Dynamical Stochastic Modeling in Biology

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MaPhySto Centre for Mathematical Physics and Stochastics Funded by The Danish National Research Foundation	DYNSTOCH Statistical Methods for Dynamical Stochastic Models EU Research Training Network

MaPhySto-DYNSTOCH workshop INFERENCE FOR PARTIALLY OBSERVED PROCESSES

MaPhySto-DYNSTOCH Workshop on

INFERENCE FOR PARTIALLY OBSERVED PROCESSES

Monday June 7 - Wednesday June 9, 2004
Department of Mathematical Sciences, University of Copenhagen

Organizers:

Martin Jacobsen (University of Copenhagen)

Michael Sørensen (University of Copenhagen)

The workshop is organized jointly by MaPhySto (The Danish National Research Foundation: Network in Mathematical Physics and Stochastics) and DYNSTOCH.

About the workshop:

The main purpose of the workshop is to discuss problems of statistical inference for models involving stochastic processes in discrete or continuous time, where complete observation of the process (on a finite time interval say) is not possible. It may of course be the observation pattern itself (e.g. discrete observations from a process in continuous time) that leads to this lack of observations, but it may also be caused by the need for introducing a large and flexible model in order to fit the data, where the flexibility is often obtained by the direct introduction of unobserved quantities such as auxiliary stochastic processes. Examples of partially observed processes are discretely observed diffusions, hidden Markov models, stochastic volatility and other models from finance, various types of time-series models, models with noisy observations and many more. Typically, the likelihood function for the actual observations is analytically untractable, and must either be maximised numerically or one must resort to suitable estimating functions. In many cases, by sheer computing power, it is in fact possible to obtain sensible parameter estimates, but there is certainly still a need to discuss more systematically when and why the methods work: how can one be certain that an estimating equation has only one solution or that some kind of likelihood, which is 'maximised' numerically, is not full of local maxima? How can one know that an estimator is consistent and perhaps even asymptotically Gaussian? And how can one determine which parameter functions it is at all possible to estimate from the partial observations - or what to do if not all the parameters are identifiable or some parameters are nearly non-identifiable? These basic problems of inference are certainly made more difficult when considering models that are only partially observed. It is hoped that the workshop will help to understand better and even raise awareness concerning these important issues! The workshop is co-organised by DYNSTOCH, a research training network financed by The Fifth Framework Programme of the European Commission , and placed in continuation of The Fifth DYNSTOCH Workshop to be held in Copenhagen 3.-5. June 2004.
Please registrer here

Invited speakers:

Ole Barndorff-Nielsen (Aarhus), Mathieu Kessler (Cartagena), Hans-Ruedi Kunsch (Zurich), Tobias Ryden (Lund), Neil Shephard (Oxford).

Participants (*: contributed talk):

Ramon van den Akker (Amsterdam), Sibylle Arnold (Zurich), Enrico Bellone (Cambridge), Bo Martin Bibby (Copenhagen), Svetlana Bizjajeva (Lund), Christian Brandt* (Mainz), Olivier Cappé (Paris), Silvia Centanni* (Perugia), Jeffrey Collamore (Copenhagen), Dominique Dehay (Rennes), Susanne Ditlevsen (Copenhagen), Mervi Eerola (Helsinki), Julie Lyng Forman (Copenhagen), Dario Gasbarra* (Helsinki), Valentine Genon-Catalot (Paris), Anne Gegout-Petit (Bordeaux), Raouf Ghomrasmi (Cartagena), Shota Gugushvili (Amsterdam), Henrik Hult (Copenhagen), Martin Jacobsen* (Copenhagen), Raffi Keheyan (Copenhagen), Franz Konecny* (Vienna), Francois Le Gland (Rennes), Erik Lindstrom (Lund), Bo Markussen* (Copenhagen), Hiroki Masudo (Kyushu), Roderick McCrorie* (Essex), Frank van der Meulen (Amsterdam), Kim Nolsøe (Cartagena), Ace North (Helsinki), Jimmy Olsson (Lund), Alessandro Platania (Cambridge), Mark Podolski (Bochum), Anders Rahbek (Copenhagen), Martin Richter (Copenhagen), Yuji Sakamoto (Hiroshima), Diegor Salmeron (Cartagena), Jurgen Schmiegel (Aarhus), Ib Skovgaard (Copenhagen), Peter Spreij* (Amsterdam), Gunnhildur Steinbakk (Oslo), Geir Storvik (Oslo), Helle Sørensen (Copenhagen), Michael Sørensen (Copenhagen), Helgi Tomasson (Reykjavik), Masayuki Uchida* (Kyushu), Nakahiro Yoshida* (Tokyo).

For more information, please contact the organizers.

Programme:

Monday June 7

09:30-10:30 Registration

10:30-10:35 Welcome

10:35-11:25 Hans-Ruedi Künsch (Zürich): 1. The particle filter for general state space models: central limit theorems and asymptotic variances.

