Homepage of Frank van der Meulen (Vrije Universiteit Amsterdam)

Professor in Mathematical Statistics

Vrije Universiteit Amsterdam
Department of Mathematics
De Boelelaan 1111, 1081 HV Amsterdam, Netherlands
Room: NU-9A-67
Email: f(dot)h(dot)van(dot)der(dot)meulen(at)vu(dot)nl

Research Summary

My research is directed to statistical inference for stochastic processes, with focus on uncertainty quantification and indirect observation schemes. I work on Bayesian computational aspects of inference for discretely observed stochastic processes on graphical models with particular emphasis on diffusion processes. I have developed general methods for simulating conditioned Markov processes based on ideas of guiding/twisting. Applications include stochastic shape deformation, inference methods for diffusions on manifolds, chemical reaction networks and filtering methods for partically observed processes defined in terms of a stochastic partial differential equation.

More generally, I am interested in Bayesian computational methods such as Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC). I have worked on piecewise deterministic processes such as the (sticky) ZigZag process. On a somewhat more theoretical level I am interested in proving posterior contraction rates for Bayesian procedures, for example in censoring or shape restricted nonparametric problems.

Finally an important aspect of my research consists of direct collaboration with researchers in fields outside mathematics. Examples include sports engineering, climate projections and maritime engineering.

Some research keywords: statistical inference for stochastic processes; Bayesian computation; filtering; graphical models; dynamical systems; shape analysis; (partial) stochastic differential equations.

If we share research interests, feel free to send me an email to discuss possibilities for collaboration.

Organisation - services to the community:

Director of teaching at the mathematics department VU and programme director at the VU master programme Business Analytics
Organiser of the nationwide Lunteren stochastics meeting.
Member of the STAR (Stochastics Applied Research) - board.

Oratie (inaugural speech): (January 24 2025): my inaugural address was published in Nieuw Archief voor de Wiskunde (inaugural). These are the presentation slides and this is one animation used.

Consulting Requests

I offer consulting services in statistics, data analytics, machine learning, and related areas. More info here.

Preprints

G. Yang, F.H. van der Meulen and S. Sommer (2026) Neural Backward Filtering Forward Guiding. arXiv Submitted.
A. Magra, F.H. van der Meulen and A.W. van der Vaart (2026) Semi-parametric Bernstein-von Mises Theorem in a Parabolic PDE Problem. arXiv Submitted
T. Pieper-Sethmacher, D. Avitabile and F.H. van der Meulen (2025) Guided filtering and smoothing for infinite-dimensional diffusions. arXiv Submitted.
F.H. van der Meulen, L. van der Graaff and E. Verhagen (2025) Monitoring athlete health through latent state modelling. Submitted. lmm4ostrc_alleen_appendix2.pdf

Publications

Full list of publications

Recent publications

S. Stroustrup, M. Akhoej Pedersen, F. van der Meulen, S. Sommer and R. Nielsen (2026) Stochastic Phylogenetic Models of Shape BioRXiv Accepted for publication in Systems Biology.
T. Pieper-Sethmacher, F.H. van der Meulen and A.W. van der Vaart (2026) Simulation of infinite-dimensional diffusion bridges. Accepted for publication in Annals of Applied Probability. arXiv.
F.H. van der Meulen and S. Sommer (2025) Backward Filtering Forward Guiding. Journal of Machine Learning Research 281, 1-51.
Marc Corstanje, Frank van der Meulen, Moritz Schauer and Stefan Sommer (2026) Simulating conditioned diffusions on manifolds. arXiv Bernoulli 32(2), 1045-1072.
Marco Reijne, Frank van der Meulen, Frans van der Helm and Arend Schwab (2025) A model on cyclist fall experiments which predicts the maximum allowable handlebar disturbance from which a cyclist can recover balance. Accident Analysis and Prevention 221.
Gefan Yang, Frank van der Meulen and Stefan Sommer (2025) Neural guided diffusion bridges.arXiv ICML 2025.
M.A. Corstanje and F.H. van der Meulen (2025) Guided simulation of conditioned chemical reaction networks. arXiv Statistical Inference for Stochastic Processes 28(8). link to SISP
T. Pieper-Sethmacher, F.H. van der Meulen and A.W. van der Vaart (2025) On a class of exponential changes of measure for stochastic PDEs arXiv Stochastic Processes and their Applications 185. link to SPA
Rikkert Hindriks, Frank van der Meulen, Michel van Putten and Prejaas Tewarie (2025) Unraveling high-order interactions in electrophysiological brain signals using elliptical distributions: Moving beyond the Gaussian approximation. Journal of Physics: Complexity 6(2), 1-15. Link to journal

