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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.