Master 2013 – Mathematical and statistical techniques
Mathematical and statistical techniques
Master 2013 – Mathematical and statistical techniques
Part I
R. Graciani & Hugo Ruiz
Master 2013 – Mathematical and statistical techniques
1- Fundamentals of probability theory and statistics
General review of probability theory: Random variables and events.
Bayes theorem. Probability distributions: binomial, Poisson, Gaussian,
Cauchy. Law of large numbers. Hoeffding’s inequality. Central-limit
theorem and Berry-Eseen theorem.
Statistical inference: Point Estimation Theory, Confidence Intervals,
Chi-2 tests, Fisher Information, Cramer-Rao bound, Maximum-likelihood
estimators, hypothesis testing, Kolmogorov-Smirnov Tests, Least
Squares, Information Theory (Typicality, mutual information,
correlations).
Hands on work using the R programming language
Master 2013 – Mathematical and statistical techniques
2- Monte-Carlo methods
• Generalities. Sampling, Integration, Optimisation.
• Importance sampling, stratified sampling, rejection sampling.
• Metropolis algorithm. Generalities: reversibility, strong ergodicity
and convergence. A priori probabilities, parallel tempering,
simulated annealing.
• Applications of the Metropolis algorithm to statistical Physics,
quantum field theory and events generation.
Hands on work using the R programming language (TBC)
Master 2013 – Mathematical and statistical techniques
Part II
X. Luri
Master 2013 – Mathematical and statistical techniques
3 - Multivariate analysis
• Data analysis and representation. Statistical distances.
Principal component analysis.
• Hierarchical and non-hierarchical clustering.
• Discriminant analysis.
Hands on work using Weka
Master 2013 – Mathematical and statistical techniques
4 - Statistical treatment techniques
• Neural networks.
• Non-parametric methods of estimation of a probability
density function: histograms, simple estimators, kernel
estimators.
Hands on work using SNSS & the R language
Master 2013 – Mathematical and statistical techniques
5 - Databases and data mining
• Basic concepts
• Introduction to data mining
• Case studies
Master 2013 – Mathematical and statistical techniques
Grading
Master 2013 – Mathematical and statistical techniques
There will be no exam for this course. Instead, 5 problem
assignments will be proposed. The grading will be based
on the marks of these assignments.
Re-evaluation: the student will have to redo and resubmit the
5 problem assignments correcting them according to the
instructions from the teachers. Once they are received they
will be evaluated and the student will pass an oral exam on
their contents. If this exam is successfully passed the mark of
the course will be fixed from the marks of the assignments,
otherwise the subject will be graded as non-passed.
Master 2013 – Mathematical and statistical techniques
Course Material: Campus virtual
http://campusvirtual2.ub.edu
Master 2013 – Mathematical and statistical techniques
Hands-on work tools
Basic programming skills are required
Master 2013 – Mathematical and statistical techniques
The R programming language
R is a free software environment for statistical computing
and graphics. It compiles and runs on a wide variety of
UNIX platforms, Windows and MacOS
Master 2013 – Mathematical and statistical techniques
“Weka” package
Master 2013 – Mathematical and statistical techniques
“Stuttgart Neural Network Simulator” package