Studying at the University of Verona
Here you can find information on the organisational aspects of the Programme, lecture timetables, learning activities and useful contact details for your time at the University, from enrolment to graduation.
Study Plan
The Study Plan includes all modules, teaching and learning activities that each student will need to undertake during their time at the University.
Please select your Study Plan based on your enrollment year.
1° Year
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2° Year activated in the A.Y. 2023/2024
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1 module among the following (a.a. 2023/24: Data protection in business organizations not activated)2 modules among the following (a.a. 2023/24: Statistical methods for business intelligence not activated)2 modules among the following (a.a. 2023/24: Complex systems and social physics not activated)2 modules among the followingLegend | Type of training activity (TTA)
TAF (Type of Educational Activity) All courses and activities are classified into different types of educational activities, indicated by a letter.
Probability for Data Science (2022/2023)
Teaching code
4S009077
Academic staff
Coordinator
Credits
12
Language
English
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
Period
Semester 1 dal Oct 3, 2022 al Jan 27, 2023.
Learning objectives
The course will provide a self-contained and mathematically rigorous introduction to modern techniques of data analysis and modeling of random phenomena, with special emphasis to the theoretical bases, typical of probability theory, necessary to develop effective solutions to the challenges characterizing heterogeneous areas, eg , finance, fault-detection, innovation forecasting, energy prediction, etc., typical of Industry 4.0, with particular reference to the challenges posed in the field of big data analytics. The presentation of concepts, problems and related theoretical / practical solutions will be oriented to the applications, also making use of specific statistical software (e.g. Matlab, R, KNIME, etc.) always maintaining a high level of mathematical rigor. The course will discuss the basics of modern Probability theory (eg: random variables, their distributions and main statistical properties, convergence theorems and applications), with particular attention to the fundamental stochastic processes (eg: Markov chains , birth and death processes, code theory with real world applications) and their applications within real world scenarios characterized by the presence of big data and related time series.
At the end of the course the student has to show to have acquired the following skills:
- knowledge of the formal basis of probability theory
- ability to use the concepts of random variables (both in a discrete and continuous environment)
- ability to develop models based on known probabilistic models, e.g., v.a. binomial, Poisson, Gaussian, Gaussian mixtures, etc.
- understanding and knowing how to use the basic theory of stochastic processes, with particular reference to Markov chain theory (discrete and continuous time), birth and death processes and related applications
- know and know how to use the basic notions in descriptive and inferential statistics
Prerequisites and basic notions
Calculus and linear algebra
Program
1. Probability, conditioning and independence.
2. Random variables and their distributions. Discrete distributions. Expectation and variance. Continuous distributions.
3. Random vectors. Independence of random variables. Covariance and correlation.
4. Limit Theorems: law of large numbers and central limit theorem. Normal approximation.
5. Normal random vectors.
6. Discrete time Markov chains. Markov Chain Monte Carlo methods.
7. Poisson processes and queuing theory. Continuous time Markov chains.
8. Introduction to random networks.
Bibliography
Didactic methods
All the topics will be illustrated in class. Additional material, as exercises, lecture notes and further references, will be available on Moodle page of the course.
The rights of students will be preserved in situations of travel limitation or confinement due to national provisions to combat COVID or in particular situations of fragile health. In these cases, you are invited to contact the teacher directly to organize the most appropriate remedial strategies.
Learning assessment procedures
The exam is scored out of a maximum of 30 points and it consists of two compulsory parts: a written test and an oral test.
Written test. It is focussed on the resolution of a set of exercises. The written test can be completed either by passing two midterm exams during the semester or by passing a regular sitting during an exam session.
Oral test. It can be taken once you have passed the written test (minimum grade: 15/30) and it increases the grade of the written test up to 3 points. At student's choice, the oral test can be carried out according to one of the following ways:
--standard oral exam, during which the student must be able to demonstrate her/his knowledge of the course material and be able to discuss the topics dealt with in the lectures;
--presentation of a project, during which the student must discuss a code for simulation she/he implemented to solve a problem related to the course contents.
A student must obtain a mark of at least 18/30 to pass the exam.
Evaluation criteria
The student must demonstrate that she/he is familiar with the basics in Probability and in Markov chain theory, that she/he can apply theory to problem-solving and she/he is able to solve exercises of appropriate difficulty.
Exam language
English
