20592  STATISTICS AND PROBABILITY
Department of Decision Sciences
SONIA PETRONE
Mission & Content Summary
MISSION
CONTENT SUMMARY
PART I : Probability recap (Prof. Sandra Fortini)
 Definition and basic properties
 Random variables. Multivariate distributions
 Expectation and conditional expectation.
 Convergence of random variables.
 Basic notions on stocastic processes. Random noise. Random walks. Markov chains. NOTE (this topic may be postponed later, when dealing with Inference on Markov chains)
Part II : Statistical inference (Prof. Sonia Petrone)
Models, Statistical Inference and Learning
Elements of nonparametric estimation.
The bootstrap.
Parametric Inference
MLE and asymptotics
Confidence intervals
Hypothesis testing and pvalues
+ Exercizes and applications (with R)
PART III  Bayesian learning (Prof Sonia Petrone)
 Fundamentals of Bayesian learning
 Bayes rule and examples.
 Bayesian linear regression (if time permits)
PART IV: Computational methods (Prof. Rebecca Graziani)
 Stochastic integration and Monte Carlo.
 Optimization. EM algorithm.
 Parametric bootstrap (if time permits)
 Markov Chain Monte Carlo.
Intended Learning Outcomes (ILO)
KNOWLEDGE AND UNDERSTANDING
 Define, describe and explain rigorously the main notions of probability and statistical learning in the frequentist and Bayesian approach.
* Identify computational strategies for fundamental complex problems
* Recognize the role of probability and statistics in "data science" and related fields
APPLYING KNOWLEDGE AND UNDERSTANDING
 Estimate and predict, and quantify uncertainty, in fundamental problems
 Achieve a solid methodological background of probability and statistics on which they can build solid competence in data science
 Make conscius statistical analysis in basic applications (with R)
 Write algorithms in Python for the implementation of computational statistic techniques, namely optimization and integration techniques.
Teaching methods
 Facetoface lectures
 Exercises (exercises, database, software etc.)
 Individual assignments
 Group assignments
DETAILS
Students will be given periodic group or individual assignments, on the theory and applications (with R) and on the implementation of computational methods (with Python).
Assessment methods
Continuous assessment  Partial exams  General exam  


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ATTENDING AND NOT ATTENDING STUDENTS
ASSIGNMENTS:
Students wil be given periodic assigments, on the theory and computational methods presented in class.
The assigments (takehome) can be done individually or in groups (up to 4 people; exceptionally with motivated request 5 people).
The assignments are meant to support and engage students to follow and verify their ongoing understanding along the lectures  actually, students usually find them very helpful!
As such, the assigments are not mandatory and are not formally evaluated; however, students' work on the assigments is acknowldged in the final exam:
*** students who did not deliver the assigments will have additional questions in the written proof, with up to 10 min of extra time. These questions do not contribute to the final grade if the are reasonably well answered; but will penalize the final grade if poorly done.
*** students who did deliver the assigments will not have to answer those additional questions.
EXAM:
The exam will consist in an individual written proof that will count 70%, and a final project on computational methods, that counts 30%.
NOTE 1: The final project is done in groups, while the written proof is individual. Therefore, the written proof may count 100% if poorly done.
NOTE 2: The exam structure might be slightly modified, in order to accomodate for unforseen issues (as it happened with the COVID19 pandemic), taking into account the students' needs. In that case, students will be promptly informed, through BBoard announcements and more.
NOTE 3: The assigments contribute to the achievement of all the learning objectices of the course;
in particular are of support to
 *define, describe and explain rigorously the main notions of probability and statistical learning in the frequentist and Bayesian approach,
which is the necessary basis for being able to *estimate and predict, and quantify uncertainty, in fundamental problems and *recognize the role of probability and statistics in "data science" and related fields;
 *Identify computational strategies for fundamental complex problems and implement those statistical techniques, *writing algorithms in Python.
The EXAM aims at assessing all the learning objectives. In particular,
 the written proof aims at assessing ILOs:
*define, describe and explain rigorously the main notions of probability and statistical learning in the frequentist and Bayesian approach and *estimate and predict, and quantify uncertainty*, and *recognize the role of probability and statistics in "data science";
 the final project aims at assessing ILOs
* Identify computational strategies for fundamental complex problems, and write algorithms in Python for the implementation of computational statistic techniques,
Teaching materials
ATTENDING AND NOT ATTENDING STUDENTS
textbook
 L. Wasserman, "All of Statistics", 2009, Springer.
More teaching material, lecture notes, R and Python code etc will be provided on BBoard.