 CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2022/2023
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

# Mathematical statistics for clinical assessment

Code Completion Credits Range Language
17DBMSH ZK 5 2P Czech
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Biomedical Technology
Synopsis:

Determinism and chance. Errors in statistics application in research.

Population and sample. Sample size and representativeness ? basic ideas.

Mathematical statistics foundations revisited: Random variable and its distribution. Discreet, absolutely continuous, and mixed random variables. Quantiles as an inverse function to the distribution function. Non-symmetric densities. Random vectors.

Dependence and independence of random variables, correlation coefficient.

Introduction to mathematical statistics and design of experiments.

Error propagation during transformations of experimental values. Point estimations: method of moments

Point estimations: maximum likelihood method. Confidence intervals.

Hypotheses testing, errors.

p-value.

Specificity and sensitivity.

Problems related to the sample size.

Bayesian theory ? fundamental principles.

Bayesian statistics.

Current trends in mathematical statistics.

Requirements:

The exam is practical, it is based on processing the student´s own date, and should support his/her dissertation. During the exam, the student shows an ability to apply and interpret selected parts of the course.

Syllabus of lectures:

1) Determinism and chance. Errors in statistics application in research.

2) Population and sample. Sample size and representativeness ? basic ideas.

3) Mathematical statistics foundations revisited: Random variable and its distribution. Discreet, absolutely continuous, and mixed random variables. Quantiles as an inverse function to the distribution function. Non-symmetric densities. Random vectors.

4) Dependence and independence of random variables, correlation coefficient.

5) Introduction to mathematical statistics and design of experiments.

6) Error propagation during transformations of experimental values. Point estimations: method of moments

7) Point estimations: maximum likelihood method. Confidence intervals.

8) Hypotheses testing, errors.

9) p-value.

10) Specificity and sensitivity.

11) Problems related to the sample size.

12) Bayesian theory ? fundamental principles.

13) Bayesian statistics.

14) Current trends in mathematical statistics.

Syllabus of tutorials:
Study Objective:
Study materials:

Required:

 C. Chatfield: Statistics for technology: a course in applied statistics. 3rd ed. Boca Raton: Chapman &amp; Hall/CRC, 1998. ISBN 0-412-25340-2

Recommended:

 Evidence-based outcome research: a practical guide to conducting randomized controlled trials for

psychosocial interventions / edited by Arthur M. Nezu and Christine Maguth Nezu.

Oxford University Press, 2008. ISBN 978-0-19-530463-3

 D.S. Silvia, J. Skilling: Data Analysis. A Bayesian Tutorial. 2nd ed. Oxford University Press, 2006. ISBN 978?0?19?856831?5.

Note:
Time-table for winter semester 2022/2023:
Time-table is not available yet
Time-table for summer semester 2022/2023:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2023-05-30
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