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Homepage of Frank van der Meulen

Associate professor
Delft University of Technology
Electrical Engineering, Mathematics and Computer Science
Delft Institute of Applied Mathematics
The Netherlands
Phone: 015-2784517
Room: E-1.180
 E-mail: f(dot)h(dot)vandermeulen(at)tudelft(dot)nl

Research summary    Consulting requests    Preprints / submitted     Publications      Short CV    Teaching  

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 with particular emphasis on diffusion- and Lévy processes. Within Bayesian estimation for diffusions, the simulation of diffusion bridges is of key importance. I have developed general methods for simulating conditioned diffusions using guided proposals. Simulations in our articles have been performed in Julia: Moritz maintains the Bridge package for this (see Bridge.jl). More recently, Marcin Mider contributed to and implemented many useful methods in JuliaDiffusionBayes. One exciting application of the developed methods is shape deformation (ongoing cooperation with Stefan Sommer (University of Copenhagen) and Alexis Arnaudon (Imperial College London)). 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.
  Together with Shota Gugushvili, 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.

Some keywords: statistical inference for stochastic processes (diffusions, Lévy processes); Bayesian computation; Bayesian asymptotics; dynamical systems; longitudinal data.

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

Consulting requests

I offer consulting services in statistics, data handling, data analytics, machine learning, quality control and related areas. For inquiries, please contact me by email.

Preprints / submitted

F.H. van der Meulen and M. Schauer (2020) Automatic Backward Filtering Forward Guiding for Markov processes and graphical models, working paper, arXiv 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.

M. Mider, M.R. Schauer and F.H. van der Meulen (2020) Continuous-discrete smoothing of diffusions, submitted, arXiv Fully revised version, good starting point if you are interested in inference for partially observed diffusions using guided proposals.

A. Arnaudon, F.H. van der Meulen, M.R. Schauer and S. Sommer (2020) Diffusion bridges for stochastic Hamiltonian systems with applications to shape analysis, submitted, arXiv , submitted (a short animation for the example in the introduction of this article is at the bottom of this webpage).

J. Bierkens, S. Grazzi, F.H. van der Meulen and M. Schauer (2020) A piecewise deterministic Monte Carlo method for diffusion bridges, arXiv, submitted.

S. Gugushvili, F.H. van der Meulen, M.R. Schauer and P. Spreij (2018) Nonparametric Bayesian volatility learning under microstructure noise, submitted.

G. Jongbloed, F.H. van der Meulen and L. Pang (2019) Bayesian nonparametric estimation in the current status continuous mark model, arXiv, under revision.

F.H. van der Meulen and M.R. Schauer (2017) On residual and guided proposals for diffusion bridge simulation arXiv 
The main point is that guided proposals (as Moritz and I have defined these) are not computationally excessive. See our updated work (jointly with Marcin Mider) "Continuous-discrete smoothing of diffusions".

R.B. Hageman, F.H. van der Meulen, A. Rouhan and M.L. Kaminski (2018) Improved Risk-Based Inspection planning through in-service Hull Structure Monitoring of FPSO hulls, submitted.

Publications

34) G. Jongbloed, F.H. van der Meulen and L. Pang (2020) Nonparametric Bayesian estimation of a concave distribution function with mixed interval censored data, accepted for publication in Brazilian Journal of Probability and Statistics.

33) L. Mészáros, F.H. van der Meulen, G. Jongbloed and G. el Sarafy (2020) A stochastic climate generator to complement existing climate change scenarios, accepted for publication in Stochastic Environmental Research and Risk Assessment (SERRA).

32) G. Jongbloed, F.H. van der Meulen and L. Pang (2020) Bayesian estimation of a decreasing density arXiv accepted for publication in Brazilian Journal of Probability and Statistics.

31) S. Gugushvili, F.H. van der Meulen, M.R. 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)

30) 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

29) S. Gugushvili, F.H. van der Meulen, M.R. 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]

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

27) 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

26) S. Gugushvili, F.H. van der Meulen, M.R. Schauer and P. Spreij (2019) Bayesian wavelet de-noising with the Caravan prior arXiv accepted for publication in ESAIM Probability and Statistics

25) 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

24) S. Gugushvili, F.H. van der Meulen, M.R. 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, to appear.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

7) Jongbloed, G. and Van der Meulen, F.H. (2009) Estimating a concave distribution function from data corrupted with additive noise. Annals of Statistics 37(2), 782-815.

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

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

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

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

2) Jongbloed, G. Meulen, F.H. van der, Vaart, A.W. van der (2005)  Nonparametric inference for Lévy driven Ornstein-Uhlenbeck processes. Bernoulli 11(5), 759-791

1) Phd-thesis  Statistical estimation for Levy driven OU-processes and Brownian semimartingales (2005), Vrije Universiteit Amsterdam


Short CV

1995-2001:  TU Delft, applied mathematics
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-now:   Associate professor at TU Delft
2012-now:   Scientific advisor for company ProjectsOne

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.

Software

I enjoy implementing new computational ideas, see my Github account.

Animation

Animation corresponding to introductory example in Diffusion bridges for stochastic Hamiltonian systems with applications to shape analysis.
Here, it is almost like seeing three times the same thing. This is actually the point! The left is forward simulated, the middle is initialisation with guided proposals (already quite good), the right is after 200 iterations.