280 citations · 707 across the 23 of their papers we have counts for
23 papers · 1 filter
Private Rate-Double-Robust Inference
Máté Kormos, Aad van der Vaart
We reconcile privacy protection and rate-double-robust inference. The privacy of individuals is protected by a local privacy mechanism: injecting noise into their sensitive data, r…
Adaptation using spatially distributed Gaussian Processes
Botond Szabo, Amine Hadji, Aad van der Vaart
We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined…
Optimal testing using combined test statistics across independent studies
Botond Szabó, Aad van der Vaart, Lasse Vuursteen +1
Combining test statistics from independent trials or experiments is a popular method of meta-analysis. However, there is very limited theoretical understanding of the power of the…
Adaptive and Efficient Isotonic Estimation in Wicksell's Problem
Francesco Gili, Geurt Jongbloed, Aad van der Vaart
We consider nonparametric estimation in Wicksell's problem which has relevant applications in astronomy for estimating the distribution of the positions of the stars in a galaxy gi…
Semi-parametric Bernstein-von Mises in Linear Inverse Problems
Adel Magra, Aad van der Vaart, Harry van Zanten
We consider a Bayesian approach for the recovery of scalar parameters arising in inverse problems. We consider a general signal-in white noise model where we have access to two ind…
Misspecified Bernstein-Von Mises theorem for hierarchical models
Geerten Koers, Botond Szabó, Aad van der Vaart
We derive a Bernstein von-Mises theorem in the context of misspecified, non-i.i.d., hierarchical models parametrized by a finite-dimensional parameter of interest. We apply our res…
Bayesian sensitivity analysis for a missing data model
Bart Eggen, Stéphanie L. van der Pas, Aad W. van der Vaart
In causal inference, sensitivity analysis is important to assess the robustness of study conclusions to key assumptions. We perform sensitivity analysis of the assumption that miss…
Asymptotics of Caliper Matching Estimators for Average Treatment Effects
Máté Kormos, Stéphanie van der Pas, Aad van der Vaart
Caliper matching is used to estimate causal effects of a binary treatment from observational data by comparing matched treated and control units. Units are matched when their prope…
Empirical and Full Bayes estimation of the type of a Pitman-Yor process
S. E. M. P. Franssen, A. W. van der Vaart
The Pitman-Yor process is a random discrete probability distribution of which the atoms can be used to model the relative abundance of species. The process is indexed by a type par…
Statistical Inference in Parametric Preferential Attachment Trees
Fengnan Gao, Aad van der Vaart
The preferential attachment (PA) model is a popular way of modeling dynamic social networks, such as collaboration networks. Assuming that the PA function takes a parametric form,…
The Bernstein-von Mises theorem for the Pitman-Yor process of nonnegative type
S. E. M. P. Franssen, A. W. van der Vaart
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…
On the Bernstein-von Mises theorem for the Dirichlet process
Kolyan Ray, Aad van der Vaart
We establish that Laplace transforms of the posterior Dirichlet process converge to those of the limiting Brownian bridge process in a neighbourhood about zero, uniformly over Gliv…
Bayesian Community Detection
Stéphanie van der Pas, Aad van der Vaart
We introduce a Bayesian estimator of the underlying class structure in the stochastic block model, when the number of classes is known. The estimator is the posterior mode correspo…
Uncertainty quantification for the horseshoe
Stéphanie van der Pas, Botond Szabó, Aad van der Vaart
We investigate the credible sets and marginal credible intervals resulting from the horseshoe prior in the sparse multivariate normal means model. We do so in an adaptive setting w…
On the Asymptotic Normality of Estimating the Affine Preferential Attachment Network Models with Random Initial Degrees
Fengnan Gao, Aad van der Vaart
We consider the estimation of the affine parameter (and power-law exponent) in the preferential attachment model with random initial degrees. We derive the likelihood, and show tha…
Posterior contraction rates for deconvolution of Dirichlet-Laplace mixtures
Fengnan Gao, Aad van der Vaart
We study nonparametric Bayesian inference with location mixtures of the Laplace density and a Dirichlet process prior on the mixing distribution. We derive a contraction rate of th…
A General Framework for Bayes Structured Linear Models
Chao Gao, Aad W. van der Vaart, Harrison H. Zhou
High dimensional statistics deals with the challenge of extracting structured information from complex model settings. Compared with the growing number of frequentist methodologies…
The Horseshoe Estimator: Posterior Concentration around Nearly Black Vectors
S. L. van der Pas, B. J. K. Kleijn, A. W. van der Vaart
We consider the horseshoe estimator due to Carvalho, Polson and Scott (2010) for the multivariate normal mean model in the situation that the mean vector is sparse in the nearly bl…
Bayesian linear regression with sparse priors
Ismaël Castillo, Johannes Schmidt-Hieber, Aad van der Vaart
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. Un…
Honest Bayesian confidence sets for the L2-norm
Botond Szabo, Aad van der Vaart, Harry van Zanten
We investigate the problem of constructing Bayesian credible sets that are honest and adaptive for the L2-loss over a scale of Sobolev classes with regularity ranging between [D; 2…
Bayes procedures for adaptive inference in inverse problems for the white noise model
B. T. Knapik, B. T. Szabó, A. W. van der Vaart +1
We study empirical and hierarchical Bayes approaches to the problem of estimating an infinite-dimensional parameter in mildly ill-posed inverse problems. We consider a class of pri…
Bayesian recovery of the initial condition for the heat equation
B. T. Knapik, A. W. van der Vaart, J. H. van Zanten
We study a Bayesian approach to recovering the initial condition for the heat equation from noisy observations of the solution at a later time. We consider a class of prior distrib…
Bayesian inverse problems with Gaussian priors
B. T. Knapik, A. W. van der Vaart, J. H. van Zanten
The posterior distribution in a nonparametric inverse problem is shown to contract to the true parameter at a rate that depends on the smoothness of the parameter, and the smoothne…