392160 Statistics, Probability and Algorithms for Bioinformatics (V) (SoSe 2004)

Contents (subject to change):

• Repetition of probability theory basics
• Computer representation of discrete and continuous,

parametric and non-parametric distributions

• IEEE floating point format; limits of precision
• Examples of important distributions and how they arise in practice
• Numerical computations with (small) probabilities; log-space;

lngamma function; factorials; binomial and multinomial coefficients

• Generation of uniform random numbers
• Generation of random numbers with special distributions
• General methods for generating random numbers
• Generation of random combinatorial objects with specified properties
• Sampling from complicated distributions
• MCMC methods
• Generating functions and applications
• Word statistics in random texts
• Repetition of basics on Statistical Testing; exact tests
• Algorithms for exact statistical tests
• Score statistics for sequence profiles (PSSMs)
• Goodness-of-fit test for the multinomial distribution
• Score statistics of local sequence alignment

Requirements for participation, required level

Prerequisites:

• Elementary probability theory and statistics
• Knowledge of MATLAB or PERL or C/C++ or Java or Python

for practical problem solving and visualization

Bibliography

Bibliography:

• William H. Press, Brian P. Flannery, Saul A. Teukolsky and William T. Vetterling

Numerical Recipes in C, Second Edition
Cambridge University Press
A classic.

• John A. Rice

Mathematical Statistics and Data Analysis, Second Edition
Duxbury Press
Relatively expensive, but easy-to-read introductory statistics text.

• W.N. Venables, D.M. Smith, and the R Development Core Team

An introduction to R
Official web page of the R project: http://www.r-project.org
R is a free version of the commercial Splus software.

• Christian P. Robert und George Casella

Monte Carlo Statistical Methods
Springer
Not very easy to read.
Has a lot of material about random number generation and MCMC methods.
Contains quite a number of misprints for a Springer statistics text.

• Ronald L. Graham, Donald E. Knuth und Oren Patashnik

Concrete Mathematics
Addison-Wesley
Contains all the mathematics a programmer or algorithmician will ever need
and more. Not very easy material, but extremely well written.

• Robert Sedgewick und Philippe Flajolet

Analysis of Algorithms
Addison-Wesley
Has many examples about how to use generating functions for the analysis of algorithms.

External comments page

http://www.techfak.uni-bielefeld.de/ags/gi/teaching.html