Te`cniques Matema`tiques i Estadstiques

Syllabus

Fundamentals of Probability Theory and Statistics

General review of probability theory. Random variables and events. Bayestheorem. Probability distrubutions: binomial, Poisson, Gaussian, Cauchy.Theorem of Large Numbers. Central-limit theorem.

Statistical Inference. Point estimation theory: consistency, unbiasedness,efficiency. Confidence intervals. 2 tests. Fisher information. Cramer-Raobound. Maximum-likelihood estimators. Hypothesis testing. Kolmogorov-Smirnov tests. Least squares.

Information theory. Typicality. Shannon entropy. Mutual Information.Correlations. Rare events.

Hands-on work: pencil-and-paper problems and programming oriented tostatistics and probability

Monte-Carlo Methods

Generalities. Sampling, integration, optimisation. Sampling. Simple probability distributions. Importance sampling, strati-

fied sampling, rejection sampling.

Metropolis Algorithm. Generalities, reversibility and convergence, paralleltempering, simulated annealing.

Applications of the Metropolis algorithm. Statistical physics, path inte-grals and quantum field theory, events generation.

Hands-on work: pencil-and-paper problems and Monte-Carlo program-ming

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Multivariate analysis and Statistical Treatment Techniques

Data analysis and representation. Statistical distances. Principal component analysis. Hierarchical and non-hierarchical clustering. Discriminant analysis Neural networks Support vector machines. Non-parametric methods of estimation of a probability density function:

histograms, simple estimators, kernel estimators.

Databases and Data Mining: basic concepts, introduction to data miningand case studies

Hands-on work: Weka, Neural-Network software & databases

Grading

There will be no exam for this course. In turn, 6 problem assignments willbe proposed during the course (two for each section). From all of them, eachstudent will be free to choose a subset covering at least 75% of the total. Gradingwill be based on this subset only. Students who desire to hand a report for morethan this percentage are of course free to do so.

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