Teacher: dr. Miljenko Huzak, professor
To train students for planning statistical experiments or observations, analysis of data and statistical inference about population based on sample by use of standard statistical models and methods for:
- Comparison and testing laws of distribution,
- Regression analysis,
- Model selection,
- Interval and point estimation of model parameters and hypothesis testing,
- Valuation of model fit,
- Dimension reduction,
- Classification/discrimination of data,
- Analysis of survival based on censored data.
After the completion of this course, students are expected to know how:
- To apply and perform Mann-Whitney-Wilcoxon’s test
- To apply and perform Kolmogorov-Smirnov test and its version, Lillefors test
- To calculate and interpret Spearman correlation coefficient, multiple correlation coefficient and partial correlation coefficient
- To calculate multiple confidence intervals and to estimate p-value of multiple tests
- To plan experiment or observation by analysing standard errors and power functions
- To set up a multivariate model, to fit it, validate and select one
- To set up a (multiple) logistic regression model, to fit it, validate and select one
- To apply computer-intensive methods (Monte Carlo, bootstrap, cross-validation) for point and interval estimation of parameters, for estimation of test statistics sample distribution, model validation and testing of hypothesis by permutation methods
- To estimate and apply survival function by Kaplan-Meier estimate
- To set up, estimate and interpret risks by use of Cox hazard model
- Nonparametric methods for law comparison. Rank tests (Mann-Whitney-Wilcoxon statistics, Spearman’s coefficient of correlation), Kolmogorov-Smirnov tests, Tests of normality (Lilliefors test), ROC curve.
- Multivariate data. Normal distribution, Multiple confidence intervals and multiple testing, Multiple correlation, Partial correlation, Linear regression models (Kronecker product, Gauss-Markov properties, model selection), MANOVA and MANCOVA models, Allocation and discrimination, Principal component analysis (the best linear prediction).
- Log-linear models. Parameter estimation, Prediction, Wald test, Model selection.
- Computer intensive methods. Monte Carlo methods, Bootstraping, Cross-validation, Permutation tests.
- Survival analysis. Kaplan-Meier estimator, Cox proportional-hazards model.