Related papers: The semiparametric Bernstein-von Mises theorem
We present a criterion for the stochastic completeness of a submanifold in terms of its distance to a hypersurface in the ambient space. This relies in a suitable version of the Hessian comparison theorem. In the sequel we apply a…
In this paper, we obtain quantitative, non-asymptotic, and data-dependent \textit{Bernstein-von Mises type} bounds on the normal approximation of the posterior distribution in exponential family models with arbitrary centring and scaling.…
We study large sample properties of Bayesian analysis of the proportional hazard model with neutral to the right process priors on the baseline hazard function. We show that the posterior distribution of the baseline cumulative hazard…
Asymptotic lower bounds for estimation play a fundamental role in assessing the quality of statistical procedures. In this paper we propose a framework for obtaining semi-parametric efficiency bounds for sparse high-dimensional models,…
We consider heteroscedastic nonparametric regression models, when both the mean function and variance function are unknown and to be estimated with nonparametric approaches. We derive convergence rates of posterior distributions for this…
This paper studies least-square regression penalized with partly smooth convex regularizers. This class of functions is very large and versatile allowing to promote solutions conforming to some notion of low-complexity. Indeed, they force…
We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the…
The nonparametric regression model with normal errors has been extensively studied, both from the frequentist and Bayesian viewpoint. A central result in Bayesian nonparametrics is that under assumptions on the prior, the data-generating…
We provide a general theoretical framework to derive Bernstein-von Mises theorems for matrix functionals. The conditions on functionals and priors are explicit and easy to check. Results are obtained for various functionals including…
We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…
The proposed approach extends the confidence posterior distribution to the semi-parametric empirical Bayes setting. Whereas the Bayesian posterior is defined in terms of a prior distribution conditional on the observed data, the confidence…
The Pitman-Yor process is a random probability distribution, that can be used as a prior distribution in a nonparametric Bayesian analysis. The process is of species sampling type and generates discrete distributions, which yield of the…
Bayesian parameter inference depends on a choice of prior probability distribution for the parameters in question. The prior which makes the posterior distribution maximally sensitive to data is called the Jeffreys prior, and it is…
This paper deals with the parametric inference for integrated signals embedded in an additive Gaussian noise and observed at deterministic discrete instants which are not necessarily equidistant. The unknown parameter is multidimensional…
As a competitive alternative to least squares regression, quantile regression is popular in analyzing heterogenous data. For quantile regression model specified for one single quantile level $\tau$, major difficulties of semiparametric…
This paper is devoted to the problem of determining the concentration bounds that are achievable in non-parametric regression. We consider the setting where features are supported on a bounded subset of $\mathbb{R}^d$, the regression…
In this paper, we establish minimax optimal rates of convergence for prediction in a semi-functional linear model that consists of a functional component and a less smooth nonparametric component. Our results reveal that the smoother…
Fitted probabilities from widely used Bayesian multinomial probit models can depend strongly on the choice of a base category, which is used to uniquely identify the parameters of the model. This paper proposes a novel identification…
While nonlinear stochastic partial differential equations arise naturally in spatiotemporal modeling, inference for such systems often faces two major challenges: sparse noisy data and ill-posedness of the inverse problem of parameter…
Parametric stochastic simulators are ubiquitous in science, often featuring high-dimensional input parameters and/or an intractable likelihood. Performing Bayesian parameter inference in this context can be challenging. We present a neural…