B005507 - TREATMENT OF EXPERIMENTAL DATA

The course is intended as an introduction to the statistical analysis of experimental data. The basic concepts of probability theory and inferential statistics (sampling theory, hypothesis testing, parametric fits) are introduced and illustrated through practical examples.

- G.Cowan, "Statistical Data Analysis", Oxford University Press.

- S.Brandt, "Statistical and Computational Methods in Data Analysis", North-Holland

Knowledge acquired:

Acquaintance with the probability distributions (binomial, normal,

exponential, Pearson's) and methods of statistical analysis

(estimators, chi-square test, linear parametric models...) most

commonly used in data modelling and analysis.





Competence acquired:

The student will be able to determine the maximal achievable

information from a data sample, assessing its degree of accuracy and

reliability, by applying the most suitable statistical models and

techniques. Such competence implies the use of computers for data

handling and numerical calculations using simple simulations.





Skills acquired (at the end of the course):

Ability to describe through a probabilistic model some typical

cases encountered in experimental sciences, in order

to provide the best estimate of the parameter of interest, or

to perform an hypothesis testing on a data sample (e.g. estimation of

an expected value through sample mean value, estimation of the

expectation time for a random process, chi-square goodness-of-fit test

in the linear case, etc.)

Oral examinations

Elements of Probability Theory:

Random variables, axiomatic theory of probability, conditional

probability and Bayes Theorem, Bayesian and frequentist

interpretations.

Probability distributions and their properties: expected value, moments, variance.

Notable examples of distributions with applications.

Multivariate distributions, covariance.

Functions of random variables, convolution of density functions, error propagation.

Binomial, multinomial and Poisson distributions, law of large numbers.

Normal distribution, central limit theorem, Pearson distribution.

Bienaymé-Chebyshev inequality.



Introduction to the analysis of experimental data:

Data samples, descriptive statistics, statistical and systematic

uncertainties, significant digits. Estimators and their properties,

the principle of maximum likelihood, confidence intervals.

Generation of samples with Monte Carlo simulation techniques.



Statistical hypothesis testing:

Test statistics, significance and p-value. Pearson's chi-square test.

Comparison of hypotheses: Neyman-Pearson lemma, likelihood ratio.



Parametric models:

Method of least squares, Gauss-Markov Theorem, linear regression.