https://www.vsb.cz/e-vyuka/cs/subject/639-3021/01
viz LMS - lms.vsb.cz
Foundations of Mathematical Statistics
| Type of study | Follow-up Master |
|---|---|
| Language of instruction | English |
| Code | 639-3021/01 |
| Abbreviation | ZMS |
| Course title | Foundations of Mathematical Statistics |
| Credits | 4 |
| Coordinating department | Department of Quality Management |
| Course coordinator | Ing. Filip Tošenovský, Ph.D. |
Osnova předmětu
1. Introduction to statistics – explanation of its use in metallurgy. Graphical representation of data samples, assessment of data type. General principles of testing.
2. Confirmation of data sample homogeneity using graphs. Outliers – their depiction, detection (box plot) and solution.
3. Confirmation of data independence using graphs. Effect of data dependence on quality of data sample processing.
4. Confirmation of normality: normal distribution, Gauss curve and its parameters, empirical histogram. Reasons why normality is required, and procedures to be followed if the normality condition is not met.
5. Descriptive characteristics of location, variability, skewness and kurtosis. The notion of robustness of numerical characteristics.
6. Student’s distribution, Fisher’s distribution, Pearson’s distribution and their graphs. Examples of using the distributions. Use of tables of quantiles and critical values.
7. Point estimation and confidence intervals. „Confidence level“ and „nivel of test“.
8. Analysis of two data samples. Testing the difference of expected values and variances. Two-sample t-test, F-test.
9. Evaluating a measure of dependence (correlation) of two variables: Pearson’s correlation coefficient, Spearman’s rank correlation coefficient.
10. Regression analysis – simple (paired) linear regression. Estimation of regression coefficients by least squares. Assessment of significance and quality of the regression function. Simple nonlinear regression models (power, exponential, logarithmic, quadratic and polynomial models).
11. Regression analysis – multivariate linear regression. Assessment of significance of the model and its regression coefficients. Use of multivariate regression.
2. Confirmation of data sample homogeneity using graphs. Outliers – their depiction, detection (box plot) and solution.
3. Confirmation of data independence using graphs. Effect of data dependence on quality of data sample processing.
4. Confirmation of normality: normal distribution, Gauss curve and its parameters, empirical histogram. Reasons why normality is required, and procedures to be followed if the normality condition is not met.
5. Descriptive characteristics of location, variability, skewness and kurtosis. The notion of robustness of numerical characteristics.
6. Student’s distribution, Fisher’s distribution, Pearson’s distribution and their graphs. Examples of using the distributions. Use of tables of quantiles and critical values.
7. Point estimation and confidence intervals. „Confidence level“ and „nivel of test“.
8. Analysis of two data samples. Testing the difference of expected values and variances. Two-sample t-test, F-test.
9. Evaluating a measure of dependence (correlation) of two variables: Pearson’s correlation coefficient, Spearman’s rank correlation coefficient.
10. Regression analysis – simple (paired) linear regression. Estimation of regression coefficients by least squares. Assessment of significance and quality of the regression function. Simple nonlinear regression models (power, exponential, logarithmic, quadratic and polynomial models).
11. Regression analysis – multivariate linear regression. Assessment of significance of the model and its regression coefficients. Use of multivariate regression.
E-learning
Povinná literatura
JAMES, G., D. WITTEN, T. HASTIE a R. TIBSHIRANI. An Introduction to Statistical Learning. NY: Springer, 2013. ISBN 978-1-4614-7138-7 .
DRAPER, N. R. and H. SMITH. Applied Regression Analysis. NY: Wiley, 1998. ISBN 978-0471170822 .
RYAN, T. P. Modern Regression Methods. NY: Wiley, 2008. ISBN 978-0470550441 .
ASHENFELTER, O. B.,P. B. LEVINE and D. J. ZIMMERMAN. Statistics and Econometrics: Methods and Applications. NY: Wiley, 2006. ISBN-13: 978-0470009451.
DRAPER, N. R. and H. SMITH. Applied Regression Analysis. NY: Wiley, 1998. ISBN 978-0471170822 .
RYAN, T. P. Modern Regression Methods. NY: Wiley, 2008. ISBN 978-0470550441 .
ASHENFELTER, O. B.,P. B. LEVINE and D. J. ZIMMERMAN. Statistics and Econometrics: Methods and Applications. NY: Wiley, 2006. ISBN-13: 978-0470009451.