Planning and Evaluation of Experiments (FSI-TPX)

Academic year 2022/2023
Supervisor: doc. Ing. Miroslav Bartošík, Ph.D.  
Supervising institute: ÚFI all courses guaranted by this institute
Teaching language: Czech
Aims of the course unit:
The aim of the course is to provide students with basic mathematical tools necessary for statistical evaluation of experimental results obtained when using other methods.
Learning outcomes and competences:
Students will be able to asses the significance of results obtained, the influence of their correlations, compare relevance of choice of models for description of experimental data, apply physical limits on estimate confidence intervals.
Prerequisites:
Mathematics, namely calculation of the basic statistical characteristics of the data set.
Course contents:
The course deals with the following topics: Basic terms and tasks. Construction of a statistical model, bias correction. Orthogonal functions, tests of residuals, addition of parameters and generalisation error. Correlation, rank-test and maximal correlation, principal components. Upper limits, significance of structures at noise level. Instructive solutions of tasks with illustrative experiments.
Teaching methods and criteria:
The course is taught through lectures explaining the basic principles illustrated on specific (real or simulated) examples. Exercises are focused on practical topics presented in lectures.
Assesment methods and criteria linked to learning outcomes:
The assessment of a student is made upon his/her performance in practicals and the competence in a discussion during the colloquium (of the topics related to the solution of the final problem of the course).
Controlled participation in lessons:
Attendance at practicals is obligatory and is monitored by the tutor. Absence may be compensated for by the agreement with the tutor depending on the length of absence.
Type of course unit:
    Lecture  13 × 1 hrs. optionally                  
    Exercise  13 × 1 hrs. compulsory                  
Course curriculum:
    Lecture Basic review of methods (distributions, expectation, variance, estimates).
Models
- construction of parametric and nonparametric (interpolation, smoothing) models
- number of degrees of freedom (polynomial fits), bias-variance trade-off
Fitting - gaussian curve analysis, parameter estimation from histogram, correlation suppression
Combination of measurements, stratification
Correlations
- distribution of correlation parameter, approximation and tests
- parameters around regression minima
- orthogonal regression
Hypothesis testing (Neyman-Persion test)
Confidence intervals
- frequentist interpretation, belt construction
- example of binomial distr. (Clopper-Pearson limit)
- conversion of measurements to confidence intervals
- upper limits (Bayesian construction, Poissonian statistics)
Fine structure - peak identification, variance estimates, statistical significance of multiple peaks
Frequency analysis
- Fourier reconstruction
- Lomb-Scargle algorithm (uneven sampling)
- construction of a periodogram

Examples from experiments
- refraction (Abbe refractometer)
- spectroscopy (transmission measurements)

Extras - constrained optimization, correction of bias, robust methods
    Exercise Students solve problems and excercises defined in the lectures.
Literature - fundamental:
1. Humlíček J.: Statistické zpracování výsledků měření, skriptum MU Brno
2. F. James: Statistical Methods in Experimental Physics (2nd ed.), World Scientific, 2009
3. R.J.Barlow: Statistics (Guide to the Use of Statistical Methods in Physical Sciences), Wiley (Manchester physics series) 1989
4. Pánek P.: Úvod do fyzikálního měření, skriptum MU Brno
Literature - recommended:
1. F. MÜNZ: Vybraná témata k vyhodnocení experimentů. Elektronický studijní materiál. MU, Brno 2014.
2. J. HUMLÍČEK: Statistické metody zpracování výsledků měření. MU, Brno 2001.
The study programmes with the given course:
Programme Study form Branch Spec. Final classification   Course-unit credits     Obligation     Level     Year     Semester  
CŽV full-time study CZV Bases of Mechanical Engineering -- GCr 2 Compulsory 1 1 W
B-FIN-P full-time study --- no specialisation -- GCr 2 Compulsory 1 3 W