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. 2021/2022
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1 module among the following (1st year: Big Data epistemology and Social research; 2nd year: Cybercrime, Data protection in business organizations, Comparative and Transnational Law & Technology)2 courses among the following (1st year: Business analytics, Digital Marketing and market research; 2nd year: Logistics, Operations & Supply Chain, Digital transformation and IT change, Statistical methods for Business intelligence)2 courses among the following (1st year: Complex systems and social physics, Discrete Optimization and Decision Making, 2nd year: Statistical models for Data Science, Continuous Optimization for Data Science, Network science and econophysics, Marketing research for agrifood and natural resources)2 courses among the following (1st year: Data Visualisation, Data Security & Privacy, Statistical learning, Mining Massive Dataset, 2nd year: Machine Learning for Data Science)Legend | 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 (2020/2021)
Teaching code
4S009077
Credits
12
Language
English
Scientific Disciplinary Sector (SSD)
MAT/06 - PROBABILITY AND STATISTICS
The teaching is organized as follows:
Parte II
Credits
7
Period
I semestre
Academic staff
Francesco Giuseppe Cordoni
Parte I
Teoria
Learning outcomes
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
Program
Probability, conditioning and independence.
Random variables and their distributions. Discrete distributions. Expectation and variance. Continuous distributions.
Random vectors. Independence of random variables. Covariance and correlation.
Limit Theorems: Law of Large Numbers and Central Limit Theorem. Normal approximation.
Normal random vectors.
Discrete time Markov Chains. Markov Chain Monte Carlo.
Poisson Processes and Queuing Theory. Continuous time Markov Chains.
Introduction to random networks.
Bibliography
| Activity | Author | Title | Publishing house | Year | ISBN | Notes |
|---|---|---|---|---|---|---|
| Parte II | S. Ross | A First Course in Probability (Edizione 10) | Pearson | 2018 | ||
| Parte II | P. Baldi | Calcolo delle Probabilità | McGraw Hill | 2007 | 9788838663659 | |
| Parte II | S. Ross | Introduction to Probability models (Edizione 12) | Academic Press | 2019 | ||
| Teoria | Durret, R. | Random graph dynamics | Cambridge university press | 2007 | ||
| Teoria | Chung, F. R. K. and Lu, L. | Random graphs | AMS Bookstore | 2006 | ||
| Teoria | Bolloas, B. | Random graphs | Cambridge university press | 2001 | ||
| Teoria | Duflo, M. | Random Iterative Models, Applications of Mathematics, 34 | SpringerVerlag, Berlin | 1997 | ||
| Teoria | Albert, R. and Barab´asi, A.-L. | Statistical mechanics of complex networks. Reviews of modern physics, 74(1):47. | 2002 | Reviews of modern physics, 74(1):47. |
Examination Methods
The exam takes place in two parts.
The first part, mandatory for all students, consists of a written test with exercises.
The second part can be carried out, at the student's choice, in one of the following ways:
- oral exam, in which the student must be able to present the concepts and models described in the course, both in the theoretical and in the applicative aspects;
- a project assigned by the teacher, which will include the writing of a code for a simulation.
