OBSERVATION AND MEASUREMENT TECHNIQUES
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- Versione italiana
- Academic year
- 2022/2023
- Teacher
- GIUSEPPE CIULLO
- Credits
- 6
- Didactic period
- Secondo Semestre
- SSD
- FIS/01
Training objectives
- The course aims to provide students with the basic tools of statistics and probability theory. As these subjects have multiple applications (fundamental science, applied research, industrial technology, engineering, social sciences, medicine, etc.) the course is general in nature, but with a special emphasis on scientific and technological applications.
The main objective of the course is to provide students with the basic theoretical knowledge and computational techniques for data processing necessary to solve application problems that require the use of statistical tools. At the end of the course students will be able to :
• Choose the model of random variable (continuous or discrete) most suited to solve a given problem, assessing the possible limits of applicability and the approximations involved;
• Given a sample of data, calculate fundamental quantities such as the mean, variance, median, mode, percentiles, etc.
• Organize and visualize the data using tables, graphs, histograms, etc.
• Make statistical inferences to a given population by studying a sample;
• Estimate the unknown parameters of the probability distribution of the population;
• Making hypothesis tests (parametric and non-parametric) on the probability distribution of the population through the study of data samples;
• Carry out a basic errors analysis;
• Perform linear or non-linear regression analysis through the method of least squares. Prerequisites
- The basics of mathematical analysis (derivatives, integrals, limits, series expansions, etc) is required for a full understanding of the arguments of the course. The exam of Mathematical Analysis I is mandatory.
And it is also required the use of calculation spreadsheets, for which a vademecum will be provided. Course programme
- The course consists in 60 hours of lessons including both theory and exercises, and is divided in the following main arguments:
1. Introductory and intuitive part on uncertainties, dimensional analysis, propagation of uncertainties, use of statistical estimators, representation of data by histograms and functional representation. Use of statistical tools, on directly collected data: random quantities and relationships between random quantities (linear regression).
2. Basics of Probability and Statistics: Basic definitions; probability mass and density; allocation function; transformations of random variables; mathematical expectation, variance and covariance
3. Discrete and continuous Random Variable models and characterization of their generic properties. Initial description on Uniform and Gaussian probability densities, extension to the linear regression, as well as to the chi-square variable.
Subsequently the Bernoulli, the Binomial, and the Poisson distribution will be studied, and if possible also other distributions will be faced.
4. Convergence of random variables convergence in distribution and in probability; central limit theorem; inequalities of Markov and Chebyshev; law of large numbers.
5. Theory of samples and data representations. Population, samples and statistical inference; sample statistics (mean, variance, median, mode, percentiles); organization and graphical representation of data.
6. Estimation theory. Estimators; method of moments; maximum likelihood method; inferential random variables (Chi-square, Student, Fisher); confidence intervals.
7. Hypothesis Tests. significativity test for Gauss and chi-square. Extension to other distribution: Uniforme, Binomial, Poisson.
8. Measure theory and regression analysis.
Measure theory and error analysis; method of least squares; correlation coefficient; linear regression and non-linear regression; linearization. Didactic methods
- The lessons are carried out both with the presentation of slides (for discursive parts, statements of theorems, problem themes, representations and presentations of data and their analysis, etc.). And on the blackboard (for calculations, proofs of theorems, solutions of problems, indications of use of spreadsheets, etc.). A copy of the slides is provided on the teacher web page after the lesson. Much of the course is devoted to exercises, which consist of solving problems on the blackboard. Time is also devoted to the observation of classroom experiences, data collection and respective analysis.
Learning assessment procedures
- The learning assessment is based on a written test and an oral test at the end of the course.
In the written test, the use of electronic spreadsheets is appropriate, therefore the student can use his PC
even with preset spreadsheets. During the written test the student is free to consult books and notes.
In the oral exam, the student will be asked for any clarifications of the written test.
However, questions will be asked on all the topics covered during the course.
The final score will be calculated considering both the grade of the writings and the oral result. Reference texts
- Reference text books are:
- A book provided by the teacher, which is an updgraded version, of his book, for engineering students.
- William Navidi “Probabilità e Statistica”
per l’Ingegneria e le Scienze
(ed. McGraw-Hill, 2006, Milano)
-Murray R. Spiegel Probabilità e statistica
Della collana Schaum
(edizioni McGraw-Hill)
