Simulation (7 ECTS)

    Course Code: 
    6125
    Semester: 
    6th
    Elective Courses
    Διδάσκων: 

    DELLAPORTAS PETROS

    Generating uniform random variables, reductive generators, random number tests, methods of generating random numbers. The inversion method, the rejection method, component method, other methods. Methods for specific distributions. Dispersion reduction techniques and the Monte Carlo integration: Monte Carlo simulation, significance sampling, opposite random variables, control random variables. Generating dependent random variables: ranked sample, exponential spaces, multivariate normal distribution, Poisson process, Markov chains, random Markov fields, Gibbs sampler, Particle filtering.

    Recommended Reading

    • Δελλαπόρτας, Π. (1994). Στοχαστικά Μοντέλα και Προσομοίωση. Σημειώσεις παραδόσεων, τμήμα Στατιστικής, Οικονομικό Πανεπιστήμιο Αθηνών. Διαθέσιμες στη διεύθυνση http://www.stat-athens.aueb.gr/~ptd/simulation.ps.
    • Devroye, L. (1986). Non-Uniform Random Variable Generation, Springer-Verlag, New York.
    • Ripley, Brian D. (1987). Stochastic Simulation, John Wiley, New York.
    • Robinson, S. (2004). Simulation: The Practice of Model Development and Use, Wiley, Chichest, UK.
    • Robert, C., Casella, G. (2010). Introducing Monte Carlo Methods with R. Springer

    (old title: Stochastic Models and Simulation)