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).
||Mathematics (especially analysis and linear algebra); solid programming skills (required!)
||9 ECTS credits
||4V+2Ü (4 hours of lectures, 2 hours of tutorials per week)
||using the SIC Course Management system (CMS)
||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.
It can be taken by students of other programs, subject to agreement with the instructor.
In particular, it can be taken as a substitute for StatsLab if necessary, but you cannot get full credits for both StatsLab and this course.
The following topics will be covered in the course; additional topics may be included, depending on time and current events.
- 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
- 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
- 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
Please refer to the SIC CMS for all details.
Lecture Times: Tue+Thu 08:30 - 10:00 via Zoom (link for registered students in the CMS)