The following table shows some **examples** of elective courses, currently offered courses change from year to year and can be found in the course catalog of the University of Zurich.

Statistical Modeling | LE 2+1 | 5 CP | |

Statistical Analysis of High-Throughput Genomic and Transcriptomic Data | LE 2+1 | 5 CP | |

R Programming | LE 3, project, half term | 2 CP | |

Longitudinal Data Analysis (not offered every year) | LE 2+1, half term | 3 CP | |

Modeling Dependent Data (not offered every year) | LE 2+1 | 5 CP | |

Foundations of Bayesian Methodology (not offered every year) | LE 2+1, every second week | 4 CP | |

Electives at ETH | |||

In this lecture a broad range of modern aspects of statistical modeling are discussed. Namely representation of high-dimensional data, principal component analysis, cross validation, bootstrap, clustering and discrimination, logistic and non-parametric regression, survival, time series and spatial statistics, neural networks and deep learning.

A range of topics will be covered, including basic molecular biology, genomics technologies and in particular, a wide range of statistical and computational methods that have been used in the analysis of DNA microarray, high throughput sequencing and cytometry experiments. In particular, lectures will include: microarray preprocessing; normalization; exploratory data analysis techniques such as clustering, PCA, multidimensional scaling, UMAP, tSNE; controlling error rates of statistical tests (FPR versus FDR versus FWER); limma (linear models for microarray analysis); mapping algorithms (for RNA/ChIP-seq); RNA-seq quantification; statistical analyses for differential count data; isoform switching; epigenomics data including DNA methylation; gene set analyses; classification; analysis of single-cell cytometry and gene expression datasets.

The lecture elaborates on programming with the S language in the R system for statistical computing and graphics. Students learn about language constructs and start to write functions. More complex tasks are addressed with the help of the S3 system for object oriented programming. Special emphasis will be put on software dissemination using R packages, on documentation infrastructure, and the R environment in general. Two hours of lectures are complemented with one hour of programming exercises and a weekly homework assignment.

Longitudinal data are frequently encountered in biostatistics, in general they are repeated measurements over time from the same individual. Students learn how to explore longitudinal data and how to analyse them with simple approaches, e.g. ANOVA and ANCOVA. Further the general linear model for continuous outcomes is studied as well as random effects models and generalized linear models for longitudinal data.

In many applications, the basic assumption of independent random quantities is unrealistic and appropriate procedures are necessary to model the dependencies. According to the type of dependency, different approaches are commonly used.

The lecture starts with a focus on an important case of dependent data: so-called longitudinal and time series data, these are in general repeated measurements over time from the same individual/observational unit.

Subsequently, spatial data are studied, starting with so-called lattice data and introducing conditional and simultaneous autoregressive (CAR and SAR) models as well as Gaussian Markov random fields. Further, classical geostatistical spatial processes are introduced and methods for estimation and prediction explored as well as some extensions discussed. Finally, students will learn how to model spatial point patterns, e.g. counts of cases of a disease over a geographical region.

Theoretical concepts, practical applications and implementations (in R) are balanced throughout the semester.

The well-established Bayesian methodology provides powerful tools for data analysis in many domains of science. The unique ability to incorporate prior knowledge makes Bayesian methods attractive especially for empirical research. This ability is attracting a growing number of practitioners who see the Bayesian paradigm as an intuitive approach to answering relevant research questions. An additional advantage is that Bayesian modeling has become easily accessible in R, which provides interfaces for general-purpose and specialized software systems for Bayesian computation. However, Bayesian methodology is often used without any deeper understanding of its intricacies. This hinders thoughtful and efficient applications of Bayesian methods in practice. This lecture reviews fundamental concepts of Bayesian methodology and provides an accessible introduction to its theoretical concepts and practical tools. Biomedical applications discussed in this lecture and an individual project establish a strong link between Bayesian theory and practice. Successful participants will be able to use the skills acquired and apply Bayesian methods in other areas of research.