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Mathematical and Statistical Methods

This tool course teaches how to extract relevant scientific information from experimental and simulated data; Modern statistical methods to handle and analyze big data flows (data mining, multivariate analysis) will be discussed.

Syllabus : " Mathematical and Statistical Methods "

- Lectures 20 hours, Tutorials 10 hours (1st Semester) -

(Pierre Désesquelles)

Chapter 1: Statistical tools
From probabilities to statistics
Distribution, pdf, distribution function
Characterization
Matrix algebra

Chapter 2: Big data
What are big data and how to handle them?
How to define information, clustering, discrimination?
Multivariate analysis, characterization, discrimination, inference, decision
How to extract information from random uncertainties, error propagation

Chapter 3: Theory/experiment confrontation
Epistemology, scientific approach/process/hypothesis, validation.
Null hypothesis method
Chi2, Kolmogorov-Smirnov and other tests
The inverse problem, solving methods

Chapter 4: Cause/effect relations
Correlation and cause/effect
Partial correlation
Multiple regression

Chapter 5: Evolving processes
States and transitions
Absorbing processes
Regular processes

Recommended textbooks:

  • Data-Driven Modeling & Scientific Computation: Methods for Complex Systems & Big Data Paperback – September 15, 2013 by J. Nathan Kutz
  • Multivariate Data Analysis (7th Edition) by Joseph F. Hair Jr, William C. Black, Barry J. Babin and Rolph E. Anderson (Feb 23, 2009)

Course prerequisites and corequisites

- basic knowledge of probability and statistics;
- basic knowledge of matrix algebra, eigenvectors/values.

Course concrete goals

On completion of the course students should be able to:

— Manipulate scientific data and extract relevant information
— Assess the uncertainties
— Validate/invalidate theoretical hypotheses
— Characterize the past and the future of evolving processes.