# Course: Statistics 2

Course type: compulsory

Lecturer: Assoc Prof Mihael Perman, Assoc Prof Jaka Smrekar

Study programme and level | Study field | Academic year | Semester |
---|---|---|---|

Applied statistics, second level | Mathematical Statistics | 1st | 2nd |

For the timeline see Curriculum.

Prerequisites:

- Enrolment into the first year of the programme is required to participate in the course.
- Prerequisits to the written exam are the successfully completed homeworks.

Content (Syllabus outline):

- Linear methods for data analysis: Linear regression, multiple and partial correlation coefficients), canonical correlation analysis, least square estimators, Gauss-Markov theorem, canonical reduction of the linear model, hypothesis testing, prediction, generalizations of linear regression.
- Analysis of variance: One factor classification, two-factor classification, test of significance.
- Parameter estimation: consistency, completeness, unbiased estimators, efficient estimators, best linear estimator, Rao-Cramer boundary, maximum likelihood method, minimax method, asymptotical properties of estimators.
- Testing of hypotheses: Fundamentals (probablistic and nonprobalistic hypotheses, types of errors, best tests). Neyman-Pearson lemma, uniformly most powerfull tests, test in general parametric models, Wilks theorem, non-parametric tests.
- Confidence intervals: Constructions, pivots, properties of confidence regions, asymptotic properties, the bootstrap.
- Multivariate analysis: Principal component analysis, factor analysis, discriminant analysis, classification mathods.
- Basic Bayesian statistics: Bayes formula, data, likelihood, apriori and aposteriory distributions, conjugate distributions pairs, Bayesian parameter estimation, Bayesian hyposthesis testing.

Objectives and competences:

Theoretical basis for the statistical modeling will be presented. Deeper mathematical methods are needed for well grounded statistical applications. Fundamentals of Bayesian analysis will be presented.

Intended learning outcomes:

Understanding of statistical applications, interplay between statistical reasoning and models.