Homepage of Frank van der Meulen

Professor in Mathematical Statistics
Vrije Universiteit Amsterdam

Department of Mathematics VU_math
De Boelelaan 1111, 1081HV Amsterdam
The Netherlands

Room: NU-9A-67
E-mail: f(dot)h(dot)van(dot)der(dot)meulen(at)vu(dot)nl

Research summary    Consulting requests    Preprints / submitted     Publications      Short CV    Teaching  
Presentations   Mathbooks

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- and Lévy processes. Within Bayesian estimation for diffusions, the simulation of conditioned diffusion processes is of key importance. Together with Moritz Schauer (University of Gothenburg) I have developed general methods for simulating conditioned Markov processes using an algorithm called backward filtering forward guiding. One exciting application of the developed methods is shape deformation (ongoing cooperation with Stefan Sommer (University of Copenhagen) and Alexis Arnaudon (Ecole Polytechnique Federale de Lausanne)). For implementation of landmark matching and template estimation, see BridgeLandmarks. Related to this topic, Marc Corstanje works in his phd-project on inference methods for diffusions on manifolds and chemical reaction networks. Thorben Pieper works on inference for stochastic partial differential equations in a project jointly supervised with Aad van der Vaart (TU Delft).

Together with Shota Gugushvili (Wageningen University), Peter Spreij (University of Amsterdam) and Moritz Schauer I have considered various problems of nonparametric function estimation, where it is assumed that the function is piecewise constant, but adjacent bins are coupled such that the values of these have positive dependence. This appears to work well in a wide range of settings and we may expand this work to other settings or possibly work on stronger theoretical validation of this approach.

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 (with Larisa Gomaz, analysis of multilevel longitudinal data), climate projections (with Lörinc Mészáros) and maritime engineering (fatigue calculations of maritime structures).

Some keywords: statistical inference for stochastic processes (diffusions, Lévy processes); Bayesian computation; Bayesian asymptotics; graphical models; dynamical systems; shape analysis, 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 the VU bachelor programme Business Analytics
- chair of the section Mathematical Statistics of the Netherlands Society for Statistics and Operations Research (VVSOR)
- organiser of the nationwide seminar in statistics (Van Dantzig seminar)
- member of the STAR (Stochastics Applied Research) - board.

Consulting requests

I offer consulting services in statistics, data handling, data analytics, machine learning, quality control and related areas. For more information, see here.

Preprints / submitted

Marc Corstane, Frank van der Meulen, Moritz Schauer and Stefan Sommer (2024) Simulating conditioned diffusions on manifolds. arXiv Submitted.
Marc Corstanje and Frank van der Meulen (2023) Guided simuation of conditioned chemical reaction networks. arXiv Submitted.

Some papers that are under revision and related to smoothing and parameter estimation for stochastic processes evolving on graphical models:
- F.H. van der Meulen and M. Schauer (2023) Compositionality in algorithms for smoothing  arXiv Submitted.
- F.H. van der Meulen (2022) Introduction to Automatic Backward Filtering Forward Guiding (v2, Nov2022)  arXiv 
(This is an informal introduction to the paper below.)
- F.H. van der Meulen and M. Schauer (2022) Automatic Backward Filtering Forward Guiding for Markov processes and graphical models, arXiv Submitted.  
In this paper we show that guided proposals as defined in previous work for diffusions can be defined for Bayesian networks and continuous time Markov processes (different from diffusions).
I gave a talk on this topic for the Laplace-demon seminar laplace demon seminar talk. The paper is presently under revision.


Topic: statistical inference for stochastic processes

D. Belomestny, F. van der Meulen, and P. Spreij (2023), Nonparametric Bayesian inference for stochastic processes with piecewise constant priors, Mathematics of Risk 2022 MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Springer, to appear. [pdf available at the 2021-22 MATRIX Annals page]
This is an overview paper, showing a common theme in various earlier applications, also jointly with S. Gugushvili and M. Schauer.

J. Bierkens, S. Grazzi, F.H. van der Meulen and M. Schauer (2023) Sticky PDMP samplers for sparse and local inference problemsarXiv, Statistics and Computing 33(8).
This paper shows how to adapt piecewise deterministic Markov processes to settings where the dominating measure is not Lebesgue measure. As an example, it shows how to sample from the posterior under a spike-and-slab prior, without the need to set any additional tuning parameter.

M.A. Corstanje, F.H. van der Meulen and M. Schauer (2023) Conditioning continuous-time Markov processes by guiding, Stochastics, 95(6), 963--996.
In the paper we show that guided processes can be defined generally for continuous-time Markov processes, not merely for diffusion processes.

