Biometrics II (Vogl)

Course Academic Credits: 3

English or German, WS 2022/2023, weekly, Fr 8:00-9:30

Grading: only homework with some theoretical and some practical examples (R-programming) of varying difficulties, which are reflected in the obtainable points

Contents: Introduction to Bayesian statistics with biological examples. In detail: 1) introduction to Bayesian statistics with examples from genetics. 2) standard distributions and their conjugate prior distributions, also with examples from biology: binomial with beta prior, Poisson with gamma prior, exponential with gamma prior, normal with normal-inverse-chisquared prior; improper priors. 3) empirical Bayes method. 4) Bayesian networks, where the conditional dependencies can be described by a directed acyclic graph (DAG); hidden Markov model (as an example for a DAG) with the forward-backward algorithm (a dynamical programming method) to calculate probabilities numerically. 5) more complicated models, where dynamic programming is impossible (with many biological examples); numerical methods: Bayes and Markov chain Monte Carlo method (Metropolis, Metropolis-Hastings, Gibbs sampling) and expectation-maximization (EM) algorithms.

- Durbin, R., Eddy, S., Krogh, A., and Mitchison, G. (1998). Biological sequence analysis. Cambridge University Press, Cambridge.
- Gelman, A., Carlin, J., Stern, H., and Rubin, D. (1995). Bayesian Data Analysis. Chapman & Hall.

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