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 (CMS)
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.

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.

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 SIC CMS for all details.

Lecture Times: Tue+Thu 08:30 - 10:00 via Zoom (link for registered students in the CMS)