Related papers: A note on non-parametric Bayesian estimation for P…
We study posterior contraction behaviors for parameters of interest in the context of Bayesian mixture modeling, where the number of mixing components is unknown while the model itself may or may not be correctly specified. Two…
We present an extension of local sensitivity analysis, also referred to as the perturbation approach for uncertainty quantification, to Bayesian inverse problems. More precisely, we show how moments of random variables with respect to the…
Spatial Gaussian process regression models typically contain finite dimensional covariance parameters that need to be estimated from the data. We study the Bayesian estimation of covariance parameters including the nugget parameter in a…
In this paper, we extend the notion of Cauchy-Schwarz divergence to point processes and establish that the Cauchy-Schwarz divergence between the probability densities of two Poisson point processes is half the squared…
In a general class of Bayesian nonparametric models, we prove that the posterior distribution can be asymptotically approximated by a Gaussian process. Our results apply to nonparametric exponential family that contains both Gaussian and…
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…
The paper develops new methods of non-parametric estimation a compound Poisson distribution. Such a problem arise, in particular, in the inference of a Levy process recorded at equidistant time intervals. Our key estimator is based on…
We consider the issue of reporting the result of search experiment in the most unbiased and efficient way, i.e. in a way which allows an easy interpretation and combination of results and which do not depend on whether the experimenters…
Point processes in time have a wide range of applications that include the claims arrival process in insurance or the analysis of queues in operations research. Due to advances in technology, such samples of point processes are increasingly…
We observe $n$ inhomogeneous Poisson processes with covariates and aim at estimating their intensities. We assume that the intensity of each Poisson process is of the form $s (\cdot, x)$ where $x$ is the covariate and where $s$ is an…
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…
We consider the problem of estimation in Hidden Markov models with finite state space and nonparametric emission distributions. Efficient estimators for the transition matrix are exhibited, and a semiparametric Bernstein-von Mises result is…
In this paper, we develop an efficient nonparametric Bayesian estimation of the kernel function of Hawkes processes. The non-parametric Bayesian approach is important because it provides flexible Hawkes kernels and quantifies their…
Bayesian methods are actively used for parameter identification and uncertainty quantification when solving nonlinear inverse problems with random noise. However, there are only few theoretical results justifying the Bayesian approach.…
In this paper, we consider the so-called Shape Invariant Model which stands for the estimation of a function f0 submitted to a random translation of law g0 in a white noise model. We are interested in such a model when the law of the…
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…
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,…
This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…
In nonparametric regression problems involving multiple predictors, there is typically interest in estimating an anisotropic multivariate regression surface in the important predictors while discarding the unimportant ones. Our focus is on…
Feature selection procedures for spatial point processes parametric intensity estimation have been recently developed since more and more applications involve a large number of covariates. In this paper, we investigate the setting where the…