Atelier du GSIG, SSC 2009

Méthodes de Monte Carlo pour l’intégration et l’optimisation

Don McLeish, Université de Waterloo, Dimanche, 31 mai, 2009, 9:00 a.m. – 12:00 p.m.; 1:30 p.m. – 4:00 p.m.

Computer simulation brings the power and flexibility of more realistic complex stochastic models to the desktop of the practitioner and amateur alike. The aim of this workshop is to provide participants with an understanding of stochastic simulation methodology and the extraordinary scope for its applications, explore basic techniques of simulation and variance reduction, and methods for estimation and optimization of noisy systems. Such methods are useful for example in the calibration of financial models, parameter estimation in a complex statistical model and in adaptive optimization techniques. Topics Include

• Uniform and non-uniform random number generation. Inverse transform and Acceptance Rejection, Poisson Processes.
• Variance Reduction: Antithetic Random numbers, Control Variates, Conditioning, Stratified Sampling, Importance Sampling, Rare event simulation, Combining estimators, Low Discrepancy Sequences and Quasi Monte Carlo.
• Simulating Stochastic Processes: Markov Chain Monte Carlo (MCMC), Gibbs Sampler, Simulation and interpolation of diffusions.
• Root-finding and Optimization of noisy systems: Stochastic optimization, the cross-entropy method, simulated annealing.