[ Main Page | Research | Publications | Management | Grants | Industrial contracts | Courses | Conferences | ALEA INRIA team | Collaborators | Other Application Areas ]


Feynman-Kac measures and Interacting Particle systems :

Selected applications on : Statistical learning, Bayesian inference, and Hidden Markov Models

(see also : selected studies, publications & MLSS 08 Lecture notes, 2011-Sino-French Summer Institute (lecture 1, lecture 2, and lecture 3) & other application areas)


This webpage presents a selected series of articles related to the use of particle methods in Bayesian statistical learning, including 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. We also recommend to consult the related webpage concerned with particle filters and their application domains.

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





Projects homepages


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

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

  • Sequential Learning (SEQUEL project, INRIA Lille)

  • Sequential Monte Carlo homepage, particle filtering (Elena Punskaya , Department of Engineering, Cambridge University)

  • Sequential Monte Carlo Methods & Particle Filters Resources (Arnaud Doucet , Department of Statistics, Oxford University)




    Recent tutorials & Surveys


  • 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)

  • 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).

  • 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).

  • An overview of existing methods and recent advances in sequential Monte Carlo (Olivier Cappe, Simon J. Godsill and Eric Moulines)

  • Hidden Markov Models (R. Van Handel, Princeton 2008)

  • Inference in Hidden Markov Models (O. Cappé, E. Moulines, T. Ryden, 2009)

  • Bayesian Filtering: From Kalman Filters to Particle Filters, and Beyond (Zhe Chen)

  • Dynamic Linear Models with R (G. Petris, S. Petrone, P. Campagnoli, Monograph 2007 2008)

    A series of recent tutorials presenting this interacting particle methodology in a more general framework are provided below

    Ph.D. thesis


  • Sequential Monte Carlo Methods for Bayesian Filtering (Ph.D. L.C. Sing Gilbert, Hong-Kong Univ. 2008)

  • Some Statistical Topics on Sequential Data Assimilation (Ph.D. A.S. Stordal, Univ. Bergen, Norway 2008)

  • Nouvelles methodes en filtrage particulaire (K. Dahia, Univ. J. Fourier, 2005)

  • Observations bruitees d'une diffusion Estimation, filtrage, applications (Ph.D. B. Favetto, Univ. Paris Descartes, Paris 2010)

  • Particle solutions to nonlinear estimation and optimization problems (Ph.D. P. Del Moral, Paul Sabatier, Toulouse 1994)

  • Some Non-Standard Sequential Monte Carlo Methods and Their Applications (Ph.D. A. Johansen, Cambridge Univ., dec. 2006 )


    Data Assimilation

  • A One Pass Sequential Monte Carlo Method for Bayesian Analysis of Massive Datasets
    (S. Balakrishnan, D. Madigan; Rudgers Univ.)

  • Stochastic Methods for Sequential Data Assimilation in Strongly Nonlinear Systems
    (D.T. Pham, INRIA-CNRS-INPG-UJF Grenoble Univ.)

  • Sampling the Posterior : An Approach to Non Gaussian Data Assimilation
    (A. Apte, M. Hairer, A; Stuart, J. Voss; Chapell Hill North Carlolina Univ., and Warwick Univ.)

  • Filtre de Kalman d'Ensemble et Filtres Particulaires pour le Modele de Lorenz
    (V.D. Tran, V. Monbet, F. Le Gland; Univ. de Bretagne Sud et IRISA INRIA Rennes)


    Approximate Bayesian Computation style methods

  • The Monte-Carlo Method for filtering with discrete-time observations. (Del Moral, P., Jacod J., and Protter Ph)
    Probability Theory and Related Fields, vol. 120, pp. 346--368 (2001).

  • Interacting Particle Filtering With Discrete Observations. ( Del Moral, P., Jacod J. )
    Sequential Monte Carlo Methods in Practice, pp. 43-77, Statistics for Engineering and Information Science. Springer.
    Eds. A. Doucet, J. F. G. de Freitas, N. J. Gordon. (2001).

  • The Monte-Carlo Method for filtering with discrete time observations. Central Limit Theorems (Del Moral, P., Jacod J.)
    The Fields Institute Communications, Numerical Methods and Stochastics,
    Ed. T.J. Lyons, T.S. Salisbury, American Mathematical Society, (2002).

