Biomedical Data Analysis and Processing

Lecturer:

Tutor:

Supervisor:

Department of Biomedical Informatics

Synopsis:

Time series analysis, trends, mutual dependency, stationarity. Correlation function and covariance function. Algorithms of correlation function estimation. Impact of removing trends to autocorrelation function. Periodogram - relationship between corellogram and periodogram. Frequency spectrum, spectrum of random signals. Linear frequency filtering. AR, ARMA, and MA processes. Spectral analysis. FFT algorithm. Non-parametric methods of the frequency spectrum estimation. Positives and negatives of the specteal analysis. Repeated measurements and analysis of their properties. AR a ARMA model parameter identification. Prediction. Bivariance analysis of time series - cross-correlation and cross-covariance and their estimation. Bispectrum.

Requirements:

- examination: written test

Syllabus of lectures:

1. Time series analysis - fundamentals; trends, mutual dependency, stationarity.

2. Correlation function and covariance function. Algorithms of correlation function estimation.

3. Impact of removing trends to autocorrelation function.

4. Periodogram - relationship between corellogram and periodogram.

5. Frequency spectrum, spectrum of random signals-

6. Linear frequency filtering.

7. AR, ARMA, and MA processes.

8. Spectral analysis. FFT algorithm.

9. Non-parametric methods of the frequency spectrum estimation. Positives and negatives of the spectral analysis.

10. Repeated measurements and analysis of their properties.

11. AR and ARMA model parameter identification.

12. Prediction.

13. Bivariance analysis of time series - cross-correlation and cross-covariance.

14. Estimation of cross-correlation and cross-covariance functions. Bispectrum.

Syllabus of tutorials:

Study Objective:

to provide students with basic methods of statistical processing time series typical for life sciences

Study materials:

[1]Diggle P.J. Time Series. A Biostatistical Introduction. Clarendon Press. Oxford 1996

[2]Weiss S.M., Indurkhya N. Predictive Data Mining

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Bakalářský studijní obor Biomedicínský technik - prezenční (compulsory elective course)