Course detail

# Planning and Evaluation of Experiments

FSI-TPXAcad. year: 2017/2018

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.

Learning outcomes of the course unit

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.

Co-requisites

Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

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

Planned learning activities and teaching methods

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).

Language of instruction

Czech

Work placements

Not applicable.

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.

Specification of controlled education, way of implementation and compensation for absences

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.

Classification of course in study plans

• Programme B3A-P Bachelor's

branch B-FIN , 3. year of study, winter semester, 2 credits, 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

seminars

13 hours, compulsory

Teacher / Lecturer

Syllabus

Students solve problems and excercises defined in the lectures.