Computational Statistics and Simulation (7 ECTS)

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

    DELLAPORTAS PETROS

    Generation of uniform random variables: congruential generators, tests of random numbers, methods for generating random variables. Inverse transform method, rejection method, composition method, other methods. Methods for specific distributions.Variance reduction techniques and Monte Carlo integration: importance sampling, antithetic random variables, control variates. Generation of dependent random variables: order statistics, exponential spacings, multivariate normal distribution, Poisson process, Markov chains, Markov random fields, Gibbs sampler. Markov Chain Monte Carlo. Particle filtering. Bootstrap: the basic idea. Nonparametric and parametric bootstrap. Standard errors and confidence intervals using bootstrap. Hypothesis testing. Bootstrap for linear regression. Bootstrap for complex data structures, block bootstrap. Jackknife and other resampling schemes. Randomization-based hypothesis testing. Exact and approximate tests. Estimation of the p-value. ANOVA, tests of correlation, tests for contingency tables, Fisher's exact test. 

    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)