a family of…

Statistics Theory · Mathematics 2016-04-21 Daniel Gaigall

The process comparing the empirical cumulative distribution function of the sample with a parametric estimate of the cumulative distribution function is known as the empirical process with estimated parameters and has been extensively…

Methodology · Statistics 2012-10-08 Ivan Kojadinovic , Jun Yan

In the setting of nonparametric multivariate regression with unknown error variance, we study asymptotic properties of a Bayesian method for estimating a regression function f and its mixed partial derivatives. We use a random series of…

Statistics Theory · Mathematics 2016-04-13 William Weimin Yoo , Subhashis Ghosal

We theoretically justify the recent empirical finding of [Teh et al., 2025] that a transformer pretrained on synthetically generated data achieves strong performance on empirical Bayes (EB) problems. We take an indirect approach to this…

Machine Learning · Statistics 2026-02-18 Nick Cannella , Anzo Teh , Yanjun Han , Yury Polyanskiy

The problem of making practical, useful goodness of fit tests in the Bayesian paradigm is largely open. We introduce a class of special cases (testing for uniformity: have the cards been shuffled enough; does my random generator work) and a…

Methodology · Statistics 2018-04-11 Persi Diaconis , Guanyang Wang

Derivatives are a key nonparametric functional in wide-ranging applications where the rate of change of an unknown function is of interest. In the Bayesian paradigm, Gaussian processes (GPs) are routinely used as a flexible prior for…

Statistics Theory · Mathematics 2025-12-30 Zejian Liu , Meng Li