| ME440 - PROBABILITY, STATISTICS AND MODELS
(objectives)
To acquire a good knowledge of the main aspects of discrete probability, statistics and their applications.
Random variables, probability distributions, elementary stochastic processes and some limit theorems. Estimators and predictions, inference, causality and correlation. Pedagogical aspects and applications to the real world through models as percolation, random cluster model, Ising model, Markov chain Monte Carlo.
|
|
Code
|
20410620 |
|
Language
|
ITA |
|
Type of certificate
|
Profit certificate
|
|
Credits
|
6
|
|
Scientific Disciplinary Sector Code
|
MAT/06
|
|
Contact Hours
|
48
|
|
Exercise Hours
|
12
|
|
Type of Activity
|
Core compulsory activities
|
|
Teacher
|
SCOPPOLA ELISABETTA
(syllabus)
Part II:
Mathematical models. Difference equations: linear and non-linear first order equations, equilibrium, stability. Cycles and periodic points.
Logistic map.
Statistical mechanics models: Ising model, percolation and random cluster model. Curie-Weiss model and metastability.
Markov Chain Monte Carlo.
(reference books)
S.Elaydi: An introduction to difference equations - Springer
S.Freidli and Y.Velenik : Statistical Mechanics of Lattice Systems -
A concrete mathematical introduction.
O.H¨aggstr¨om: Finite Markov Chain and Algorithmic Applications,
London Mathematical Society-Student Texts 52
|
|
Dates of beginning and end of teaching activities
|
From to |
|
Attendance
|
not mandatory
|
|
Evaluation methods
|
Written test
Oral exam
|
|
Teacher
|
CANDELLERO ELISABETTA
(syllabus)
1) Elements of basic probability: combinatorics, axioms of probability, conditional probability and independence, random variables (discrete and continuous) with main distributions, limit theorems, examples.
2) Elements of Statistics: random sampling, definition of statistical model and statistics, sufficient/minimal/complete statistics, moment method, maximal likelihood estimators, confidence interval, hypothesis testing, examples.
3) Analysis of specific models.
(reference books)
- Calcolo delle probabilita' (Sheldon Ross)
- Recommended exercises on the Team of the course
- Other written material can be found on the Team of the course
|
|
Dates of beginning and end of teaching activities
|
From to |
|
Delivery mode
|
Traditional
|
|
Attendance
|
not mandatory
|
|
|
Università Roma Tre