Richard Nickl’s Publications Page

Books

[A] Mathematical foundations of infinite-dimensional statistical models. (with E. Giné). xiv+690 pp., Cambridge University Press (2016).
[B] Bayesian non-linear statistical inverse problems, xi+159 pp., European Mathematical Society (EMS) Press (2023).

Papers

[54] On low frequency inference for diffusions without the hot spots conjecture. (with G.S. Alberti, D. Barnes, A. Jambhale), arXiv 2024.
[53] Bernstein-von Mises theorems for time evolution equations, arXiv 2024. [video]
[52] Bayesian nonparametric inference in McKean-Vlasov models. (with G.A. Pavliotis, K. Ray), Annals of Statistics, to appear.
[51] On posterior consistency of data assimilation with Gaussian process priors: the 2D Navier-Stokes equations. (with E. Titi), Annals of Statistics 52 (2024), 1825-1844.
[50] Consistent inference for diffusions from low frequency measurements. Annals of Statistics 52 (2024), 519-549.
[49] On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions. (with A. S. Bandeira, A. Maillard, S. Wang), Philosophical Transactions of the Royal Society A 381 (2023).
[48] On log-concave approximations of high-dimensional posterior measures and stability properties in non-linear inverse problems. (with J. Bohr), Annales de l’Institut Henri Poincaré (Probab. Statist.), to appear.
[47] On polynomial-time computation of high-dimensional posterior measures by Langevin-type algorithms. (with S. Wang). Journal of the European Mathematical Society (JEMS) 26 (2024), 1031-1112.
[46] On some information-theoretic aspects of non-linear statistical inverse problems. (with G. P. Paternain). Proceedings ICM (2022), 5516-5538
[45] Statistical guarantees for Bayesian uncertainty quantification in non-linear inverse problems with Gaussian process priors. (with F. Monard, G.P. Paternain). Annals of Statistics 49 (2021) 3255-3298.
[44] Consistent inversion of noisy non-Abelian X-ray transforms. (with F. Monard, G.P. Paternain). Communications on Pure and Applied Mathematics 74 (2021) 1045-1099.
[43] Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem. (with M. Giordano). Inverse Problems 36 (2020).
[42] On statistical Calderón problems. (with K. Abraham). Mathematical Statistics and Learning 2 (2019) 165-216.
[41] Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions. (with K. Ray). Annals of Statistics 48 (2020) 1383-1408.
[40] Convergence rates for penalised least squares estimators in PDE-constrained regression problems. (with S. van de Geer, S. Wang). SIAM/ASA Journal of Uncertainty Quantification 8 (2020) 374-413.
[39] Efficient estimation of linear functionals of principal components. (with V. Koltchinskii, M. Löffler). Annals of Statistics 48 (2020) 464-490.
[38] Bernstein - von Mises theorems for statistical inverse problems II: compound Poisson processes. (with J. Söhl). Electronic Journal of Statistics 13 (2019) 3513-3571.
[37] Bernstein - von Mises theorems for statistical inverse problems I: Schrödinger equation. Journal of the European Mathematical Society (JEMS) 22 (2020) 2697-2750.
[36] Efficient nonparametric Bayesian inference for X-ray transforms. (with F. Monard, G.P. Paternain). Annals of Statistics 47 (2019) 1113-1147.
[35] A conversation with Dick Dudley. (with V. Koltchinskii, P. Rigollet). Statistical Science 34 (2019) 169-175.
[34] Inference on covariance operators via concentration inequalities: k-sample tests, classification, and clustering via Rademacher complexities. (with A. Kashlak, J. Aston). Sankhya A 81 (special vol. on statistics on manifolds) (2019) 214-243.

[33] Adaptive confidence sets for matrix completion. (with A. Carpentier, O. Klopp, M. Löffler). Bernoulli 24 (2018) 2429-2460.
[32] On Bayesian inference for some statistical inverse problems with partial differential equations. Bernoulli News 24 (2) (2017) 5-9
[31] Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions. (with J. Söhl). Annals of Statistics 45 (2017) 1664-1693.
[30] Comments on: High-dimensional simultaneous inference with the bootstrap. (with M. Löffler). TEST 26 (2017) 731-733.
[29] High-frequency Donsker theorems for Lévy Measures. (with M. Reiß, J. Söhl, M. Trabs). Probability Theory and Related Fields 164 (2016) 61-108.
[28] A sharp adaptive confidence ball for self-similar functions. (with B. Szabó). Stochastic Processes and Applications (memorial issue for E. Giné) 126 (2016) 3913-3934.
[27] The mathematical work of Evarist Giné. (with V. Koltchinskii, S. van de Geer, J. Wellner). Stochastic Processes and Applications (memorial issue for E. Giné) 126 (2016) 3607-3622 [Catalan translation]
[26] On signal detection and confidence sets in low rank inference problems. (with A. Carpentier). Electronic Journal of Statistics 9 (2015) 2675-2688.
[25] Uncertainty quantification for matrix compressed sensing and quantum tomography problems. (with A. Carpentier, J. Eisert, D. Gross). In: High Dimensional Probability VIII: The Oaxaca volume (eds. N. Gozlan, R. Latala, K. Lounici, M. Madiman), Progress in Probability 74 (2019), 385-430.
[24] Invited Discussion of: “Frequentist coverage of adaptive nonparametric Bayesian credible sets”. Annals of Statistics 43 (2015) 1429-1436.
[23] On the Bernstein-von Mises phenomenon for nonparametric Bayes procedures. (with I. Castillo). Annals of Statistics 42 (2014) 1941-1969.
[22] Confidence Sets in Sparse Regression. (with S. van de Geer). Annals of Statistics 41 (2013) 2852-2876.

