30408  ADVANCED MATHEMATICS AND STATISTICS  MODULE 2 (ADVANCED STATISTICAL METHODS)
Department of Decision Sciences
ANTONIO LIJOI
Suggested background knowledge
Mission & Content Summary
MISSION
CONTENT SUMMARY
 Review of discrete and continuous random variables.
 Moment generating function.
 Random vectors.
 Transformations of random vectors.
 Simulation of random variables.
 Laws of large numbers and the central limit theorem.
 Parametric statistical models.
 Parameter estimation: minimum variance and unbiased estimators, maximum likelihood and Bayesian methods.
 Hypothesis testing.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
 Deal with intermediate statistical and probabilistic tools that lie at the foundations of modern Data Science and Machine Learning applications.
 Develop a multivariable thinking that is essential to understand and model large and complex datasets.
 Identify drawbacks and merits of both the frequentist and the Bayesian approaches to statistical inference.
 Profitably attend advanced courses in Probability and Stochastic Processes, Statistics and Machine Learning.
APPLYING KNOWLEDGE AND UNDERSTANDING
 Tailor statistical models to specific experiments, with the aim of addressing estimation and hypothesis testing problems.
 Study relationships among multivariate data, with the aim of drawing predictions and impacting decisionmaking processes.
 Interpret the output of basic statistical procedures in view of actual applications to real data.
Teaching methods
 Lectures
DETAILS
Assessment methods
Continuous assessment  Partial exams  General exam  


x  x 
ATTENDING AND NOT ATTENDING STUDENTS
1) The exam consists of either two partial written tests or of a single general written test.
Both partial and general exams are written tests with exercises. They aim at assessing the students' ability to solve simple problems in Probability and Mathematical Statistics. They require the application of analytical tools and univariate and multivariate calculus techniques that have been taught during the course. The probabilistic component of the course will be also relevant for solving exercises related to Statistics. The first partial exam covers the part on Probability Theory of the program, while the second partial exam focuses on Mathematical Statistics topics. The general exam is on the whole program. 
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
F.J. SAMANIEGO, Stochastic Modeling and Mathematical Statistics, Boca Raton, FL, CRC Press, 2014.