Course detail

Planning and Evaluation of Experiments

FSI-TPXAcad. year: 2023/2024

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.

Language of instruction

Czech

Number of ECTS credits

2

Mode of study

Not applicable.

Guarantor

doc. Ing. Miroslav Bartošík, Ph.D.

Department

Institute of Physical Engineering (ÚFI)

Entry knowledge

Mathematics, namely calculation of the basic statistical characteristics of the data set.

Rules for evaluation and completion of the course

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).
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.

Aims

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.
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Humlíček J.: Statistické zpracování výsledků měření, skriptum MU Brno (CS)
F. James: Statistical Methods in Experimental Physics (2nd ed.), World Scientific, 2009 (EN)
R.J.Barlow: Statistics (Guide to the Use of Statistical Methods in Physical Sciences), Wiley (Manchester physics series) 1989 (EN)
Pánek P.: Úvod do fyzikálního měření, skriptum MU Brno (CS)

Recommended reading

F. MÜNZ: Vybraná témata k vyhodnocení experimentů. Elektronický studijní materiál. MU, Brno 2014. (CS)
J. HUMLÍČEK: Statistické metody zpracování výsledků měření. MU, Brno 2001. (CS)

Classification of course in study plans

  • Programme B-FIN-P Bachelor's, 3. year of study, winter semester, compulsory

Type of course unit

 

Lecture

13 hours, optionally

Teacher / Lecturer

doc. Ing. Miroslav Bartošík, Ph.D.

Syllabus

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

13 hours, compulsory

Teacher / Lecturer

doc. Ing. Miroslav Bartošík, Ph.D.

Syllabus

Students solve problems and excercises defined in the lectures.