[21] Nonparametric Bernstein-von Mises Theorems in Gaussian White Noise. (with I. Castillo). Annals of Statistics 41 (2013) 1999-2028.
[20] Adaptive Confidence Sets in L_2. (with A. Bull). Probability Theory and Related Fields 156 (2013) 889-919.

[19] Spatially Adaptive Density Estimation by Localised Haar Projections. (with F. Gach , V. Spokoiny), Annales de l’Institut Henri Poincaré (Probab. Statist.) 49 (2013) 900-914.
[18] A Donsker Theorem for Lévy Measures. (with M. Reiß). Journal of Functional Analysis 263 (2012) 3306-3332.

[17] Concentration Inequalities and Confidence Bands for Needlet Density Estimators on Compact Homogeneous Manifolds. (with G. Kerkyacharian, D. Picard). Probability Theory and Related Fields 153 (2012) 363-404.
[16] Rates of Contraction for Posterior Distributions in L_r-metrics, 1 ≤r≤∞. (with E. Giné). Annals of Statistics 39 (2011) 2883-2911.

[15] On Adaptive Inference and Confidence Bands. (with M. Hoffmann). Annals of Statistics 39 (2011) 2383-2409.

[14] Global Uniform Risk Bounds for Wavelet Deconvolution Estimators. (with K. Lounici). Annals of Statistics 39 (2011) 201-231.
[13] Adaptive Estimation of the Distribution Function and its Density in Sup-Norm Loss by Wavelet and Spline Projections. (with E. Giné). Bernoulli 16 (2010) 1137-1163.
[12] Efficient Simulation-Based Minimum Distance Estimation and Indirect Inference. (with B.M. Pötscher). Mathematical Methods of Statistics 19 (2010) 327-364.
[11] Confidence Bands in Density Estimation. (with E. Giné). Annals of Statistics 38 (2010) 1122-1170.
[10] Uniform Limit Theorems for Wavelet Density Estimators. (with E. Giné). Annals of Probability 37 (2009) 1605-1646.
[9] An Exponential Inequality for the Distribution Function of the Kernel Density Estimator, with Applications to Adaptive Estimation. (with E. Giné). Probability Theory and Related Fields 143 (2009) 569-596.
[8] On Convergence and Convolutions of Random Signed Measures. Journal of Theoretical Probability 22 (2009) 38-56.
[7] Uniform Central Limit Theorems for Sieved Maximum Likelihood and Trigonometric Series Estimators on the Unit Circle. In: High Dimensional Probability V: The Luminy Volume (eds. C. Houdré, V. Koltchinskii, D. Mason, M. Peligrad) IMS Collections 5 (2009) 338-356.
[6] Adaptation on the Space of Finite Signed Measures. (with E. Giné). Mathematical Methods of Statistics 17 (2008), 113-122.
[5] A Simple Adaptive Estimator of the Integrated Square of a Density. (with E. Giné). Bernoulli 14 (2008), 47-61.
[4] Uniform Central Limit Theorems for Kernel Density Estimators. (with E. Giné). Probability Theory and Related Fields 141 (2008), 333-387.
[3] Donsker-Type Theorems for Nonparametric Maximum Likelihood Estimators. Probability Theory and Related Fields 138 (2007), 411-449.
[2] Bracketing Metric Entropy Rates and Empirical Central Limit Theorems for Function Classes of Besov- and Sobolev-Type. (with B.M. Pötscher). Journal of Theoretical Probability, 20 (2007), 177-199.
[1] Empirical and Gaussian Processes on Besov classes. In: High Dimensional Probability IV, (eds. E. Giné, V. Koltchinskii, W. Li, J. Zinn). IMS Lecture Notes 51 (2006), 185-195.