11:25-11:50 Coffee

11.50-12.25 Roderick McCrorie (Essex): Identifying the parameters of vector Ornstein-Uhlenbeck processes on the basis of discrete data.

12:25-13:00 Masayuki Uchida (Kyushu): Approximate martingale estimating functions under small perturbations of dynamical systems.

13:00-14:00 Lunch

14:00-14:35 Christian Brandt (Mainz): Reconstruction of a discretely observed branching diffusion with immigration.

14:35-15:10 Nakahiro Yosida (Tokyo): Estimation for a stochastic differential equation with jumps: sampling and asymptotic expansions.

15:10-15:30 Coffee

15:30-16:40 Mathieu Kessler (Cartagena): Statistical inference for a random scale perturbation of an AR(1) process.

Tuesday June 8

09:30-10:40 Neil Shephard (Oxford): An introduction to bipower variation.

10:40-11:10 Coffee

11:10-11:50 Hans-Ruedi Künsch (Zürich): 2. Partially observed stochastic differential equations: the approach of van Eyink et al and its application to the particle filter.

11:50-12:25 Franz Konecny (Vienna): Optimal nonlinear and linear filtering of Poisson cluster processes

12:25-13:00 Silvia Centanni (Perugia): A simulation approach to filtering and estimation of doubly stocahstic Poisson processes with marks.

13:00-14:00 Lunch

14:00-15:10 Ole Barndorff-Nielsen (Aarhus): The mathematics of bipower variation.

15:10-15:30 Coffee

15:30-16:05 Peter Spreij (Amsterdam): Nonparametric volatility density estimation.

16:05-16:40 Bo Markussen (Copenhagen): Renormalization in Brownian calculus for the purpose of inference.

Wednesday June 9

09:30-10:40 Tobias Rydén (Lund): Likelihood inference in state space models -- some theoretical and practical aspects.

10:40-11:15 Coffee

11:15-11:50 Dario Gasparra (Helsinki): Hidden Markov model for estimation of parental limkage phase and short map distances using pooled haploid tissues.

11:50-12:25 Martin Jacobsen (Copenhagen): It is not a perfect world: estimation from discrete observations of the CKLS diffusion model.

The time table includes time for discussion: invited speakers 10 minutes except Könsch 1, 5 minutes, 2, 10 minutes. Contributed talks 5 minutes.

Monday June 7
09:30-10:30	Registration
10:30-10:35	Welcome
10:35-11:25	Hans-Ruedi Künsch (Zürich): 1. The particle filter for general state space models: central limit theorems and asymptotic variances.
11:25-11:50	Coffee
11.50-12.25	Roderick McCrorie (Essex): Identifying the parameters of vector Ornstein-Uhlenbeck processes on the basis of discrete data.
12:25-13:00	Masayuki Uchida (Kyushu): Approximate martingale estimating functions under small perturbations of dynamical systems.
13:00-14:00	Lunch
14:00-14:35	Christian Brandt (Mainz): Reconstruction of a discretely observed branching diffusion with immigration.
14:35-15:10	Nakahiro Yosida (Tokyo): Estimation for a stochastic differential equation with jumps: sampling and asymptotic expansions.
15:10-15:30	Coffee
15:30-16:40	Mathieu Kessler (Cartagena): Statistical inference for a random scale perturbation of an AR(1) process.
Tuesday June 8
09:30-10:40	Neil Shephard (Oxford): An introduction to bipower variation.
10:40-11:10	Coffee
11:10-11:50	Hans-Ruedi Künsch (Zürich): 2. Partially observed stochastic differential equations: the approach of van Eyink et al and its application to the particle filter.
11:50-12:25	Franz Konecny (Vienna): Optimal nonlinear and linear filtering of Poisson cluster processes
12:25-13:00	Silvia Centanni (Perugia): A simulation approach to filtering and estimation of doubly stocahstic Poisson processes with marks.
13:00-14:00	Lunch
14:00-15:10	Ole Barndorff-Nielsen (Aarhus): The mathematics of bipower variation.
15:10-15:30	Coffee
15:30-16:05	Peter Spreij (Amsterdam): Nonparametric volatility density estimation.
16:05-16:40	Bo Markussen (Copenhagen): Renormalization in Brownian calculus for the purpose of inference.
Wednesday June 9
09:30-10:40	Tobias Rydén (Lund): Likelihood inference in state space models -- some theoretical and practical aspects.
10:40-11:15	Coffee
11:15-11:50	Dario Gasparra (Helsinki): Hidden Markov model for estimation of parental limkage phase and short map distances using pooled haploid tissues.
11:50-12:25	Martin Jacobsen (Copenhagen): It is not a perfect world: estimation from discrete observations of the CKLS diffusion model.