European Institute for Statistics, Probability, Stochastic Operations Research
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June 4 - 6, 2012


 "Parameter Estimation for Dynamical Systems"







Differential equations (deterministic or stochastic) play a fundamental role in modelling dynamic phenomena in fields as diverse as physics, biology, finance, engineering, chemistry, biochemistry, neuroscience, ecology, meteorology, pharmacology, and others. Models defined via differential equations (or systems of differential equations) usually depend on finite or possibly infinite-dimensional parameters. In order to obtain a model that is useful in practice, it is critical to know these parameters, or to estimate them in case they are unknown. The workshop aims at providing a meeting place for researchers and practitioners in the area of parameter estimation for deterministic and stochastic differential equations, who will review different methods used to tackle the problems arising in these fields, assess the achieved progress, and identify future research directions. It is hoped that by bringing together experts in statistical estimation for differential equations, a fertile ground for exchange of mutually beneficial ideas will be created. The emphasis of the workshop is on presentation of new methodological work with a good balance from applications. Importantly, appropriateness of either deterministic or stochastic models in various contexts will be discussed and due attention to both the frequentist and the Bayesian approaches to parameter estimation of differential equations will be paid.

The workshop is a follow-up on the Workshop on Parameter Estimation for Dynamical Systems (PEDS-I) held on 8 - 10 June 2009 at Eurandom.



Bart Bakker Philips Research bart.bakker@philips.com
Shota Gugushvili Vrije Universiteit Amsterdam s.gugushvili@vu.nl
Chris Klaassen Universiteit van Amsterdam & EURANDOM c.a.j.klaassen@uva.nl
Aad van der Vaart Vrije Universiteit Amsterdam & EURANDOM aad@cs.vu.nl





Florence d'Alché-Buc Université d'Evry-Val d'Essonne
Lorenz Biegler Carnegie Mellon University
Mark Girolami University College London
Rikkert Hindriks Universiteit Twente
Stefano Iacus Università degli Studi di Milano
Michael Sørensen University of Copenhagen
Eberhard Voit Georgia Institute of Technology
Darren Wilkinson Newcastle University
Harry van Zanten Eindhoven University of Technology




We have reached the maximum number of participants and have closed the registration as from March 28.


Participants have to arrange their own hotel bookings. For hotel reservations we suggest to consult the webpage VVV Eindhoven Eindhoven Hotels. There is also a possibility to stay at our preferred hotel Crown Inn at a reduced rate of 69 euros per night (single room; excl. tax/breakfast).
Please email Patty Koorn for instructions on how to profit from this special offer.
For invited speakers hotel accommodation will be arranged by the organization. You are requested to indicate the arrival and departure dates on the registration form.



Monday June 4 (note: changed time schedule due to cancellation of a speaker)

10.00 - 11.00 Registration  
11.00 - 11.15 Opening  
11.15 - 12.00 Harry van Zanten Nonparametric Bayes inference for scalar diffusions
12.00 - 13.00 Lunch  
13.00 - 13.30 Boumediene Hamzi On parameter estimation of nonlinear stochastic differential equations in reproducing kernel Hilbert spaces
13.30 - 14.00 Umberto Picchini Inference for SDE models via Approximate Bayesian Computation
14.00 - 14.15 Break  
14.15 - 15.00 Lorenz Biegler On-line state and parameter estimation of nonlinear dynamic systems: a nonlinear programming framework
15.00 - 15.45 Michael Sørensen Martingale estimating functions for stochastic differential equations with jumps
15.45 - 16.15 Bartek Knapik Bayesian inverse problems - recovery of the initial condition for the heat equation
16.15 - 17.30 Poster session  
18.30 - Conference dinner  


Tuesday June 5

09.15 - 10.00 Rikkert Hindriks Meanfield modeling of healthy and pathological EEG rhythms
10.00 - 10.45 Darren Wilkinson Bayesian inference for Markov processes with application to biochemical network dynamics
10.45 - 11.00 Break  
11.00 - 11.30 Mélanie Prague Bayesian MAP Estimation in models with random effects based on ordinary differential equations applied to treatment monitoring in HIV
11.30 - 12.00 Syed Murtuza Baker A parameter estimation framework for kinetic models of biological systems
12.00 - 13.00 Lunch  
13.00 - 13.30 Sabine Hug Bayesian model selection validates a biokinetic model for zirconium processing in humans
13.30 - 14.00 Christiane Fuchs Bayesian inference on diffusion models for protein dynamics
14.00 - 14.15 Break  
14.15 - 15.00 Mark Girolami MCMC Sampling for Intractable MJP Models of Chemical
Kinetics via the Linear Noise Approximation
15.00 - 15.45 Stefano Iacus Recent results on volatility change point estimation for stochastic differential equations
15.45 - 16.15 Anders Jensen A Markov Chain Monte Carlo approach to parameter estimation in the FitzHugh-Nagumo model
16.15 - 16.45 Break  
16.45 - 17.30 Discussion  