  • Portfolio Optimization with Discrete Proportional Transaction Costs under Stochastic Volatility ( H-Y. Kim, F. Viens, Purdue Univ. 2009)

  • State-Observation Sampling (L. E. Calvet, V. Czellar, HEC Paris 2011)

  • Convolution particle filters for parameter estimation in general state-space models (F. Campillo, V. Rossi, 2006)

  • Nonlinear filtering in discrete time : A particle convolution approach (V. Rossi, J.P. Vila)

  • Filtrage non lineaire en temps discret par convolution de particules (V. Rossi, J.P. Vila, 2003)

  • An Adaptive Sequential Monte Carlo Method for Approximate Bayesian Computation(Pierre Del Moral, Arnaud Doucet , Ajay Jasra)
    (preliminary version) Statistics and Computing (2011-2012).

  • On sequential Monte Carlo, partial rejection control and approximate Bayesian computation (G. Peters, Y. Fan, S.A. Sisson, 2009)

  • Strong consistency of Bayesian estimator under discrete observations and unknown transition density (A. Kohatsu-Higa, N. Vayatis, K.Yasuda, 2010)

  • Parameter estimation for hidden Markov models with intractable likelihoods (T.A. Dean, A. Jasra, S.S. Singh, G.W. Peters, 2011)



    Bayesian Methodology


  • Nonlinear Filtering : Interacting Particle Resolution.( Del Moral P., Markov Processes and Related Fields, vol. 2, no; 4, pp. 555-580, 1996)

  • Scalable Bayesian reduced order models for simulated high-dimensional multiscale dynamical systems
    (P.S. Koutsourelakis, E. Bilionis, 2010)

  • Estimation procedure for a hidden Markov chain model with applications to finance, climate data and earthquake analysis (I. Florescu and F. Levin, Stevens Institute of Technology)

  • Parameter Estimation and Asymptotic Stability in Stochastic Filtering (A. Papavasiliou, Warwick Univ.)

  • A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters.
    (P.S. Koutsourelakis, Cornell Univ. 2008 )

  • Investigations particulaires pour l'inférence statistique et l'optimisation de plans d'expériences
    (E. Parent, B. Amzal, Ph. Girard; J. Soc. Stat. France (2008))

  • Methodes particulaires et Fusions de donnees (Fr. Caron, Journees d'etude Meteo-SMAI-DSNA, Toulouse 2010)

  • An efficient computational approach for prior sensitivity analysis and cross-validation (L. Bornn, A. Doucet, and R. Gottardo, 2010 )

  • Particle approximations of the score and observed information matrix in state space models with application to parameter estimation (G. Poyiadjis, A. Doucet, S.S. Singh, Biometrika 2011 )

  • Efficient Bayesian Inference for Switching State-Space Models using Particle Markov Chain Monte Carlo Methods (N. Witheley, Ch. Andrieu, A. Doucet, 2010 )

  • Parameter Inference for Stopped Processes (A. Jasra, N. Kantas, Imperial College)

  • Likelihood-free estimation of model evidence (X. Didelot, R.G. Everitt, A.M. Johansen, D.J. Lawson, 2010 )

  • Estimating genealogies from linked marker data: a Bayesian approach (Dario Gasbarra, Matti Pirinen , Mikko J Sillanpaa and Elja Arjas, BMC Bioinformatics)

  • Sequential Monte Carlo without likelihoods (A.M. Johansen, A. Doucet, M. Davy, 2007)

  • Particle methods for maximum likelihood estimation in latent variable models (G. Peters, Y. Fan, S.A. Sisson, 2009)

  • Méhodes Monte Carlo Séquentielles Pour l'Analyse Spectrale Bayesienne. (M. Davy and P. Del Moral and A. Doucet; CNRS, Nice Sophia Antopolis Univ., UBC Vancouver )

  • Online Parameter Estimation for Partially Observed Diffusions(G. Poyiadjis, S.S. Singh, A. Doucet; Cambridge Univ., UBC Vancouver)

  • Applications of Interacting Particle Methods for Parameter Estimation in Hidden Markov Models (O. Cappe, E. Moulines, T. Ryden; CNRS, ENST, et Lund Univ.)