Some older publications

J. Bierkens, S. Grazzi, F.H. van der Meulen and M. Schauer (2023) Sticky PDMP samplers for sparse and local inference problems, arXiv, Statistics and Computing 33(1).
A. Arnaudon, F.H. van der Meulen, M.R. Schauer and S. Sommer (2022) Diffusion bridges for stochastic Hamiltonian systems and Shape Evolutions, arXiv SIAM Journal on Imaging Sciences (SIMS), 15(1), 293-323.
M. Mider, M.R. Schauer and F.H. van der Meulen (2021) Continuous-discrete smoothing of diffusions, arXiv , Electronic Journal of Statistics 15, 4295-4342
M. Schauer, F.H. van der Meulen and H. van Zantenj (2017). Guided proposals for simulating multi-dimensional diffusion birdges. Bernoulli 23(4A), 2917--2950
G. Jongbloed, G. and F.H. van der Meulen (2009) Estimating a concave distribution function from data corrupted with additive noise. Annals of Statistics 37(2), 782-815.
G. Jongbloed, F.H. van der Meulen and A.W. van der Vaart (2005) Nonparametric inference for LÃ©vy driven Ornstein-Uhlenbeck processes. Bernoulli 11(5), 759-791.
F.H. van der Meulen (2005) Statistical estimation for Levy driven OU-processes and Brownian semimartingales , Phd-thesis, Vrije Universiteit Amsterdam.

Some "outreach" publications

F.H. van der Meulen (2025) Statistiek: het onzichtbare zichtbaar maken. Nieuw Archief voor Wiskunde 26(2), 109--117.
A. di Bucchianico, L. Iapichino, N. Litvak, F.H. van der Meulen and R. Wehrens (2018) Mathematics for Big Data Nieuw Archief voor wiskunde, 282-287. pdf reprinted in `The Best Writing on Mathematics 2019' link to book

Unpublished

F.H. van der Meulen and M.R. Schauer (2017) On residual and guided proposals for diffusion bridge simulation arXiv
F.H. van der Meulen and M. Schauer (2022) Automatic Backward Filtering Forward Guiding for Markov processes and graphical models, arXiv Working paper that evolved into two manuscripts Backward Filtering Forward Guiding (with Stefan Sommer) and Compositionality in algorithms for smoothing (with Andi Q. Wang). I gave a talk on a preliminary version of this work at the Laplace-demon seminar laplace demon seminar talk
F.H. van der Meulen (2022) Introduction to Automatic Backward Filtering Forward Guiding (v2, Nov2022) arXiv (This is an informal introduction to Backward Filtering Forward Guiding)

Short CV

2001--2005: PhD student, VU Amsterdam
2005--2007: Researcher at IBIS UvA
2007--2017: Assistant professor, TU Delft
2018--2022: Associate professor, TU Delft
2022--now: Full professor, VU Amsterdam

Teaching

I have taught coursed in statistics, probability, analysis and linear algebra in the bachelor and master for over 10 years. For the courses financial time series (minor Finance at TU Delft) and statistical inference (master course at TU Delft) I have written lectures notes: statistical inference and time-series.

Fall 2025 I will teach a seminar on Sequential Monte Carlo methods for msc students at VU.

Software

I enjoy implementing new computational ideas, see my Github account. Some of the packages I have written include

BridgeLandmarks (Julia-registrered package containing code for stochastic deformation models using bridge simulation, written with M. Schauer)
BayesianDecreasingDensity (Bayesian nonparametric estimation of a decreasing density)
Bdd (Bayesian decompounding of discrete distribution, written with S. Gugushvili)
PointProcessInference (nonparametric estimation of the intensity of a non-homogeneous Poisson process, written with S. Gugushvili and M. Schauer)

Presentations

Likelihood representations for discretely observed stochastic processes (Bergamo-Waseda Workshop on Inference for Stochastic Processes and Applications, January 2023). slides
Backward Filtering Forward Guiding (Warwick Algorithms and Computationally Intensive Inference Seminar (ACIIS), December 2022). slides
Continuous-discrete smoothing of diffusions (Imperial college, December 2017). slides
Nonparametric Bayesian Decompounding (European Meeting of Statisticians Amsterdam 2015). slides
Convergence rates of posterior distributions for Brownian semimartingale models (European Meeting of Statisticians 2005 Oslo). slides

Math Books

Here are some books in math I like:

Probability 1 and 2 by Albert Shiryaev (just wonderful how everything is set ready in the very first chapter to do the more advanced stuff; I also very much like the statistically oriented examples).
Linear Algebra Done Right by Sheldon Axler (a didactical masterpiece, not for a first introduction to linear algebra).
Introductory Functional Analysis with Applications by Erwin Kreyszig (a classic).
Vector Calculus, Linear Algebra and Differential forms by John Hubbard and Barbara Burke Hubbard (I haven't seen other books with such a unique combination of topics explained well; btw, why doesn't this book ship for any affordable price to The Netherlands?)
Pattern Recognition and Machine Learning by Christopher Bishop.
Probably Theory by Edwin Jaynes (for anyone something to disagree on in this book, but I learned a lot from it and it surely influenced my point of view on statistics).
R for Data Science by Hadley Wickham and Garrett Grolemund (I think the tidyverse packages are a great service to practitioners).
A Student's Guide to Bayesian Statistics by Ben Lambert (many people that use statistics never learned math; this book explains the Bayesian approach well, also conceptually the more advanced topics).
Asymptotic Statistics by Aad van der Vaart.