Advanced Statistics

course ID

Lecturer

Dott. Giuseppe Consolini

CFU

10

Length

14 Weeks

Semester DD

First

Course details

Introduction to probability theory (5 hrs.); Functions of distributions: representation and properties (6 hrs.); Limit theorems for probability (7 hrs.); Outlines of large deviation theory and statistics of extreme events (4 hrs.); Introduction to non-parametric statistical analysis (4 hrs.); Non-parametric tests for normality, stationarity, correlation and randomness (12 hrs.); Introduction to information theory: Shannon entropy, Kulback-Leibler distance, mutual information and correlation measure, causality (6 hrs.); Maximum entropy method with applications (4 hrs.); Practical application exercises: methods for deriving distributions from time series, Normality tests, stationarity analysis, applications of non-parametric statistical analysis methods, application of information theory to real data (48 hrs.)

Co-teaching: Prof. Berrilli Francesco 

Objectives

LEARNING OUTCOMES:
The aim of the course is to provide the basic knowledge of the methods for the non-parametric and parametric statistical analysis of large dataset. In detail, the course is devoted to the description of different  methods and tests for the comparison of statistical properties of different large dataset, and also for the study of the existence of a linear and nonlinear correlation among datasets using also approaches based on information theory.   

KNOWLEDGE AND UNDERSTANDING: 
basic principles and concepts of the advanced statistics and information theory and its implementation on data sets 

APPLYING KNOWLEDGE AND UNDERSTANDING:
to apply the basic principles and concepts of advanced statistics and information theory to get a quantitative description of the observed phenomena and of the nature of the correlation among sets of physical data. 

MAKING JUDGEMENTS: 
capacity to extract independently the fundamental information on physical systems through the statistical analysis and the information theory, and to be capable of discerning the relevance of the works in the specific field.

COMMUNICATION SKILLS:
to the student is required to be able to explain the nature of the statistical relations and analysis and the inference and correlation among different datasets of physical systems to both a specialized and not-specialized audience

LEARNING SKILLS:
capacity to unterstand the importance of the different elements determining the dynamics of physical systems by the statistical analysis.