Feynman-Kac measures and Interacting Particle systems :

Selected applications on : Risk analysis and Rare event simulation

(see also : AREVA 2011, IHP 2010, Bonn 2006, Bonn 2008 , 2011-Sino-French Summer Institute (lecture 1, lecture 2, and lecture 3) & other application areas)

This webpage presents an overview of resources concerned with stochastic particle methods in risk analysis and rare event simulation.

Stochastic Hybrid Systems, Aircraft Conflits
Optics Communications Networks
Financial risk analysis
Biochemical networks
Satellite versus debris collisions
Networks and Queueing Systems
Rare event particle sampling models
Feynman-Kac particle models and performance analysis
This list of topics is clearly far from being exhaustive, and it is partially biased towards my work on stochastic particle models. More references and links to this subject can be added on demand. This webpage also contains some articles on the particle and sequential Monte Carlo methodology, and the performance analysis of these algorithms.

Software BiiPS

The software BIIPS is a general software developed by the INRIA team ALEA for bayesian inference with interacting particle systems, a.k.a. Sequential Monte Carlo methods. A demonstration of the BiiPS software for estimating the stochastic volatility of financial data can be found in
- BIIPS : Bayesian inference with interacting Particle Systems in Finance,

Rare events, projects homepages

Advanced Learning Evolutionary Algorithms (ALEA project, Centre INRIA Bordeaux Sud-Ouest)

Mathematical Science Fondation of Paris & AREVA, Meeting on Rare event models

Calibration and uncertainty propagation in numerical codes for IFREMER (ALEA industrial project with IFREMER)

Rare Event Simulation (ARC RARE, INRIA)

Applications of Interacting Particle Systems to Statistics (IRISA, INRIA Rennes)

Rare Event, announcements webpage (Communication Networks, Bremen University)

Complex physical and chemical systems (David Chandler Group, Department of Chemistry, University of California, Berkeley)

Slides, Lecture notes

Simulation d'evenements rares Slides GT Projet AST&Risk Univ. Lyon, december 2008.

An introduction to particle simulation of rare events Workshop OPUS, IHP Paris 2010.

Horizon Maths, Les maths se devoilent aux industriels; Fondation Science Maths de Paris, Tour AREVA, dec. 2011.
(programme) ( lecture notes (in french) & (presentation video) )

Sino-French Summer Institute 2011.Beijing, China, June 13-25, 2011. ((lecture note 1), (lecture note 2), and (lecture note 3))

INRIA Workshop on Statistical Learning Institut Henri Poincaré Paris, December 5-6, 2011 ( (lecture notes) )

University of Cambridge, Statistics Laboratory seminar, Feb. 2010. (lecture notes)

Importance splitting for rare event simulation F. Cerou, Simulation of hybrid dynamical systems and applications to molecular dynamics, IHP Paris 2010.

Sampling per Mode for Rare Event Simulation in Switching Diffusions (Jaroslav Krystul, François Le Gland, and Pascal Lezaud, slides RESIM 2010)

Rare Event Simulation for a Static Distribution A. Guyader, CMAP Polytechnique 2009

Particle Methods for Rare Event Monte Carlo Paul Dupuis, ASEAS, Arlington, VA 2009

A variance reduction method for computing VaR Nadia Oudjane, Journees MAS 2008

Option pricing: a new adaptive Monte carlo method VaR Nadia Oudjane, J.M. Marin

Exact and Efficient Simulation of Correlated Defaults Kay Giesecke, Management Science and Engineering Stanford University

Introduction to Rare Event Simulation for Processes with Light Tailed Increments Thomas Dean Signal Processing and Communications Laboratory 2009

Simulation estimators in a dynamic model for food contaminant exposure Jessica Tressou; Food Risk Analysis Methodologies 2007

Sequential Monte Carlo: Selected Methodological Applications Adam M. Johansen. Warwick University Centre for Scientific Computing

