Lecture: Probabilistic Models and Data Analysis – WS15/16

Instructor: Prof. Dr. Verena Wolf
Assistants: Alexander Andreychenko, Charalampos Kyriakopoulos
News: Midterm is on Dec 16, at 12:00.

Materials: CMS system 

Schedule: Wed, 12:00 -13:30, Building E2 1 – Room 007

Tutorial slot:  Tue, 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 exercises are solved/presented during the two slots and the homework consists in watching videos which will be uploaded at the course homepage.

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.

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

Exam Schedule: tba

Using 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 – REVIEW OF PROBABILITY AND RANDOM VARIABLES
    • Events and their probabilities
    • Rules of probability
    • Combinatorics
    • Conditional probability and independence
    • Distribution of a random variable
    • Expectation and variance
    • Families of discrete distributions
    • Families of continuous distributions
  • 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
    • Confidence intervals
    • Hypothesis testing
    • Chi-square tests
    • tba
    • Bayesian inference

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