Wednesday June 6

09.15 - 09.45 Jonathan Jaeger Bayesian ODE-penalized B-spline model with Gaussian mixture as error distribution
09.45 - 10.15 Javier Gonzalez Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations
10.15 - 10.45 Ivan Vujacic A new statistical framework to infer gene regulatory networks with hidden transcription factors
10.45 - 11.00 Break  
11.00 - 11.30 Joep Vanlier Targeted experimental design using the posterior predictive distribution
11.30 - 12.00 Andreas Raue A study for inference in the presence of non-identifiability: Bayesian MCMC sampling vs.\ profile likelihood approach
12.00 - 13.00 Lunch  
13.00 - 13.45 Florence d' Alché-Buc Estimation of nonparametric dynamical models within Reproducing Kernel Hilbert Spaces for biological network inference
13.45 - 14.30 Aberhard Voit Quantification of Metabolic Pathway Models: Beyond Acceptable Parameter Fits
14.30 - 14.45 Closing  



Florence d’Alché-Buc (INRIA-Saclay & Université d’Evry)

Estimation of nonparametric dynamical models within Reproducing Kernel Hilbert Spaces for biological network inference

We consider the problem of network inference that occurs for instance in sys- tems biology. A dynamical system (a gene regulatory network) is observed through time and the goal is to infer the dependence structure between state variables (mRNAs concentrations) from time series. Works concerning net- work inference usually rely on sparse linear models estimation or Granger causality tools. A very few address the issue in the nonlinear cases. In this work, we propose a nonparametric approach to dynamical system modeling that makes no assumption about the nature of the underlying nonlinear sys- tem. We develop a general framework based on Reproducing Kernel Hilbert Spaces based on matrix-valued kernels to identify the dynamical system and retrieve the target network. As in the linear case, the network inference task calls for sparsity control. We show very good results both in autoregressive models and differential equations estimation on DREAM benchmarks as well as on the IRMA datasets.

Lorenz Biegler (Carnegie Mellon University)

On-line state and parameter estimation of nonlinear dynamic systems: a non- linear programming framework

Model based schemes for process control and on-line optimization require knowledge of the process states. Since measurements are available for a subset of the state vector, the remaining states need to be estimated from (often noisy) measurements and the process model, along with an uncertainty description. Among a number of estimation strategies, this task can be ad- dressed with Moving Horizon Estimation (MHE). Under reasonable assump- tions for process models and measurements, MHE has a fundamental statistical basis and allows the direct inclusion of nonlinear first principles process mod- els as well as process constraints. More recently, the development of
efficient, large-scale optimization tools leads to the application of MHE to challenging process systems. In this talk we discuss the efficient on-line application of MHE for potentially large process systems. The MHE problem is formulated using an advanced step approach with a nonlinear programming (NLP) problem, solved in back- ground, and the NLP solution updated on-line as new measurements are made available. This two-step approach is enabled by two efficient NLP-based algorithms; for the background solution the IPOPT NLP solver is used, while sIPOPT, a related NLP sensitivity code, is used for the on-line updates. In addition to the efficient solution of the moving horizon estimation problem, a key consideration is the formulation and update of the arrival cost, which represent the uncertainty description of
previous states not included in the current measurement window. Arrival costs can be estimated from a variety of state estimation approaches such as the Extended Kalman Filter, Particle Filter, Ensemble Kalman Filter and the Unscented Kalman Filter. This talk includes a detailed discussion and comparison of these strategies to estimate the arrival cost, and demonstate their impact on performance of MHE. In particular, we show that much shorter MHE horizons can be considered with more accurate arrival costs. Alternately, the accuracy of the arrival cost estimates becomes less critical for MHE when longer horizons can be considered through faster NLP solvers. This is also facilitated by faster updates of the covariance matrices for the arrival costs. In particular, we show that updates of smoothed state estimates and associated covariance matrices can be obtained directly from the KKT matrix. Moreover, the extension of these updates to more complex multi-rate estimation schemes is straightforward. These resulting approaches are demon- strated for the on-line estimation of a nonlinear distillation process, modeled with 252 differential-algebraic equations.