Stochastic Hybrid Systems, Aircraft Conflits

Modelling of stochastic hybrid systems with applications to accident assessment (J. Krystul Ph.D. thesis, University of Twente 2006)

Sequential Monte carlo Simulation of Rare Event Probability in Stochastic Hybrid Systems (J. Krystul, H. P. Blom; Twente Univ., and National Aerospace Lab. Amsterdam)IFAC 2005

Probabilistic Reachability Analysis for Large Scale Stochastic Hybrid Systems (Henk A.P. Blom, G.J. (Bert) Bakker and Jaroslav Krystul, CDC 2007)

Free flight safety risk modelling and simulation (H.A.P. Blom, G.J. Bakker, B. Klein Obbink and M.B. Klompstra; International Conference on Research in Air Transportation ICRAT 2006, at Beograd, Serbia, June 24-28, 2006.)

Air traffic complexity and the interacting particle system method: An integrated approach for collision risk estimation (Maria Prandini, Henk A.P. Blom and G.J. (Bert) Bakker; 2011 American Control Conference)

Trans-dimensional simulation for rare event estimation on stochastic hybrid systems (N. Kantas, J.M. Maciejowski; iFly project 2007 )

Sequential Monte carlo Simulation for the Estimation of Small Reachability Probabilities for Stochastic Hybrid Systems (J. Krystul, H. P. Blom; Twente Univ., and National Aerospace Lab. Amsterdam)

Sequential Monte carlo Simulation of Collision Risk in Free Flight Air Traffic (H. P. Blom, G.J. Bakker, J. Krystul, M.H.C. Everdij, B.K. Obbink, M.B. Klompstra; Twente Univ.)

Probabilistic Aircraft Conflict detection (M. Prandini, O.J. Watkins; Brescia and Cambridge Univ.)

Branching and Interacting Particle Interpretations of Rare Event Probabilities. Del Moral P., Lézaud P., Stochastic Hybrid Systems: Theory and Applications., 51 p. (2006).

Modelling and estimation of separation criteria for airbone time-based spacing operation (I. R. de Oliveira, Paulo S. Cugnasca, Henk A.P. Blom, Bert (G.J.) Bakker; National Aerospace Laboratory NLR, The Netherlands)

Optics Communications

Genealogical Particle Analysis of Rare Events Del Moral P., Garnier J., The Annals of Applied Probability Vol. 15, pp. 2496-2534 (2005).

Simulation of Rare Events in Fiber Optics by Interacting Particle Systems Garnier J., Del Moral P. Optics Communications Vol. 257, pp. 205-214 (2006).

Grandes deviations et erreurs de transmission par solitions dans les fibres optiques (E. Gautier, A. Debussche; CREST INSEE, IRMAR et ENS Cachan Bretagne)

Financial risk analysis

Interacting Particle Systems for the Computation of Rare Credit Portfolio Losses (Rene Carmona, Jean-Pierre Fouque, Douglas Vestal)

Particle methods for the estimation of credit portfolios loss distribution (R. Carmona, S. Crepey, Bendheim Center for Finance ORFE, Princeton University, and Departement de Mathematiques Universite d'Evry Val d'Essonne, 2009)

Importance sampling and interacting particle systems for the estimation of markovian credit portfolio loss distribution. (R. Carmona, S. Crepey, Bendheim Center for Finance ORFE, Princeton University, and Departement de Mathematiques Universite d'Evry Val d'Essonne, 2009)

Interacting path systems for credit portfolios risk analysis (P. Del Moral, Fr. Patras, HAL-INRIA 7169, 2010)

Sequential Importance Sampling And Resampling For Dynamic Portfolio Credit Risk (Shaojie Deng Kay Gieseckey Tze Leung Lai, Operation Research 2010)

Exact and Efficient Simulation of Correlated Defaults (K. Giesecke, H. Kakavand, M. Mousavi, and H. Takada; SIAM Financial Math 2010)

