Stochastic Simulation

Summary

The student who follows this course will get acquainted with computational tools used to analyze systems with uncertainty arising in engineering, physics, chemistry, and economics. Focus will be on sampling methods as Monte Carlo, quasi Monte Carlo, Markov Chain Monte Carlo.

Content

  • Random variable generation
  • Simulation of random processes
  • Simulation of Gaussian random fields.
  • Monte Carlo method; output analysis
  • Variance reduction techniques (antithetic variables, control variables, importance sampling, stratification)
  • Quasi Monte Carlo methods
  • Markov Chain Monte Carlo methods (Metropolis-Hasting, Gibbs sampler) Other topics that may be addressed if time allows:
  • Stochastic optimization (stochastic approximation, simulated annealing)
  • Rare events simulations
  • Estimation of derivatives
  • Filtering problem; particle filters

Learning Prerequisites

  • Required courses
    • basic Probability and Statistics; Numerical Analysis;
  • Recommended courses
    • Applied Stochastic Processes (or equivalent)
  • Important concepts to start the course
    • Knowledge of basic courses in mathematics, probability, statistics and numerical analysis.
    • Some experience of computer programming is assumed.

Learning Outcomes

By the end of the course, the student must be able to:

  • Analyze the convergence of sampling algorithms
  • Implement sampling methods for different stochastic processes
  • Compare the efficiency of different sampling algorithms
  • Choose appropriate sampling algorithms
  • Propose efficient sampling methods for different stochastic problems

References

  • Simulation by Sheldon M. Ross
  • Stochastic Simulation by Asmussen and Glynn
  • Monte Carlo Statistical Methods by Robert and Casella
  • Handbook of Monte Carlo Methods by Kroese, Taimre, Botev
  • Handbook of Markov Chain Monte Carlo by Brooks, Gelman, Jones, Meng