30408 - ADVANCED MATHEMATICS AND STATISTICS - MODULE 2 (ADVANCED STATISTICAL METHODS)

BEMACS (7 credits - II sem. - OB  |  SECS-S/01)

Course Director:
ANTONIO LIJOI

Classes: 25 (II sem.)

Instructors:
Class 25: ANTONIO LIJOI

The course introduces students to the fundamentals of Probability Theory and Statistical Inference. These is complemented by an in-depth presentation of elementary simulation and computational techniques that are routinely used to implement most common statistical procedures.

• Review of discrete and continuous random variables.
• Random vectors.
• Transformations of random variables and of random vectors.
• Simulation of random variables.
• Strong laws of large numbers and the central limit theorem.
• Parametric statistical models.
• Parameter estimation: maximum likelihood and Bayesian methods.
• Hypothesis testing.
• Regression models.

A general written exam or two partial written exams (one in the middle and one at the end of the course).
There are no different assessment methods or exam programs between attending and non-attending students.

• F.J. SAMANIEGO, Stochastic Modeling and Mathematical Statistics, Boca Raton FL, CRC Press, 2014.
• M. LAVINE, Introduction to Statistical Thought, 2013, available on: http://people.math.umass.edu/~lavine/Book/book.html

It is required that students have solid knowledge of calculus and of basic programming tools.