Mathematical Institute, University of Leiden

Moritz Schauer

Mathematical Institute | University of Leiden

Contact/E-mail

Snellius Building
Niels Bohrweg 1
2333 CA Leiden
Room number 232

m.r.schauer@math.leidenuniv.nl

University of Leiden Address Book

Stations

2015 –   Postdoc at the Mathematical Institute, University of Leiden. Projects: Causal Discovery from High-Dimensional Data in the Large-Sample Limit
2014 – 2015  Postdoc at the Korteweg-de Vries Institute for Mathematics, University of Amsterdam, VICI project Foundations of nonparametric Bayes procedures.
2010 – 2014  PhD candidate at the Delft Institute of Applied Mathematics, Delft University of Technology in cooperation with EURANDOM and support by the STAR cluster of the Dutch Science Foundation NWO.
2004 – 2009  Diplom-Mathematik at University of Hamburg, Department Mathematical Statistics and Stochastic Processes.

Research interest

Nonparametric Bayesian inference for diffusion processes.

Conditional diffusion processes / diffusion bridges.

Bayesian inference on graphs and causal inference.

Journal

Publications

Preprints

With Frank van der Meulen, Joris Bierkens: Simulation of elliptic and hypo-elliptic conditional diffusions. arXiv:1810.01761, 2018.

With Frank van der Meulen, Shota Gugushvili, Peter Spreij: Nonparametric Bayesian volatility learning under microstructure noise. arxiv:1805.05606, 2018.

With Denis Belomestny, Shota Gugushvili, Peter Spreij: Nonparametric Bayesian inference for Lévy subordinators. arxiv:1804.11267, 2018.

With Richard C. Kraaij: A generator approach to stochastic monotonicity and propagation of order. arxiv:1804.10222, 2018.

With Frank van der Meulen, Shota Gugushvili, Peter Spreij: Fast and scalable non-parametric Bayesian inference for Poisson point processes. arxiv:1804.03616, 2018.

With Frank van der Meulen, Shota Gugushvili, Peter Spreij: Nonparametric Bayesian volatility estimation. arxiv:1801.09956, 2018.

With Frank van der Meulen: Continuous-discrete smoothing of diffusions. arxiv:1712.03807, 2017.

With Frank van der Meulen, Shota Gugushvili, Peter Spreij: Nonparametric Bayesian estimation of a Hölder continuous diffusion coefficient. arxiv:1706.07449, 2017.

Monography/Thesis

Bayesian inference for discretely observed diffusion processes. Ph.D. Thesis. Delft University of Technology, 2015.

Articles

With Frank van der Meulen: Bayesian estimation of incompletely observed diffusions. Stochastics 90 (5), 2018, pp. 641–662, 10.1080/17442508.2017.1381097.

With Frank van der Meulen, Jan van Waaij: Adaptive nonparametric drift estimation for diffusion processes using Faber-Schauder expansions. Statistical Inference for Stochastic Processes, 2017, 10.1007/s11203-017-9163-7.

With Frank van der Meulen: Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals. Electronic Journal of Statistics 11 (1), 2017, 10.1214/17-EJS1290.

With Frank van der Meulen, Harry van Zanten: Guided proposals for simulating multi-dimensional diffusion bridges. Bernoulli 23 (4A), 2017, pp. 2917–2950, 10.3150/16-BEJ833.

With Frank van der Meulen, Harry van Zanten: Reversible jump MCMC for nonparametric drift estimation for diffusion processes. Computational Statistics & Data Analysis 71, 2014, pp. 615–632, ISSN 0167-9473, 10.1016/j.csda.2013.03.002.

Book chapter

With Christos Pelekis: Network Coloring and Colored Coin Games. In: S. Alpern, R. Fokkink et al. (ed.): Search Theory: A Game Theoretic Perspective. Springer, 2013. ISBN-13: 978-146146824, 10.1007/978-1-4614-6825-7_4. Note: The proof therein is based on a uniform bound on the median of the number of sources (resp. sinks) in a graph with randomly oriented edges (randomly oriented graphs) of independent interest.

Software publications

Bridge 0.7. Zenodo 10.5281/zenodo.1100978. Ongoing work, see below.

With Shota Gugushvili: MicrostructureNoise. Zenodo 10.5281/zenodo.1241010. 2018.

Bibliography and author information

 arXiv  https://arxiv.org/a/0000-0003-3310-7915.html

  http://orcid.org/0000-0003-3310-7915

Preferred names in citations are “Moritz Schauer” and “M. Schauer”.

Download .bib-file

Agenda

The Thematic Seminar 2018: Machine Learning and Statistics for Structures.

Software packages

Bridge.jl

A statistical toolbox for diffusion processes written in julia.

The package allows for simulation of univariate and multivariate stochastic processes in continuous time, and also from conditional diffusion processes (similar to Brownian bridges, namesakes of this package)

Several examples illustrate how the functions in this package can be used in Bayesian inference for drift and diffusion coefficients using the Metropolis-Hastings algorithm, see F. v. d. Meulen, M. Schauer: Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals. Electronic Journal of Statistics 11 (1), 2017, 10.1214/17-EJS1290.

CausalInference.jl

Julia package for causal inference, graphical models and structure learning with the PC algorithm. This package contains for now the classical PC algorithm, tested on random DAGs by comparing the result of the PC algorithm using the *d*-separation oracle with CPDAGs computed with Chickering's DAG->CPDAG conversion algorithm (implemented as `dsep` and `cpdag` in this package). See the documentation for the implemented functionality.

Open source contributions

See github.com/mschauer.