  • Likelihood based inference for observed and partially observed diffusions (S. Chib, M.K. Pitt, N. Shepard; Washington Univ., Warwick Univ., and Oxford Univ.)

  • A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters (P.S. Koutsourelakis)

  • Conditional likelihood estimators for hidden Markov models and stochastic volatility models (V. Genon-Catalot, T. Jeantheau, C. Laredo; Marne la Vallee University and INRA Jouy en Josas)

  • Computational Advances for and from Bayesian Analysis (C. Andrieu, A. Doucet, C.P. Robert; Bristol Univ., Cambridge Univ., and Paris Dauphine Univ.)

  • Monte Carlo Smoothing for Nonlinear Time Series (S.J. Godsill, A. Doucet, M. West; Cambridge Univ., and Duke Univ.)

  • On Sequential Monte Carlo Sampling of Discretely Observed Stochastic Differential Equations (Simo Sarkka, Helsinki Univ.)


    Stochastic Sampling Models and Stochastic Methods

  • Nonlinear Filtering : Interacting Particle Resolution.( Del Moral P., Markov Processes and Related Fields, vol. 2, no; 4, pp. 555-580, 1996)

  • Uniform stability of a particle approximation of the optimal filter derivative. Del Moral, P. and Doucet, A. and Singh, S.S.
    Technical Report CUED/F-INFENG/TR 668. Cambridge University Engineering Department. (2011)

  • Forward Smoothing Using Sequential Monte Carlo.
    Del Moral, P. and Doucet, A. and Singh, S.S. Technical Report CUED/F-INFENG/TR 638. Cambridge University Engineering Department. (2011)

  • A Backward Particle Interpretation of Feynman-Kac Formulae
    Pierre Del Moral, Arnaud Doucet and Sumeetpal S. Singh (HAL-INRIA RR-7019 (07-2009)) vol 44, no. 5, pp. 947--976 M2AN (sept. 2010)

  • Efficient Likelihood Evaluation of State-Space Representations (D.N. DeJong , G. V. Moura, R. Leisenfeld, J.F. Richard, 2011)

  • Sequential Monte Carlo Methods for Normalized Random Measure with Independent Increments Mixtures (J.E. Griffin, 2011)

  • Stability of Sequential Markov Chain Monte Carlo Methods (A. Eberle, C. Marinelli, Bonn Univ.)

  • Parameter Estimation and Asymptotic Stability in Stochastic Filtering (A. Papavasiliou, Warwick Univ.)

  • Bayesian filtering. From Kalman filters to Particle filters and beyond (Zhe Chen, McMaster Univ. Canada.)

  • Gradient Feynman-Kac flows (P.A. Coquelin, R. Deguest, R. Munos, CMAP et INRIA Futur Lille)

  • Sensitivity analysis in HMMs with application to likelihood maximization (P.A. Coquelin, R. Deguest, R. Munos)

  • Uncertainty quantification in complex systems using approximate solvers. (Phaedon-Stelios Koutsourelakis, 2008)

  • Equilibrium Sampling from Nonequilibrium Dynamics (M. Rousset, G. Stoltz; CERMICS)

  • Smoothing Algorithms for State Space Models (M. Briers, A. Doucet, S. Maskell; QuinetiQ and Cambridge Univ.)

  • Fix Lag Sequential Monte Carlo (A. Doucet, S. Senecal; Cambridge Univ. and The Institute of Statistical Mathematics Tokyo)

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

  • Open-loop regulation and tracking control based on a genealogical decision tree (K. Najim, E. Ikonen and P. Del Moral; Oulu Univ., Toulouse Univ., Nice Sophia Antipolis Univ.)

  • On a class of genealogical and interacting Metropolis Models. (Del Moral P., Doucet A. )
    Séminaire de Probabilités XXXVII, Ed. J. Azéma and M. Emery and M. Ledoux and M. Yor, Lecture Notes in Mathematics 1832, Springer-Verlag Berlin, pp. 415--446 (2003).

  • On the stability of interacting processes with applications to filtering and genetic algorithms (Del Moral P., Guionnet A. Annales de l'Institut Henri Poincaré, Vol. 37, No. 2, 155-194 (2001)).

  • 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).

  • 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).

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

  • 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).