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Course unit
SCP7079197, A.A. 2017/18

Information on the course unit
Degree course Second cycle degree in
SC2377, Regulation 2017/18, A.Y. 2017/18
Number of ECTS credits allocated 6.0
Course unit English denomination STOCHASTIC METHODS
Website of the academic structure http://datascience.scienze.unipd.it/2017/laurea_magistrale
Department of reference Department of Mathematics
Mandatory attendance No
Language of instruction English

Teacher in charge PAOLO DAI PRA MAT/06

ECTS: details
Type Scientific-Disciplinary Sector Credits allocated
Educational activities in elective or integrative disciplines MAT/06 Probability and Mathematical Statistics 6.0

Mode of delivery (when and how)
Period First semester
Year 1st Year
Teaching methods frontal

Organisation of didactics
Type of hours Credits Hours of
Hours Individual
Lecture 6.0 48 102.0 No turn

Start of activities 02/10/2017
End of activities 19/01/2018

Prerequisites: Basic notions of differential and integral calculus, linear algebra and probability.
Target skills and knowledge: The aim of this course in to introduce tools from the theory of Probability and Stochastic Processes that have high impact in the study of networks as well as algorithmic and computational tools. Using the software R (R development Core Team, 2006), specific problems will be dealt with via computer simulation.
Examination methods: Written exam
Assessment criteria: The final grade is based on the results in the written exam. In the exam student are asked to implement in specific applications the tools learned in the course. Correctness and efficiency will be particularly valued.
Course unit contents: 1. Probability reviews.
• discrete and continuous distributions
• random variables, expectation and conditional expectation
• approximation of probability distributions.

2. Markov chains and random walks
• Markov Chain and their stationary distribution
• Monte Carlo (MCMC), convergence of MCMC-based algorithms
• Electrical networks.

3. Random graphs
• Erdos-Renyi graphs: connectivity, giant component.
• Random regular graphs
• Dynamic graphs. Preferential attachment.
Planned learning activities and teaching methods: Frontal lessons. Some problems will be solved in classroom via computer simulation
Additional notes about suggested reading: The teacher in charge will provide lecture notes, exercises and scientific papers.
Textbooks (and optional supplementary readings)
  • P. Dai Pra, Stochastic Methods for Data Science. --: --, 2017. Lecture notes