S. Gugushvili, F. van der Meulen, M. Schauer and P. Spreij (2022), Nonparametric Bayesian volatility learning under microstructure noise, Japanese Journal of Statistics and Data Science 6(1), 551-571. [pdf]

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

S. Sommer, M. Schauer and F. van der Meulen  Stochastic flows and shape bridges. In Statistics of Stochastic Differential Equations on Manifolds and Stratified Spaces (hybrid meeting), number 48 in Oberwolfach Reports, pp. 18–21. Mathematisches Forschungsinstitut Oberwolfach, 2021. doi: 10.4171/OWR/2021/48. null ; Conference date: 03-10-2021 Through 09-10-2021.

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     
Good starting point if you are interested in inference for partially observed diffusions using backward filtering forward guiding.

J. Bierkens, S. Grazzi, F.H. van der Meulen and M. Schauer (2021) A piecewise deterministic Monte Carlo method for diffusion bridges, arXiv, Statistics and Computing 31(3)

J. Bierkens, F.H. van der Meulen and M. Schauer (2020) Simulation of elliptic and hypo-elliptic conditional diffusions. Advances in Applied Probability. 52, 173–212.

F.H. van der Meulen, M. Schauer, S. Grazzi, S. Danisch and M. Mider (2020) Bayesian inference for SDE models: a case study for an excitable stochastic-dynamical model, Nextjournal, https://nextjournal.com/Lobatto/FitzHugh-Nagumo

S. Gugushvili, F.H. van der Meulen, M. Schauer and P. Spreij (2020) Non-parametric Bayesian estimation of a Holder continuous diffusion coefficient Brazilian Journal of Probability and Statistics 34(3), 537-579.  (pdf)

S. Gugushvili, F.H. van der Meulen, M. Schauer and P. Spreij (2020) Fast and scalable non-parametric Bayesian inference for Poisson point processes arXiv at researchers.one (a very nice initiative, please have a look)
[corresponding code is on zenodo https://zenodo.org/record/1215901#.Wtg3N9NuZTY]

S. Gugushvili, F.H. van der Meulen and P.J. Spreij (2018) A non-parametric Bayesian approach to decompounding from high frequency data. Statistical Inference for Stochastic Processes, 21, 53-79.

S. Gugushvili, F.H. van der Meulen, M. Schauer and P. Spreij (2018) Nonparametric Bayesian volatility estimation arXiv, MATRIX Annals, Editors: David R. Wood, Jan de Gier, Cheryl E. Praeger, Terence Tao. MATRIX Book Series, Vol 2, Springer

F.H. van der Meulen and M. Schauer (2017) Bayesian estimation of incompletely observed diffusions, Stochastics 90(5), 641-662.

F.H. van der Meulen and M. Schauer (2017) Bayesian estimation of discretely observed multi-dimensional diffusion processes using guided proposals,  Electronic Journal of Statistics 11(1), 2358--2396.

M. Schauer, F.H.  van der Meulen and J.H. van Zanten (2017) Guided proposals for simulating multi-dimensional diffusion bridges, Bernoulli 23(4A), 2917--2950

F.H. van der Meulen, M. Schauer, J. van Waaij (2017)  Adaptive nonparametric drift estimation for diffusion processes using Faber-Schauder expansions,  Statistical Inference for Stochastic Processes 21(3), 603-628.

F.H. van der Meulen, M. Schauer and J.H. van Zanten (2014) Reversible jump MCMC for nonparametric drift estimation for diffusion processes, Computational Statistics and Data Analysis 71, 615--632.

S. Gugushvili, S., P. Spreij and F.H. van der Meulen (2015) Non-parametric Bayesian inference for multi-dimensional compound Poisson processes. Modern Stochastics: Theory and Applications 2(1), 1--15.

F.H. van der Meulen and J.H. van Zanten (2013) Consistent nonparametric Bayesian inference for discretely observed scalar diffusions, Bernoulli 19(1), 44–63.

F.H. van der Meulen, A.W. van der Vaart and J.H. van Zanten (2006) Convergence rates of posterior distributions for Brownian semimartingale models Bernoulli 12(5), 863-888

G. Jongbloed and F.H. van der Meulen (2006) Parametric estimation for subordinators and induced OU-processes Scandinavian Journal of Statistics 33(4), 825-847

G. Jongbloed, F.H. van der Meulen and A.W. van der Vaart (2005)  Nonparametric inference for Lévy 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.

Topic: deconvolution, decompounding, denoising, censoring...

G. Jongbloed, F.H. van der Meulen and L. Pang (2022) Bayesian nonparametric estimation in the current status continuous mark model, SJS, Scandinavian Journal of Statistics 49(3), 1329-1352.

G. Jongbloed, F.H. van der Meulen and L. Pang (2021) Nonparametric Bayesian estimation of a concave distribution function with mixed interval censored data, Brazilian Journal of Probability and Statistics 35(3), 544-568.

