Uusi opinto-opas (sisältäen myös opetusohjelmat) lukuvuodelle 2018-2019 sijaitsee osoitteessa https://opas.peppi.utu.fi . Tältä sivustolta löytyvät enää vanhat opinto-oppaat ja opetusohjelmat.

The new study guide (incl. teaching schedules) for academic year 2018-2019 can be found at https://studyguide.utu.fi. This site contains only previous years' guides.

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Archived Curricula Guide 2016–2018
Curricula Guide is archieved. Please refer to current Curricula Guides
TÄHT7023 Statistical methods 6 ECTS
Organised by
Person in charge
Harry Lehto
Planned organizing times
Period(s) I II III IV
2016–2017 X
Preceding studies
Good familiarity with a higher level programming language, such as FORTRAN90/95, FORTRAN77, C++, C, Pascal, JAVA, Mathematica. The knowledge of excel or open office spreadsheet programs is not sufficient for the completion of the studies.

Learning outcomes

The student will understand and be able to:
write programs that can be run on real data or self programmed artificial data;
calculate mean, standard deviations, and other statistical parameters;
evaluate when normal distribution is a suitable approximation and when other probability distributions are needed;
understand the meaning and difference between "sigma" and confidence levels;
calculate estimates for the confidence levels of a set of measurements;
compare statistical parameters from different datasets or to model data;
quantify whether a small deviation observed in the data is significant;
plan observations based on statistical requirements for the data;
understand that Pearson's correlation coefficient and linear regression are fully independent measures of the data;
understand that all correlations need not to be linear;
perform a least squares fit to a dataset and critically evaluate when it is a sensible thing to do;
evaluate when non-parametric tests are more suitable for analysis of the data;
understand the concepts of time series analysis in evenly spaced and unevenly spaced data;
evaluate the goodness of a random number generator in one's simulations;
understand the conceptual difference and similarities between a direct and an inverse problem;
evaluate when a bayesian analysis method is suitable for problem solving;
make a real attempt for a bayesian analysis solving.


Introduction to statistical methods for data analysis and interpretation in astronomy and physics.
Measurements and their handling, probability distributions, error estimation, tests, correlation coefficients, analysis of variances. Least squares methods, other optimization methods. Non-parametric tests. Time series analysis, noise generators.
Inverse problems, introduction to Bayesian methods, Bayesian methods in practice.
The course contains a number of demanding computer exercises that require programming.

Teaching methods

Teaching method Contact Online
Lectures 28 h 0 h
Exercises 12 h 0 h

Homework and computer tasks

Teaching language


Modes of study

Option 1
Available for:
  • Degree Programme Students
  • Other Students
  • Doctoral Students
  • Exchange Students
Written exam
  • In English
Participation in classroom work
  • In English

Minimum 50% of exercises and the final exam.


Numeric 0-5.

Recommended year of study

4. year autumn
5. year autumn

MSc-degree students, year 1 or 2

Study materials

Supporting material e.g. Press, Flannery, Teukolsky ja Vetterling,
Numerical Recipes (FORTRAN) the art of computing (2nd ed. or more recent).

Other supporting material to English speaking students will be addressed separately at the beginning of the course.

Belongs to following study modules

Department of Physics and Astronomy
Department of Physics and Astronomy
Department of Physics and Astronomy
Department of Physics and Astronomy
Department of Chemistry
Archived Teaching Schedule. Please refer to current Teaching Shedule.
Department of Physics and Astronomy
DP in Physical Sciences
DP in Physics Education Track
DP in Physical Sciences
DP in Theoretical Physics
Finnish Study Modules