Lecture “Statistics, Probability and Applications in Bioinformatics (SPAB)”

Specialized course, B.Sc. and M.Sc. Bioinformatics, Saarland University.
Elective course, M.Sc. CS, DS/AI, and related, Saarland University (substitute for StatsLab).

Prerequisites Mathematics (especially analysis and linear algebra); solid programming skills (required!)
Credits 9 ECTS credits
Required time 4V+2Ü (4 hours of lectures, 2 hours of tutorials per week)
Language English
Registration using the SIC Course Management system
Details available after registration in the Course Management system

Target audience (IMPORTANT!)

This course is offered as a specialized lecture in the B.Sc. or M.Sc. Bioinformatics degrees, for 9 ECTS credits.

Topics

The following topics will be covered in the course; additional topics may be included, depending on time and current events.

Probability

  • randomness
  • uniform distributions on finite sets (Laplace spaces)
  • elementary and advanced combinatorics
  • finite, discrete and continuous probability spaces
  • random variables
  • discrete probability distributions and where they come from
  • probability distributions and OOP, scipy.stats
  • conditional probabilities
  • Bayes’ Theorem, simple version
  • continuous probability distributions
  • a glimpse at measure theory
  • posterior distributions

Statistics

  • descriptive statistics
  • moments of random variables (expectation, variance, …)
  • parametric models
  • statistical testing (frequentist view)
  • statistical testing (Bayesian view)
  • parameter estimation: moments, maximum likelihood
  • parameter estimation in mixture models: EM algorithm
  • regression (simple linear, logistic, robust, multiple)
  • regularization and Bayesian view on estimation
  • robust regression
  • multiple regression
  • logistic regression

Stochastic Processes

  • stochastic processes
  • Poisson process
  • models for random sequences
  • Markov chains
  • Markov processes: models of sequence evolution
  • Hidden Markov Models and applications
  • Probabilistic Arthimetic Automata and applications
  • distribution of DNA Motif Occurrences: compound Poisson
  • significance of pairwise sequence alignment
  • the PCR process

Applications in Bioinformatics

  • tests for differential gene expression
  • Bayesian view on differential gene expression
  • high-dimensionality low-sample problem
  • multiple testing

Winter 2021/22

Please refer to the CMS for all details.

Literature

  • Krengel
  • Stirzaker

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