June 4  6, 2012
"Parameter
Estimation for Dynamical Systems"
(PEDSII)
SUMMARY
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 infinitedimensional 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 followup on the Workshop on Parameter Estimation for
Dynamical Systems (PEDSI)
held on 8  10 June 2009 at Eurandom.
ORGANIZERS
INVITED SPEAKERS
REGISTRATION
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.
PROGRAMME
Monday June 4 (note: changed time schedule due to
cancellation of a speaker)
Tuesday June 5
Wednesday June 6
ABSTRACTS
Florence d’AlchéBuc
(INRIASaclay & 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 matrixvalued
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)
Online state and parameter estimation of nonlinear dynamic systems: a non
linear programming framework
Model based schemes for process control and online 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, largescale optimization tools leads to the application of MHE to
challenging process systems. In this talk we discuss the efficient online
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 online as new
measurements are made available. This twostep approach is enabled by two
efficient NLPbased algorithms; for the background solution the IPOPT NLP solver
is used, while sIPOPT, a related NLP sensitivity code, is used for the online
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 multirate estimation schemes is straightforward. These
resulting approaches are demon strated for the online estimation of a
nonlinear distillation process, modeled with 252 differentialalgebraic
equations.
PRESENTATION
Mark Girolami (University
College London)
MCMC Sampling for Intractable MJP Models of Chemical
Kinetics via the Linear Noise Approximation
PRESENTATION
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
~10^{5}
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 lowdimensional and
contain few parameters, hence can be analyzed semianalytically. 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.
PRESENTATION
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, onedimensional ergodic diffusion processes, [3] con
sidered a least squares approach. The problems of the changepoint of drift for
continuously observed ergodic diffusion processes have been treated in [5]. For
general Itˆo processes [6] have considered quasimaximum 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.
References
[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] Csörgő,
M.; Horváth,
L.: Limit Theorems in Changepoint 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.
PRESENTATION
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
differentialintegral 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.
References
 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). Itô
conditional moment generator and the estimation of shortrate processes. Journal
of Financial Econometrics, 1, 250–271.
PRESENTATION
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 bestsuited 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.
PRESENTATION
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 ”plugandplay” 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 highdimensional 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.
PRESENTATION
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.
PRESENTATION
CONTRIBUTED TALKS
(abstracts)
CONTRIBUTED TALKS (presentations)
Baker  Fuchs 
Gonzalez 
Hamzi  Hug 
Jaeger 
Jensen 
Knapik 
Picchini 
Prague 
Raue  Vanlier 
Vujacic
POSTERS
PRACTICAL INFORMATION
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 northeastern 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

CONTACT
For more information please contact
Mrs. Patty Koorn,
Workshop officer of
Eurandom
Sponsored by:
Last updated
250612,
by
PK
