This course will cover topics in the general area of Monte Carlo methods and their application domains. The topics include Markov chain Monte Carlo and Sequential Monte Carlo methods, Genetic algorithms, Quantum and Diffusion Monte Carlo techniques, as well as branching and interacting particle methodologies. The lectures cover discrete and continuous time stochastic models, starting from traditional sampling techniques (perfect simulation, Metropolis-Hasting, and Gibbs-Glauber models) to more refined methodologies such as self interacting and mean field type Interacting Particle Systems methodologies. To name a few, forward/backward particle filters, Ensemble Kalman filers, interacting Kalman filters, Sequential Monte Carlo, genealogical tree based samplers, particle Gibbs and particle Metropolis-Hastings, interacting Metropolis-Hastings, multiple-level splitting, and many others.
The course offers a pedagogical introduction to the theoretical foundations of these advanced stochastic models, combined with a series of concrete illustrations taken from different application domains. The applications considered in these lectures will range from Bayesian statistical learning (hidden Markov chain, statistical machine learning), risk analysis and rare event sampling (mathematical finance, and industrial risk assessment), operation research (global optimization, combinatorial counting and ranking), advanced signal processing (stochastic nonlinear filtering and control and data association), computational and statistical physics (Feynman-Kac formulae on path spaces, molecular dynamics, Schrodinger’s ground states, Boltzmann-Gibbs distributions, and free energy computation). Some textbooks which can be useful for supplemental reading are:
- Stochastic Processes: From Applications to Theory. P. Del Moral, & S. Penev Chapman and Hall/CRC (2016).
- Mean field simulation for Monte Carlo integration. P. Del Moral. Chapman & Hall/CRC Monographs on Statistics & Applied Probability (2013).
- Feynman-Kac formulae. Genealogical and interacting particle approximations. P. Del Moral. Springer New York. Series: Probability and Applications (2004).
- Branching and Interacting Particle Systems Approximations of Feynman-Kac Formulae.P. Del Moral & L. Miclo (2000). Seminaire de Probabilities, Lecture Notes in Mathematics.
- Fundamentals of Stochastic Filtering. A. Bain and D. Crisan. Springer, Stochastic Modelling and Applied Probability, Vol. 60 (2009).
- Inference in Hidden Markov Models. O. Capp_e, E. Moulines, and T. Ryden. Springer series in Statistics (2005).
- An Introduction to Sequential Monte Carlo. N. Chopin , O. Papaspiliopoulos, Springe Series in Statistics (2020).
The lectures will be held as below:
Wed 13 March 1pm-3pm
Wed 20 March 1pm-3pm
Thu 21 March 10am-12pm
Wed 27 March 1pm-3pm
- Short bio:
- Since 2007, Pierre Del Moral is a Research Director (first class since 2011) at INRIA.
- In 2014-2016, he was Professor at the School of Mathematics and Statistics of the University of New South Wales in Sydney, Australia.
- In 2011-2014, he also joined the Applied Mathematical Center of the Polytechnique School in Paris as a Professor “charge de cours”. After a masters degree in pure mathematics in 1989 in the University Paul Sabatier in Toulouse in the field of Cohomology, Dynamical Systems, Hyperbolic Geometry and Algebraic Geometry, he joined the LAAS Automation and Control Institute of the C.N.R.S. (Centre National de la Recherche Scientifique). He obtained a PhD in 1994 in signal processing with one of the first study on stochastic particle methods in nonlinear filtering and optimal control problems. From 1992 to 1995, he also served as a lecturer in mathematics at the “Ecole Nationale Superieure de l’Aeronautique et de l’Espace”, and as a research engineer in the company Steria-Digilog, working on particle filters in tracking problems arising in radar and sonar signal processing problems.
- In 1995, he joined the C.N.R.S. as a junior research fellow in mathematics and physics at the Probability and Statistical department of the University Paul Sabatier in Toulouse, and he received in 2002 the higher degree of research (H.D.R.) in Mathematics. In 2004, he joined the Lab. J. A. Dieudonne of the University of Nice and Sophia-Antipolis as a full Professor of Mathematics in the field of Probability and stochastic processes. He has also been a visiting professor in the russian academy of sciences as well as in several international universities, including Beijing, Cambridge, Edmonton, Erlangen, La Havana, Helsinki, Melbourne, Montreal, Moscow, St Petersbourg, Sydney, Tokyo, Oxford, Princeton, Purdue, and Wuhan University.
- Pr. Del Moral is one of the principal designers of the modern and the recently developing theory on stochastic particle methods in nonlinear filtering, numerical physics, engineering and information theory. He has published over 200 papers in pure and applied probability journals, and he is the author of the books “Mean field simulation for Monte Carlo integration”, Chapman and Hall/CRC Press, monographs on Stats and Applied Probability (2013), and “Feynman-Kac formulae. Genealogical and interacting particle approximations”, Springer New York, Series: Probability and Applications (2004). His current research interests are : bayesian inference and nonlinear filtering, multiple targets tracking problems, rare event analysis, calibration and uncertainty propagations in numerical codes, particle absorption models, Monte Carlo methods, stochastic algorithms, branching processes and interacting particle systems.