79192 - Computational Statistics

Course Unit Page

Academic Year 2018/2019

Learning outcomes

The student will learn computational techniques useful in the context of classical and bayesian estimation. In particular, the student will be able to: - find estimates for one or more parameters using iterative algorithms; - evaluate the bias and the precision of the estimates using resampling methods. The student will be able to implement all the computational techniques studied during the course with the statistical software R. Furthermore, the student will be able to perform real data analyses in a critical way in terms of both choice of the best technique to apply and interpretation of results.

Course contents

Introduction to computational statistics and R programming.

Random Variable Generation. Uniform simulation, the inverse transform, general transformation methods, discrete distributions.

Monte Carlo Integration. Introduction, classical Monte Carlo integrazione. Importance sampling.

Monte Carlo Optimization. Introduction, numerical optimization methods, stochastic search (basic solutions, stochastic gradient methods, simulated annealing), stochastic approximation (optimizing Monte Carlo approximations, the EM algorithm, Monte Carlo EM).

Readings/Bibliography

  • BRAUN W.J. & MURDOCH D.J. (2007). A First Course in Statistical Programming with R. Cambridge University Press

  • ROBERT C. & CASELLA G. (2010). Introducing Monte Carlo Methods with R. New York: Springer-Verlag.

Teaching methods

  • Lectures
  • Tutorial sessions in computer laboratory

Assessment methods

The exam aims to assess the achievement of learning objectives:

- know and implement the main simulazione techniques from discrete and continuo variables,
- use the main simulation techniques studied for solving integrals,
- solve and implement numerical optimization algorithms.

The final mark of the Numerical Analysis course is defined as the arithmetic mean of the marks obtained by a written test for the Numerical Analysis module and a written exam for the Computational Statistics module.

Teaching tools

Slides available at campus.unibo.it.

Office hours

See the website of Silvia Bianconcini