Extreme Value Analysis of Huge Datasets: Tail Estimation Methods in High-Throughput Screening and Bioinformatics
Doctoral thesis, 2011
This thesis presents results in Extreme Value Theory with applications to High-Throughput Screening and Bioinformatics. The methods described here, however, are applicable to statistical analysis of huge datasets in general. The main results are covered in four papers. The first paper develops novel methods to handle false rejections in High-Throughput Screening experiments where testing is done at extreme significance levels, with low degrees of freedom, and when the true null distribution may differ from the theoretical one. We introduce efficient and accurate estimators of False Discovery Rate and related quantities, and provide methods of estimation of the true null distribution resulting from data preprocessing, as well as techniques to compare it with the theoretical null distribution. Extreme Value Statistics provides a natural analysis tool: a simple polynomial model for the tail of the distribution of p-values. We exhibit the properties of the estimators of the parameters of the model, and point to model checking tools, both for independent and dependent data. The methods are tried out on two large scale genomic studies and on an fMRI brain scan experiment. The second paper gives a strict mathematical basis for the above methods. We present asymptotic formulas for the distribution tails of probably the most commonly used statistical tests under non-normality, dependence, and non-homogeneity, and derive bounds on the absolute and relative errors of the approximations. In papers three and four we study high-level excursions of the Shepp statistic for the Wiener process and for a Gaussian random walk. The application areas include finance and insurance, and sequence alignment scoring and database searches in Bioinformatics.
estimation of False Discovery Rates
distribution tail
F−test
high level excursions
multiple testing
High-Throughput Screening
small sample sizes
Extreme Value Statistics
HTS
quality control
limit theorems
quantile estimation
comparison of pre-processing methods
SmartTail
Shepp statistic
Gaussian random walk
correction of theoretical p-values
Bioinformatics
Wiener process
test power
analysis of huge datasets
Student t−test
Welch statistic
exotic options.
Torsdagen den 3 november 2011, kl. 10.15, Hörsal Pascal, Matematiska Vetenskaper, Chalmers Tvärgata 3
Author
Dmitrii Zholud
Chalmers, Mathematical Sciences
University of Gothenburg
Subject Categories
Other Mathematics
ISBN
978-91-628-8354-6
Torsdagen den 3 november 2011, kl. 10.15, Hörsal Pascal, Matematiska Vetenskaper, Chalmers Tvärgata 3