Option pricing: a new adaptive Monte carlo method VaR Nadia Oudjane, J.M. Marin

Exact and Efficient Simulation of Correlated Defaults Kay Giesecke, Management Science and Engineering Stanford University

Satellite versus debris collisions

Estimating satellite versus debris collision probabilities via the adaptive splitting technique (Rudy Pastel, ONERA 2011)

Offshore structure reliability

Z. Guede, P. Del Moral, E. Tantar, and A. Tantar
Application of a particle filter based subset simulation metho to the reliability assessment of marine structure.
Proceedings of the 31th International Conference on Ocean, Offshore and Artic Engineering, OMAE2012, July 1-6, 2012, Rio de Janeiro, Brazil (2012)

Networks and Queueing Systems

Simulation of Rare Event in Queueing Systems (Elena Rashkova, Dimitar Radev Department of Communication Technique and Technologies, University of Rousse, 2008)

Computer simulation of rare event for M/M/1/N queuing system (Elena Rashkova, Dimitar Radev; 2007 international conference on Computer systems and technologies)

Rare Event Simulation of Stochastic Activity Networks Using Partition of the Region Technique (A.J. Bidgoly, M.A. Azgomi; Univ. Teheran, Iran)

Rare event simulation

Branching and Interacting Particle Interpretations of Rare Event Probabilities. Del Moral P., Lézaud P., Stochastic Hybrid Systems: Theory and Applications., 51 p. (2006).

On Adaptive Resampling Procedures for Sequential Monte Carlo Methods (joint work with Arnaud Doucet, Ajay Jasra, Statistics and Computing (2011))

Sequential Monte Carlo for Rare event estimation (HAL-INRIA RR-6792 (2009)) F. Cerou, P. Del Moral, T. Furon, A. Guyader; Statistics and Computing, DOI: 10.1007/s11222-011-9231-6 (2011).

A sequential Monte Carlo approach to computing tail probabilities (Hock Peng Chan, and B. Tze Leung Lai; National University of Singapore and Stanford 2010)

An overview of importance splitting for rare event simulation Jerome Morio, Rudy Pastel, and Francois Le Gland 2010.

Limit Theorems for multilevel splitting algorithms in the simulation of rare events (F. Cerou, P. Del Moral, F. LeGland, P. Lezaud) Proceedings of the 2005 Winter Simulation Conference M. E. Kuhl, N. M. Steiger, F. B. Armstrong, and J. A. Joines, eds. (2005).

Some recent improvements to importance splitting ( F. Cerou, P. Del Moral, A. Guyader, F. LeGland, P. Lezaud, H. Topart) Proceedings of 6th International Workshop on Rare Event Simulation, Bamberg, Germany (2006).

Adaptive Multilevel Splitting for Rare Event Analysis (F. Cerou, A. Guyader; IRISA-INRIA Rennes)

Splitting for Rare Event Simulation (P. Lecuyer, B. Tuffin; Montreal Univ. and IRISA-INRIA Rennes)

Splitting with Weight Windows to Control the Likelihood Ratio in Importance Sampling (P. Lecuyer, B. Tuffin; Montreal Univ. and IRISA-INRIA Rennes)

Sampling per Mode for Rare Event Simulation in Switching Diffusions (Jaroslav Krystul, François Le Gland, and Pascal Lezaud, 2010)

Efficient Simulation for Large Deviation Probabilities of Sums of Heavy tailed Random Variables (J.H. Blanchet, J. Liu; Harvard Univ.)

Efficient Monte Carlo Simulation via The Generalized Splitting Method (Zdravko I. Botev, Dirk P. Kroese, 2010)

State-dependent Importance Sampling for Rare-event Simulation: An Overview and Recent Advances (J.H. Blanchet, H. Lam; Columbia and Boston Univ. 2011)

Sequential Monte Carlo Samplers for Rare Events (A.M. Johansen, P. Del Moral, A. Doucet; Cambridge Univ., Nice-Sophia Antipolis Univ, UBC Univ. Vancouver)

Simulation of diffusions by means of importance sampling paradigm (Madalina Deaconu and Antoine Lejay; Ann. Appl. Probab. Volume 20, Number 4 (2010)).

