Professor in Mathematical
Statistics Vrije Universiteit Amsterdam Department of Mathematics VU_math De Boelelaan 1111, 1081HV Amsterdam The Netherlands Room: NU-9A-35 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 Mathbooks

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
diffusion bridges 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). Recently I have also worked on piecewise deterministic processes such as the (sticky) ZigZag process (with Sebastiano Grazzi and Joris Bierkens). 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).

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). Recently I have also worked on piecewise deterministic processes such as the (sticky) ZigZag process (with Sebastiano Grazzi and Joris Bierkens). 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; longitudinal data.
*

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

F.H. van der Meulen (2022)
Introduction to Automatic Backward Filtering Forward Guiding
(v2, Nov2022) arXiv

This is an
attempt to introduce some of the ideas of the paper
Automatic Backward Filtering Forward Guiding for Markov
processes and graphical models, (written jointly with M.
Schauer) in a friendly way.

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). The guided processes introduced in the paper are obtained by using an approximation to Doob's h-transform. Furthermore, we fully explain the compositional structure of the backward filtering forward guiding algorithm. I gave a talk on this topic for the Laplace-demon seminar laplace demon seminar talk. In the submitted version, some parts of earlier versions of the paper (that go deeper into categorical aspects) have been left out. I hope we will summarise the main findings on this in a separate note.

**Topic: statistical inference for
stochastic processes
**

S.
Gugushvili, F.H. van der Meulen, M. Schauer and P. Spreij
(2022) *Nonparametric Bayesian volatility learning under
microstructure noise, *Accepted for publication in
Japanese Journal of Statistics and Data Science.

J.
Bierkens, S. Grazzi, F.H. van der Meulen and M. Schauer (2022) *Sticky
PDMP samplers for sparse and local inference problems*, arXiv, Accepted for publication in
Statistics and Computing.

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 (2022) *Conditioning
continuous-time Markov processes by guiding*, arXiv Accepted for publication in
Stochastics.

In the paper we show that guided processes can
be defined generally for continuous-time Markov processes, not
merely for diffusion processes.

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** ****
**

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)

[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.

G. Jongbloed, F.H. van der Meulen and L. Pang (2022)

G. Jongbloed, F.H. van der Meulen and L. Pang (2021)

G. Jongbloed, F.H. van der Meulen and L. Pang (2021)

S. Gugushvili, E. Mariucci and F.H. van der Meulen (2020)

S. Gugushvili, F.H. van der Meulen, M.R. Schauer and P. Spreij (2019)

G. Jongbloed, G. and F.H. van der Meulen (2009)

L. Gomaz, DJ Veeger, E. van der Graaff, B. van Trigt and F.H. van der Meulen (2021)

R.B. Hageman, F.H. van der Meulen, A. Rouhan and M.L. Kaminski (2021)

L. Mészáros, F.H. van der Meulen, G. Jongbloed and G. el Sarafy (2021)

L. Mészáros, F.H. van der Meulen, G. Jongbloed and G. el Sarafy (2021)

K. Hartman, A. Wittich, J.J. Cai, F.H. van der Meulen and J.M.N. Azevedo (2016)

F.H. van der Meulen, S. Luca, G. Overal, A. di Bucchianico and G. Jongbloed (2014)

F.H. van der Meulen, R. Hageman (2013)

L.S.G.L. Wauben, W.M.U. van Grevenstein, R.H.M. Goossens, F.H. van der Meulen and J.F. Lange (2011)

F.H. van der Meulen, M.B. Vermaat and P. Willems (2010)

F.H. van der Meulen, H. de Koning and J. de Mast (2009)

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

Outreach

N. Litvak and F.H. van der Meulen (2015)

A. di Bucchianico, L. Iapichino, N. Litvak, F.H. van der Meulen and R. Wehrens (2018)

G. Jongbloed and F.H. van der Meulen (2011)

F.H. van der Meulen (2021)

F.H. van der Meulen and M.R. Schauer (2017)

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

2022-now: Full professor at Vrije Universiteit
Amterdam

2012-now: Scientific advisor for company ProjectsOne

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.

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)

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.