Unit STATISTICAL METHODS IN DATA ANALYSIS
- Course
- Physics
- Study-unit Code
- GP005484
- Location
- PERUGIA
- Curriculum
- Astrofisica e astroparticelle
- Teacher
- Maura Graziani
- Teachers
-
- Maura Graziani
- Hours
- 42 ore - Maura Graziani
- CFU
- 6
- Course Regulation
- Coorte 2022
- Offered
- 2022/23
- Learning activities
- Affine/integrativa
- Area
- Attività formative affini o integrative
- Academic discipline
- FIS/07
- Type of study-unit
- Opzionale (Optional)
- Type of learning activities
- Attività formativa monodisciplinare
- Language of instruction
- Italian
- Contents
- Probability calculus recalls. MonteCarlo method for calculating integrals / experiment simulation. Methods for estimating quantities from series of experimental measurements: least squares, maximum likelihood, confidence intervals. Hypothesis tests: simple, complex, goodness of fit.
- Reference texts
- Cowan, Statistical Data Analysis; Lecture notes on the Unistudium online platform.
- Educational objectives
- The main objective of the course is to provide theoretical tools and practical experience in the analysis of experimental data.
The main knowledge acquired will be:
- basic elements of probability theory and Monte Carlo simulation techniques.
- knowledge of the main statistical distributions and their properties.
- knowledge of the possible statistical methods to estimate quantities starting from experimental measurements and evaluate the error.
The main skills (i.e. the ability to apply the acquired knowledge) will be:
- to write simple programs for the analysis of experimental data with different statistical techniques
- to write simple programs for the generation of Monte Carlo simulations
- to correctly evaluate the measurement uncertainties in the analysis of experimental data and test their description using theoretical models - Prerequisites
- The topics covered by the course require the student's familiarity with differential, integral, matrix calculus and the development of series functions. Moreover, all these notions should have already been acquired during the three-year degree in the exams of Mathematical Analysis and Geometry. Practical exercises will also be held on the computer, therefore familiarity with the use of computers and the ability to write simple C programs is required.
- Teaching methods
- 2 hours of face-to-face lectures, accompanied by computer exercises on specific problems.
- Other information
- The attendance to the lectures is not mandatory however is strongly recommended.
- Learning verification modality
- The exam consist of a written report on a data analysis problem assigned at the end of the course and an oral interview of approximately 45 '. The report must be made available to the teacher at least one week before the oral exam.
For information on support services for students with disabilities and / or SLD, visit the page http://www.unipg.it/disabilita-e-dsa - Extended program
- Probability calculus recalls: frequentist, Bayesian approach.
Random variables, multidimensional random variables and their transformations.
Expectation values and moments.
Tchebycheff theorem and Bienaymé - Tchebycheff inequality.
Error propagation, independence and correlation.
Statistical distributions: binomial, multinomial, Poissonian, Gaussian, Student's t.
Central limit theorem.
Monte-Carlo method: Monte Carlo as a simulation and integration method.
Numerical integration algorithms vs. Monte-Carlo algorithms Dimensionality.
Variance reduction techniques.
Random number generation according to given distributions.
Variable change.
Hit / miss.
Generations of random numbers with uniform distribution.
Generation algorithms.
Marsaglia effect and quality.
Methods for estimating quantities from series of experimental measurements: definition of the problem.
Properties of the distribution of an estimate: consistency, bias, variance of an estimate, efficiency.
Maximum likelihood: its properties, application on binned data, use to determine the parameters of physical distributions with counting experiments. Least squares, Gauss-Markov theorem. Multinormal distribution.
Technique of orthonormal functions. Fit of histograms with and without constraints.
Confidence intervals. Central confidence intervals. Normal distribution mean.
Confidence interval on variance. Case of discrete variables.
Hypothesis tests: simple, complex.
Neymann-Pearson test.
Fisher's Discriminants.
Goodness of fit.
Kolmogorov-Smirnov Test Run Test.