Estimation of rare events probabilities in computer experiments (Yves Auffray, Pierre Barbillon, Jean Michel Marin (2011)).

A multi-resolution Bayesian framework for the identification of spatial variability of material properties (P.S. Koutsourelakis; Safety, Reliability and Risk of Structures, Infrastructures and Engineering Systems 2010)

Accurate Uncertainty Quantification Using Inaccurate Models (P.S. Koutsourelakis Cornell University, 2010)

Genealogical Particle Analysis of Rare Events Del Moral P., Garnier J., The Annals of Applied Probability Vol. 15, pp. 2496-2534 (2005).

Genealogical Models in Entrance Times Rare Event Analysis F. Cerou, Del Moral P. Le Gland F., Lezaud P. Alea, Latin American Journal of Probability And Mathematical Statistics (2006).

An Introduction to Interacting Simulated Annealing (Juergen Gall, Bodo Rosenhahn, and Hans-Peter Seidel, Max-Planck Institute for Computer Science)

The Gibbs Cloner for Combinatorial Optimization, Counting and Sampling (R. Rubinstein, Technion 2008)

Effective branching splitting method under cost contraint (Agnes Lagnoux-Renaudie 2007)

Randomized Algorithms with Splitting: Why the Classic Randomized Algorithms do not Work and how to Make them Work (R. Rubinstein, Technion 2009)

Exact distributions and Sequential Monte Carlo for Change Point Analysis (Christopher F. H. Nam, John A. D. Aston and Adam M. Johansen, University of Warwick, 2010)

Monte Carlo Methods (Adam M. Johansen and Ludger Evers, Bristol University, Lecture Notes 2007)

Feynman-Kac particle models and performance analysis

Particle Methods: An introduction with applications (Pierre Del Moral, Arnaud Doucet) HAL-INRIA RR-6991 [50p] (2009), 2008 Machine Learning Summer School, Springer LNCS/LNAI Tutorial book no. 6368 (2010-2011).

Pierre Del Moral, Peng Hu, Liming Wu
On the concentration properties of Interacting particle processes HAL-INRIA RR-7677 (2011),
Foundations and Trends in Machine Learning, Vol. 3, No. 3 - 4, 225-389 (2012). (online article, 167 pages)

A non asymptotic variance theorem for unnormalized Feynman-Kac particle modelsFr. Cerou, P. Del Moral, A. Guyader HAL-INRIA RR-6716 (2008) . Annales de l'Institut Henri Poincare Probab. Statist. Volume 47, Number 3, 629-649 (2011).

Sequential Monte Carlo Samplers (Del Moral P., Doucet A., Jasra A) Journal of the Royal Society of Statistics, Series B. vol. 68, No. 3, pp. 411-436 (2006).

Particle Markov chain Monte Carlo methods (Ch. Andrieu, Arnaud Doucet, R. Holenstein , J. R. Statist. Soc. B (2010))

Sequentially Interacting Markov Chain Monte Carlo (A. Doucet, A.E. Brockwell; UBC and Carnegie Mellon Univ.)

On Adaptive Resampling Procedures for Sequential Monte Carlo Methods(Del Moral P., Doucet A., Jasra A) HAL-INRIA RR-6700 [46p], (Oct. 2008). To appear in Bernoulli (2011-2012).

Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae with Applications to Non-Linear Filtering (Del Moral P., Miclo L.)
Séminaire de Probabilités XXXIV, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor. Lecture Notes in Mathematics, Springer-Verlag Berlin, Vol. 1729, 1-145 (2000).

Feynman-Kac Formulae, Genealogical and Interacting Particle Systems with Applications Del Moral P., Springer New York; Springer Heidelberg,
Series: Probability and its Applications, [585 pages] (April 2004).