Statistics and Reliability in Medicine
Code  Completion  Credits  Range  Language 

A6M33SSL  Z,ZK  5  2P+2C  Czech 
 Vztahy:
 During a review of study plans, the course X01SMM can be substituted for the course A6M33SSL.
 It is not possible to register for the course A6M33SSL if the student is concurrently registered for or has already completed the course X01SMM (mutually exclusive courses).
 The requirement for course A6M33SSL can be fulfilled by substitution with the course X01SMM.
 Garant předmětu:
 Lecturer:
 Tutor:
 Supervisor:
 Department of Cybernetics
 Synopsis:

The course extends previous course EA0B01PSI (Probability, Statistics, and Theory of Information) by specific statistical methods used in biology and medicine. Planning and evaluation of statistical studies is given particular attention. Moreover, the course deals with description, analysis and modeling of reliability issues in the context of technical systems, as well as elaborates reliability estimation for complex systems. Methods and tools for systems backup are introduced.
 Requirements:

We assume knowledge of the probability theory foundations in the extent taught in the first part of course A0B01PSI (Probability, Statistics, and Theory of Information)
Students must successfully pass the entry test of course prerequisities in the first week of the semester to get an assessment. If a student fails in this test and does not cancel the course enrollment, the enrollment lapses. As an equivalent of the entry test, a successfully finished course listed among the SSL prerequisities (see above) may be accepted if the student studied the course as a part of her study plan in the BMII programme.
 Syllabus of lectures:

1. Rehearsal: relevant concepts of probability theory.
2. Introduction to statistics. Types of variables. Observational study vs experiment. Parameter estimation.
3. Method of moments. Maximum likelihood estimation.
4. Interval estimates.
5. Hypothesis testing. Errors of the 1st and 2nd kind. ROC.
6. Comparing two distributions. Pair experiment. ANOVA.
7. Goodness of fit test. Test of independence. Correlation test.
8. Linear regression.
9. Basics of reliability. Exponential distribution of defects.
10. Basic classification of defects. Computing composite reliabilities.
11. Reliability of systems.
12. Redundancy and system backup.
13. Markov models for reliability analysis.
 Syllabus of tutorials:

1. Review of probability theory.
2. Features of parameter estimators. CLV.
3. Parameter estimation: method of moments, maximal likelihood.
4. Interval estimates.
5. Hypothesis testing.
6. Hypothesis testing: comparing two distributions.
7. Goodness of fit tests.
8. Correlation, regression.
9. Reliability of system elements.
10.11. Reliability of complex systems, examples.
12.13. Markov models in reliability.
 Study Objective:

Statistical tests and estimation methods, reliability theory.
 Study materials:

[1] Wasserman, L.: All of Statistics: A Concise Course in Statistical Inference. Springer Texts in Statistics, Corr. 2nd printing, 2004.
[2] Papoulis, A., Pillai, S.U.: Probability, Random Variables, and Stochastic Processes. McGrawHill, Boston, USA, 4th edition, 2002.
[3] Hoang, P. (Ed.): Handbook of Reliability Engineering, Springer Verlag, London/Berlin/Heidelberg, 2003,
ISBN 1852334533, 663 pp.
 Note:
 Further information:
 http://cw.felk.cvut.cz/doku.php/courses/a6m33ssl/start
 No timetable has been prepared for this course
 The course is a part of the following study plans: