Course Description
As a central component of the IMPACT program, six sessions per week are offered with subject-specific content for the preparation of studies. Four of these six sessions are dedicated to repeating the most important mathematical and statistical basics and are distributed over the four-week long IMPACT program as described in the following:
Step 1
In the first two weeks, a repetition of the concept of probability and its implications will take place. These two weeks prepare for the exam of the pre-requisite course “Probability”.
In detail, this includes:
- Concepts of probability, distributions, conditional probability and independence, Bayes’ rule, sequences of events,
- Sampling, Binomial distribution, Normal approximation, Poisson distribution,
- Random variables, expectation and variance,
- Probability densities, Exponential and Gamma distributions, substitutions, cumulative distribution functions,
- Joint distributions, Uniform and Normal distributions, and
- Dependence, conditional distributions, covariance and correlation.
Step 2
The remaining two weeks are dedicated to an exhaustive introduction to statistical inference. These four weeks prepare for the exam of the pre-requisite course “Inference”.
In detail, this includes:
- Parametric point estimation: method of moments and maximum likelihood; consistency; sufficiency; error, bias and loss; completeness; Rao-Cramer-bound; invariance; Bayesian estimation,
- Parametric interval estimation: confidence intervals, especially for Normal distribution parameters, finding methods, Bayesian estimation, and
- Tests of hypotheses: simple and composite hypotheses, loss function, (uniformly) most powerful tests, unbiased tests, tests for (multivariate) Normal distribution parameters, Chi-square tests, relation to confidence intervals.