General information 
Course unit name: Mathematical and Statistical Techniques
Course unit code: 568423
Academic year: 20192020
Coordinator: Francesc Xavier Luri Carrascoso
Department: Department of Quantum Physics and Astrophysics
Credits: 6
Single program: S
Estimated learning time 
Total number of hours 150 
Facetoface and/or online activities 
60 
 Lecture 
Facetoface 
60 
Supervised project 
40 
Independent learning 
50 
Recommendations 
Students are recommended to have basic programming skills to follow this course. 
Competences to be gained during study 
— Understand a problem, connect it with acquired knowledge, propose a solution and test it.

Learning objectives 
Referring to knowledge
— Get acquainted with fundamental results of probability theory and statistics. Understand their relevance to important issues in experimental and theoretical physics. 
Teaching blocks 
1. Fundamental concepts 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; Centrallimit theorem and BerryEsseen theorem
* Introduction to R
* Statistical inference: point estimation theory, confidence intervals, chisquared test, Fisher information, CramerRao bound, maximumlikelihood estimators, hypothesis testing, KolmogorovSmirnov tests, least squares, information theory (typicality, mutual information, correlations)
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
3. Multivariate analysis and statistical treatment techniques
* Data analysis and representation; Statistical distances; Principal component analysis
* Hierarchical and nonhierarchical clustering
* Discriminant analysis
* Neural networks
* Support vector machines
* Nonparametric methods of estimation of a probability density function: histograms, simple estimators, kernel estimators
4. Databases and data mining
* Basic concepts
* Introduction to data mining
* Case study: the Gaia archive
5. Practical work
* Introduction to R
* Introduction to WEKA (data analysis and data mining)
Official assessment of learning outcomes 
There is no exam for this subject. Instead, 5 problemsolving assignments are set during the course. Grading is based on the assessment of the reports submitted.
Examinationbased assessment

Reading and study resources 
Consulteu la disponibilitat a CERCABIB
Book
Crawley, Michael J. The R book. Chichester : Wiley & Sons, 2007
DeGroot, Morris H. Probability and statistics. 4th ed. Boston : Pearson Education, cop. 2012
https://cercabib.ub.edu/iii/encore/record/C__Rb1536375?lang=cat
https://cercabib.ub.edu/iii/encore/record/C__Rb1727639?lang=cat
Article
Weinzierl, Stephan. "Introduction to Monte Carlo method", a: http://arxiv.org/abs/hepph/0006269
Conferences 