Lecture: Probabilistic Models and Data Analysis – WS17/18

Instructor: Prof. Dr. Verena Wolf
Assistant: Michael Backenköhler

CMS:
Please register in the CMS for the lecture. There you can find course materials, news, and more.

News:

  • You can now register in the CMS.
  • The first lecture will be Tuesday, 17 October in bldg. E2 1, room 007.
  • There will be no lecture on Wednesday, 18 October!

Schedule:
Tuesday 12:15 – 13:45, Building E2 1, Room 007 (tutorial slot from 24th on)
Wednesday 12:15 – 13:45, Building E2 1, Room 007

Objectives:
The aim of this course is to give students of bioinformatics and computer science a solid background in probability and statistics as well as detailed knowledge about computer simulation of stochastic models, parameter estimation and hypothesis testing. Students will also learn how to use software tools such as R and Matlab to analyse data and probabilistic models. This course is a flipped classroom course, which means that the two lecture/tutorial slots will be used for exercises/examples/questions and discussion of the material and participants have to prepare for these slots by either watching videos or reading the lecture notes.

Prerequisites:
The course is open to students from bioinformatics and computer science. Mathematical skills as well as basic programming skills are of advantage but not mandatory. We expect participants to have basic knowledge about random variables. For the following topics, we have material (notes, videos) for revision. Please register at our cms system.

  • Events and their probabilities
  • Rules of probability
  • Combinatorics
  • Conditional probability and independence
  • Distribution of a random variable
  • Expectation and variance

Certification Conditions:
There will be two written exams. The assignments are optional but bonus points may be obtained during the tutorial.

Exam:  TBD

Matlab:
As a part of the assignments, the participants will have to program in Matlab. Instructions on how to get access to Matlab.

Syllabus:

  • PART I – SHORT REVIEW OF PROBABILITY AND RANDOM VARIABLES
  • PART II – COMPUTER SIMULATIONS AND STOCHASTIC PROCESSES
    • Simulation of random variables
    • Monte Carlo methods
    • Markov chains
    • Hidden Markov models
  • PART III – INTRODUCTION TO STATISTICS AND STATISTICAL INFERENCE
    • Simple descriptive and graphical statistics
    • Parameter estimation: Maximum Likelihood, Bayesian Inference, …
    • Confidence intervals
    • Hypothesis testing
    • Multiple Testing

Text Books:

  • Probability and Statistics for Computer Scientists, Michael Baron, Taylor & Francis, 2013
  • Simulation Modelling and Analysis. Averill M. Law, Mcgraw-Hill, 2006.
  • Introduction to the Numerical Solution of Markov Chains. William J. Stewart, Princeton Univ. Pr., 1994.
  • INTRODUCTION TO PROBABILITY. C. Grinstead and L. Snell