Content:

Fundamentals of probability theory:

• basic concepts of probability theory (probability space, random variable, distribution),
• distribution of real-valued random variables (binomial, Poisson, exponential and normal distribution, etc.),
• expected value, variance, covariance,
• distribution of random vectors, multivariate normal distribution as an example,
• conditional probability, independence,
• law of large numbers,
• central limit theorem. 
   

Fundamentals of statistics:

• parameter estimator,
• interval estimator,
• tests.

Outlook on the following areas:

• Monte Carlo simulation,
• linear regression,
• big data and machine learning,
• Markov chains.

Contact time:

4 + 2 SWS / 56 h Vorlesungen

2 SWS/ 84 h Übungen

Requirements: 

Grundlagen der Mathematik I (Analysis und Lineare Algebra) 

Angebotsturnus: 

KIS

Contact Time: 

4 SWS

Contents:

• Linear regression models
• Parametric curve fitting
• Likelihood ratio tests
• Data adaptive model selection
• Analysis of Variance (ANOVA)
• Experimental design
• Stationary stochastic processes
• Autoregressive and ARMA-processes
• Parameter estimation and model selection for time series
• Trend and seasonality
• Forecasting by exponential smoothing and the Box-Jenkins method
• Linear filters

Contact time: 

4 SWS / 50 h Lectures 

2 SWS / 54 h Tutorials

Prerequisites (Contents): 

Elementary probability theory and statistics (e.g. Praktische Mathematik: Stochastik). 

Frequency of occurence: 

The lecture is given once per year, in the summer term.

KIS

OLAT 

 Contents:

Processing and statistical analysis of three-dimensional image data, in particula

• Random closed sets and their characteristics
• Discretisation and three-dimensional connectivity
• Mathematical morphology</il>
• Methods of image processing: filtering, segmentation, Euclidean distance transform, labelling, watershed transform
• Estimates of geometric characteristics for random closed sets from image data

Contact Time:

2 SWS / 26 h Vorlesungen

2 SWS / 26 h Übung/Praktikum

Prerequisites (Contents):

The lecture "Stochastic Methods" from the Bachelor degree program in mathematics. Further knowledge of stochastics (e.g. ‘Time Series Analysis’ or ‘Probability Theory’) is an advantage, but not essential.

KIS  

OLAT

Content:

• Asymptotic analysis of M-estimators, especially of Maximum-Likelihood-estimators
• Bayes and Minimax-estimators
• Likelihood-ratio-tests: asymptotic analysis and examples (t-test, chi²-goodness-of-fit-test)
• Glivenko-Cantelli-theorem, Kolmogorov-Smirnov-test
• Differentiable statistic functionals and examples of applications (derivation of asymptotic results, robustness)
• Resampling methods on the basis of Bootstrap.

Contact time: 

4 SWS / 60 h Lectures 

2 SWS / 30 h Tutorials 

Requirements:

Elementary probability theory and statistics (e.g. Praktische Mathematik: Stochastik)

Frequency of occurrence:

The lecture is given once per year, in the winter term. 

KIS

OLAT

Appointments upon prior arrangement. If you are interested in participating the seminar, please directly contact Prof. Dr. Claudia Redenbach via Email (claudia.redenbach@rptu.de). The kick-off meeting will take place in the first week of lectures.

KIS

OLAT