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Uncertainty Quantification and Modern Statistical Inference

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Publications

Efficient nonparametric Bayesian inference for $X$-ray transforms

Author(s): François Monard, Richard Nickl, Gabriel P. Paternain
Published in: The Annals of Statistics, 47/2, 2019, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/18-aos1708

Consistency of Bayesian inference with Gaussian process priors in an elliptic inverse problem

Author(s): Matteo Giordano, Richard Nickl
Published in: Inverse Problems, 36/8, 2020, Page(s) 085001, ISSN 0266-5611
Publisher: Institute of Physics Publishing
DOI: 10.1088/1361-6420/ab7d2a

Nonparametric statistical inference for drift vector fields of multi-dimensional diffusions

Author(s): Richard Nickl, Kolyan Ray
Published in: The Annals of Statistics, 48/3, 2020, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-aos1851

"Bernstein - von Mises theorems for statistical inverse problems I: Schr\""odinger equation"

Author(s): Nickl, Richard
Published in: Journal of the European Mathematical Society, 4, 2019, ISSN 1435-9855
Publisher: European Mathematical Society Publishing House

Efficient Nonparametric Bayesian Inference For X-Ray Transforms

Author(s): Monard, François; Nickl, Richard; Paternain, Gabriel P.
Published in: Annals of Statistics, 4, 2019, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics

Adaptive confidence sets for matrix completion

Author(s): Alexandra Carpentier, Olga Klopp, Matthias Löffler, Richard Nickl
Published in: Bernoulli, 24/4A, 2018, Page(s) 2429-2460, ISSN 1350-7265
Publisher: Chapman & Hall
DOI: 10.3150/17-BEJ933

Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions

Author(s): Richard Nickl, Jakob Söhl
Published in: The Annals of Statistics, 45/4, 2017, Page(s) 1664-1693, ISSN 0090-5364
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/16-AOS1504

Consistent Inversion of Noisy Non‐Abelian X‐Ray Transforms

Author(s): François Monard, Richard Nickl, Gabriel P. Paternain
Published in: Communications on Pure and Applied Mathematics, 74/5, 2021, Page(s) 1045-1099, ISSN 0010-3640
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/cpa.21942

Bernstein–von Mises theorems for statistical inverse problems II: compound Poisson processes

Author(s): Richard Nickl, Jakob Söhl
Published in: Electronic Journal of Statistics, 13/2, 2019, ISSN 1935-7524
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/19-ejs1609

On signal detection and confidence sets for low rank inference problems

Author(s): Alexandra Carpentier, Richard Nickl
Published in: Electronic Journal of Statistics, 9/2, 2015, ISSN 1935-7524
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/15-ejs1087