Frank van der Meulen

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

Frank van der Meulen

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). For implementation of landmark matching and template estimation, see BridgeLandmarks. Related to this topic, together with Marc Corstanje I have worked 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, climate projections 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:

Oratie (inaugural speech): uitgesproken op 24 Januari 2025: tekst oratie presentatie oratie animatie SIR

Consulting Requests

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

Preprints / Submitted

Two papers that are related to smoothing and parameter estimation for stochastic processes evolving on graphical models:

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 categorical part has evolved into the manuscript "Compositionality in algorithms for smoothing". The statistical part will evolve into a separate manuscript.

Publications

Topic: statistical inference for stochastic processes


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

Outreach
Other work

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.

Software

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

Presentations

Math Books

Here are some books in math I like: