Course detail
Planning and Evaluation of Experiments
FSI-TPX Acad. year: 2023/2024 Winter semester
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
Supervisor
Department
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.
The study programmes with the given course
Programme B-FIN-P: Physical Engineering and Nanotechnology, Bachelor's, compulsory
Type of course unit
Lecture
13 hours, optionally
Teacher / Lecturer
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
Syllabus
Students solve problems and excercises defined in the lectures.