Mark Girolami (University College London)

MCMC Sampling for Intractable MJP Models of Chemical Kinetics via the Linear Noise Approximation


Rikkert Hindriks (Universiteit Twente)

Meanfield modeling of healthy and pathological EEG rhythms

Although the first EEG rhythms in human subjects were recorded almost a century ago and their cognitive and clinical correlates are well documented, there is still no consensus on how the brain generates these rhythms. Sci- entific understanding of the generation of EEG rhythms is advanced by a continuous dialog between experiment and mathematical modeling. Since the EEG signal is a macroscopic quantity, reflecting the average activity of populations of about
~105 nerve cells, microscopic models in which the behavior of individual nerve cells is simulated are unpractical. In contrast, neuronal meanfield models aim to describe the average behavior of large populations of nerve cells, thereby making a direct connection with the EEG. Moreover, they are low-dimensional and contain few parameters, hence can be analyzed semi-analytically. After introducing neuronal meanfield modeling, I will discuss two applications. The first one is concerned with the effect of anesthetic agents on EEG rhythms and the second with a pathological condition known as status epilepticus. We will see that our modeling efforts provide insight into the underlying biophysical mechanisms and lead to specific predictions that can be tested in the laboratory.


Stefano Iacus (Universit`a degli Studi di Milano)

Recent results on volatility change point estimation for stochastic differential equations

The problem of change point has been considered initially in the framework of independent and identically distributed data by many authors, see e.g. [2]. Recently, it naturally moved to context of time series analysis, see for ex- ample, [4], [1]. Indeed, change point problems have originally arisen in the context of quality control, but the problem of abrupt changes in general arises in many contexts like epidemiology, rhythm analysis in electrocardiograms, seismic signal processing, study of archeological sites and financial markets. For discretely observed, one-dimensional ergodic diffusion processes, [3] con- sidered a least squares approach. The problems of the change-point of drift for continuously observed ergodic diffusion processes have been treated in [5]. For general Itˆo processes [6] have considered quasi-maximum likelihood estimation. In this talk, we review recent theoretical results on change point analysis for the volatility term in discretely observed stochastic differential equations and their software solutions for the R statistical environment.
[1] Chen, G.; Choi, Y.K.; Zhou, Y.: Nonparametric estimation of structural change points in volatility models for time series. Journal of Econometrics, no. 126, 79–144, (2005)
[2] Cs
örgő, M.; Horváth, L.: Limit Theorems in Change-point Analysis. New York: Wiley, (1997)
[3] De Gregorio, A.; Iacus, S.M.: Least squares volatility change point estimation for partially observed diffusion processes. Communications in Statistics, Theory and Methods, no. 37, issue 15, 2342–2357, (2008)
[4] Lee, S.; Ha, J.; Na, O.; Na, S.: The Cusum test for parameter change in time series models. Scandinavian Journal of Statistics, no. 30, 781–796, (2003)
[5] Kutoyants, Y.: Statistical Inference for Ergodic Diffusion Processes. Springer- Verlag, London, (2004)
[6] Iacus, S.M., Yoshida, N.: Estimation for the change point of the volatility in a stochastic differential equation, (2009), submitted.


Lennart Ljung (Linköpings universitet)

The control community’s approach to parameter estimation for dynamical systems: system identification

Estimating parameters in dynamical systems is a problem that is present in many scientific areas. Many different approaches and algorithms have been suggested and various frameworks have been developed for the problem area. Automatic Control is the community that deals with controlling dynamical systems, and for that reliable models are required. “System Identification” is the term that is used in the control community for building mathematical models of dynamical systems from data. This talk will give an overview of how the control community views and formulates this task. At the same time, some of the current issues, open problems and hot topics in system identification are reviewed. The tasks are illustrated by some real applications.

Michael Sørensen (University of Copenhagen)

