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Course 2021-2022 a.y.

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

BEMACS
Department of Decision Sciences

Course taught in English


Go to class group/s: 25

BEMACS (7 credits - II sem. - OB  |  SECS-S/01)
Course Director:
ANTONIO LIJOI

Classes: 25 (II sem.)
Instructors:
Class 25: ANTONIO LIJOI


Suggested background knowledge

Solid knowledge of calculus and of basic programming tools in R facilitates students’ understanding of the topics covered during the course.


Mission & Content Summary
MISSION

Data Science has recently emerged as one of the most exciting interdisciplinary research areas both in academia and among practitioners. The unprecedented availability of data is setting a variety of theoretical and computational challenges for statistics and is, thus, fueling novel groundbreaking developments in the field. Researchers and professional data scientists who want to play a leading role in such a new scenario must definitely have a solid mastery of topics in Probability and Statistics. The main aim of the course is to introduce students to intermediate-level tools in Probability Theory and Statistical Inference. The first part is devoted to investigating mathematical aspects of probability, with a special emphasis on multivariate distributions and limiting theorems. In the second part, students are guided through the methodological core of point estimation (both from a frequentist and Bayesian perspective) and hypothesis testing. These theoretical aspects are complemented by an in-depth presentation of elementary simulation and computational techniques that are routinely used within most common statistical procedures.

CONTENT SUMMARY
  • Review of discrete and continuous random variables.
  • Random vectors.
  • Moment generating function.
  • Transformations of random variables and 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
At the end of the course student will be able to...
  • Deal with intermediate statistical and probabilistic tools that lie at the foundations of modern Data Science 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 courses on advanced topics in Probability and Stochastic Processes, Statistics and Machine Learning.
APPLYING KNOWLEDGE AND UNDERSTANDING
At the end of the course student will be able to...
  • 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 decision-making processes.
  • Interpret the output of basic statistical procedures in view of actual applications to real data.

Teaching methods
  • Face-to-face lectures
  • Online lectures
DETAILS

  


Assessment methods
  Continuous assessment Partial exams General exam
  • Written individual exam (traditional/online)
  •   x x
    ATTENDING AND NOT ATTENDING STUDENTS

    1) The exam consists of either two partial written tests or of a general written test.
    2) In order to pass the exam one has to get at least 18/30, either as the mark of the general exam or as an average, with equal weights, of the two partial exams. In the latter case, in order to pass the exam, the minimum mark one has to get in one of the two partial exams is 15/30. 
    3) Those who pass the mid-term exam on the 19th of March 2021, may take the second partial either on the 12th of May or on the 1st of June, 2021.
    4) Students whose average mark of the two partial exams is no larger than 17/30 or have obtained a mark of 14/30, or below, in one of the two tests have to take the general exam.

     

    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 mid-term 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.