Related papers: Wasserstein convergence in Bayesian deconvolution …
This paper studies convergence behavior of latent mixing measures that arise in finite and infinite mixture models, using transportation distances (i.e., Wasserstein metrics). The relationship between Wasserstein distances on the space of…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
We study posterior contraction rates for mixing measures in homoscedastic location-scale mixture models with infinitely many components. While posterior convergence at the level of densities is well understood, ensuring convergence of the…
We investigate the asymptotic behavior of parametric Bayes estimators under a broad class of loss functions that extend beyond the classical translation-invariant setting. To this end, we develop a unified theoretical framework for loss…
The Bayesian Synthetic Likelihood (BSL) method is a widely-used tool for likelihood-free Bayesian inference. This method assumes that some summary statistics are normally distributed, which can be incorrect in many applications. We propose…
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…
Given a sample from a discretely observed compound Poisson process, we consider non-parametric estimation of the density $f_0$ of its jump sizes, as well as of its intensity $\lambda_0.$ We take a Bayesian approach to the problem and…
Density deconvolution deals with the estimation of the probability density function $f$ of a random signal from $n\geq1$ data observed with independent and known additive random noise. This is a classical problem in statistics, for which…
Sampling from nonsmooth target probability distributions is essential in various applications, including the Bayesian Lasso. We propose a splitting-based sampling algorithm for the time-implicit discretization of the probability flow for…
Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications…
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…
The empirical Bayes $g$-modeling approach via the nonparametric maximum likelihood estimator (NPMLE) is widely used for large-scale estimation and inference in the normal means problem, yet theoretical guarantees for uncertainty…
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling according to an approximate prior $\mathcal{P}$, and establish…
We study the Riemannian Langevin Algorithm for the problem of sampling from a distribution with density $\nu$ with respect to the natural measure on a manifold with metric $g$. We assume that the target density satisfies a log-Sobolev…
This work proposes a Bayesian rule based on the mixture of a point mass function at zero and the logistic distribution to perform wavelet shrinkage in nonparametric regression models with stationary errors (with short or long-memory…
In this article we recover the distribution function (and possible density) of an arbitrary random variable that is subject to an additive measurement error. This problem is also known as deconvolution and has a long tradition in…
In this paper, a methodology is investigated for signal recovery in the presence of non-Gaussian noise. In contrast with regularized minimization approaches often adopted in the literature, in our algorithm the regularization parameter is…
Efficiently aggregating data from different sources is a challenging problem, particularly when samples from each source are distributed differently. These differences can be inherent to the inference task or present for other reasons:…
The asymptotic behaviour of empirical measures has plenty of studies. However, the research on conditional empirical measures is limited. Being the development of Wang \cite{eW1}, under the quadratic Wasserstein distance, we investigate the…
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…