Martingale estimating functions for stochastic differential equations with jumps

Methods are discussed for estimating parameters in stochastic differential equation driven not only by a Wiener process, but also by another stochastic mechanism that causes the process to make jumps. This other mechanism can be a Lvy process, or more generally, a random measure on a suitable space. Solutions to such SDEs, called diffusions with jumps, are often use as models for financial time series. When the data are continuous time observations, likelihood inference for diffusions with jumps has long been well understood; see e.g. Sørensen (1991). However, continuous time observations are not avail- able in practice, and for discrete time observations the likelihood function is not explicitly known and usually extremely difficult to calculate numerically. Therefore alternatives like estimating functions are even more useful for jump diffusions than for classical Wiener driven SDEs. We present a highly flexible class of diffusions with jumps for which explicit optimal martingale estimating functions of the type introduced by Kessler and Sørensen (1999) are available. These are based on eigenfunctions of the generator of the diffusion. The class of Pearson diffusions, investigated in Forman and Sørensen (2008), has the property that the generator maps polynomials into polynomials. Therefore it is easy to find polynomial eigenfunctions. Here we generalize these ideas and consider a class of diffusions with jumps for which the generator has the same property using ideas from Zhou (2003). The generator of a diffusion with jumps is considerably more complicated that that for a classical diffu- sion: It is a differential-integral operator. However, it turns out that a simple condition on the compensator of the jump measure is enough to ensure that explicit optimal martingale estimating functions can be found. We illustrate the general theory by concrete examples. The talk is based on joint work with
Mathias Schmidt.
- Forman, J. L. and Sørensen, M. (2008). The Pearson diffusions: A class of statistically tractable diffusion processes. Scandinavian Journal of Statistics, 35, 438–465.
- Kessler, M. and Sørensen, M. (1999). Estimating equations based on eigen- functions for a discretely observed diffusion process. Bernoulli, 5, 299–314.
- Sørensen, M. (1991). Likelihood methods for diffusions with jumps. In Prabhu, N.U. and Basawa, I.V. (eds.): Statistical Inference
in Stochastic Processes, Marcel Dekker, New York, 67–105.
- Zhou, H. (2003). It
ô conditional moment generator and the estimation of short-rate processes. Journal of Financial Econometrics, 1, 250–271.


Eberhard Voit (Georgia Institute of Technology)

Quantification of Metabolic Pathway Models: Beyond Acceptable Parameter Fits

Over the past decade, time series data have become available in biology at an increasing rate. The trend is to be welcomed, as these data contain enor- mous information, which however is implicit and needs to be extracted with computational means. Time series data are particularly beneficial for analy- ses of metabolic pathway systems, because these are strongly constrained by stoichiometric and other intrinsic features, which effectively bound the space of admissible parameter values that need to be specified in order to translate the pathway system into a computable structure. The overriding quality cri- terion for sets of estimated parameter values is usually the squared residual error between data and model. In this presentation, I will discuss several ex- amples where this natural criterion is insufficient. Special emphasis will be placed on the considerable challenge that the best-suited functional forms for describing biological processes are often not even known when a system is to be estimated. This structural uncertainty clearly complicates any estimation strategy, but I will show that it can be ameliorated if the right types of time series data are available.


Darren Wilkinson (Newcastle University)

Bayesian inference for Markov processes with application to biochemical network dynamics

A number of interesting statistical applications require the estimation of pa- rameters underlying a nonlinear multivariate continuous time Markov process model, using partial and noisy discrete time observations of the system state. Bayesian inference for this problem is difficult due to the fact that the discrete time transition density of the Markov process is typically intractable and computationally intensive to approximate. It turns out to be possible to develop particle MCMC algorithms which are exact, provided that one can simulate exact realisations of the process forwards in time. Such algorithms, often termed ”likelihood free” or ”plug-and-play” are very attractive, as they allow separation of the problem of model development and simulation implementation from the development of inferential algorithms. Such techniques break down in the case of perfect observation or high-dimensional data, but more efficient algorithms can be developed if one is prepared to deviate from the likelihood free paradigm, at least in the case of diffusion processes. The methods will be illustrated using examples from population dynamics and stochastic biochemical network dynamics.


Harry van Zanten (Eindhoven University of Technology)

Nonparametric Bayes inference for scalar diffusions

In this talk I will present recent developments in the area of nonparametric Bayesian inference for stochastic differential equations. Both computational methods and theoretical results about the asymptotic behavior of posterior distributions will be discussed.
Based on joint papers with: Frank van der Meulen, Yvo Pokern, Moritz Schauer, Andrew Stuart.



CONTRIBUTED TALKS (presentations)

Baker - Fuchs - Gonzalez - Hamzi - Hug - Jaeger - Jensen - Knapik - Picchini - Prague - Raue - Vanlier - Vujacic





Conference Location
The workshop location is Eurandom, Den Dolech 2, 5612 AZ Eindhoven, Laplace Building, 1st floor, room LG 1.105.

Eurandom is located on the campus of Eindhoven University of Technology in the Laplace Building (marked with LG on this map). The building is located at 15 minutes walking distance from the central railway station of Eindhoven. Take the northern exit from the station and walk in the north-eastern direction until you reach a crossing at Professor Doctor Dorgelolaan. The university campus is located on the other side of that street. Detailed directions via Google Maps are available here.

For travel information to Eindhoven please check http://www.eurandom.tue.nl/contact.htm



For more information please contact Mrs. Patty Koorn,
Workshop officer of  Eurandom


Sponsored by:






Last updated 25-06-12,
by PK