G. Jongbloed, F.H. van der Meulen and L. Pang (2021) Bayesian estimation of a decreasing density Brazilian Journal of Probability and Statistics
Vol. 35(2), 392--420.

S. Gugushvili, E. Mariucci and F.H. van der Meulen (2020) Decompounding discrete distributions: a non-parametric Bayesian approach arXiv Scandinavian Journal of Statistics 47(2), 464--492 SJS

S. Gugushvili, F.H. van der Meulen, M.R. Schauer and P. Spreij (2019) Bayesian wavelet de-noising with the Caravan prior arXiv ESAIM Probability and Statistics 23, 947--978

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. 

Topic: applied statistics

L. Gomaz, B. van Trigt, F. van der Meulen and D.J. Veeger (2024) Predicting elbow load based on individual pelvis and trunk (inter)segmental rotations in fastball pitching, Sports Biomechanics.
DOI: 10.1080/14763141.2024.2315230

L. Gomaz, D.J. Veeger, E. van der Graaff, B. van Trigt and F.H. van der Meulen (2021) Individualised Ball Speed Prediction in Baseball Pitching based on IMU Data, accepted for publication in Sensors.

R.B. Hageman, F.H. van der Meulen, A. Rouhan and M.L. Kaminski (2021) Improved Risk-Based Inspection planning through in-service Hull Structure Monitoring of FPSO hulls, to appear in Marine Structures.

L. Mészáros, F.H. van der Meulen, G. Jongbloed and G. el Sarafy (2021) Climate change induced uncertainties in Phytoplankton spring bloom dynamics, accepted for publication in Frontiers in Marine Science.

L. Mészáros, F.H. van der Meulen, G. Jongbloed and G. el Sarafy (2021) A stochastic climate generator to complement existing climate change scenarios, Stochastic Environmental Research and Risk Assessment (SERRA) 35, 719--736.

K. Hartman, A. Wittich, J.J. Cai, F.H. van der Meulen and J.M.N. Azevedo (2016) Estimating the age of Rissos dolphins (Grampus griseus) based on skin appearance. Journal of Mammology 97(2), 490--502.

F.H. van der Meulen, S. Luca, G. Overal, A. di Bucchianico and G. Jongbloed (2014) Modeling a water purification process for quality monitoring. Proceedings of the 98th Study Group Mathematics with Industry, 36--54

F.H. van der Meulen, R. Hageman (2013) Fatigue Predictions using Statistical Inference within the Monitas II Project, Proceedings of the Twenty-hrid International Offshore and Polar Engineering, 463--471.

L.S.G.L. Wauben, W.M.U. van Grevenstein, R.H.M. Goossens, F.H. van der Meulen and J.F. Lange (2011) Operative notes do not reflect reality in laparoscopic cholecystectomy. The British journal of surgery. 98(10), 1431-1436.

F.H. van der Meulen, M.B. Vermaat and P. Willems (2010) Case Study: An application of Logistic Regression in a Six Sigma project in Healthcare. Quality Engineering 23, 113-124.

F.H. van der Meulen, H. de Koning and J. de Mast (2009)  Non-repeatable gauge R&R studies assuming temporal or patterned object variation. Journal of Quality Technology 41(4), 1-14.

M.B. Vermaat, F.H. van der Meulen and R.J.M.M. Does (2008) Asymptotic Behaviour of the Variance of the EWMA Statistic for Autoregressive Processes Statistics and Probability Letters 78(12), 1673-1682

H.J.J. Ramaker, E.N.M. van Sprang, J.A. Westerhuis, S.P. Gorden, F.H. van der Meulen and A.K. Smilde (2006) Performance assessment and improvement of control charts for statistical batch process monitoring Statistica Neerlandica 60(3), 339-360 2)


N. Litvak and F.H. van der Meulen (2015) Networks & Big Data. Nieuw Archief voor Wiskunde 5(2), 138--139.

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

G. Jongbloed and F.H. van der Meulen (2011) Geurproef niet meer in gebruik in strafzaken (in dutch) Stator, pages 38-43.

F.H. van der Meulen (2021)
Een uitnodiging tot data science met R  (in dutch).

Other work

F.H. van der Meulen and M.R. Schauer (2017) On residual and guided proposals for diffusion bridge simulation arXiv 

Short CV

2001-2005:  PhD student at Vrije Universiteit Amsterdam
2005-2007:  Consultant/researcher at the Institute for Business and Industrial Statistics at the University of Amsterdam (IBIS UvA)
2007-2017:  Assistant professor at TU Delft
2018-2022:  Associate professor at TU Delft
2012-2023:  Scientific advisor for company ProjectsOne
2022-now:   Full professor at Vrije Universiteit Amterdam


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.


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)


- 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.