The areas of expertise of the group include:
Extremes
Extreme events are events with a low frequency of occurrence but a high impact, as e.g. earthquakes, floods and stock market crashes. If one wants to infer about extreme events then estimation should naturally be based on the largest observations in a sample. At the theoretical level this means that we are interested in studying the tail of a distribution function. Typical quantities of interest are indices of tail decay, extreme quantiles, small tail probabilities and measures of extreme dependence.
Time series
A time series is a data set that is collected sequentially over time and has a natural ordering. Such data sets arise in various fields such as economics, engineering, biology, astrophysics, medicine, etc. The observations are expected to be related to each other and methodologies developed for independent and identically distributed data might no longer be valid and hence analysing, modelling, and forecasting the dynamics of time series data requires statistical methods specifically developed for such data.
Missing values in multivariate statistics
In most cases datasets with more than a few variables will have missing values for some entries. Due to the enormous rise in data during the past decades this problem is of high relevance. Examples include morphometric data in palaeontology or molecular data such as genetic markers or proteins markers from living beings. One possible approach to do inference from such datasets is to fill in the empty entries in a way that allows for taking into account the extra uncertainty introduced by imputing values.
Statistical demography
The dynamics of populations in natural environments, whether humans, birds or orchids, are determined by the rates at which individuals die and reproduce. These demographic rates are regulated by intrinsic mechanisms such as growth, maturation or ageing, and by external environmental factors. Understanding these mechanisms and how they interact in regulating vital rates and population dynamics is fundamental for a wide range of disciplines, from actuarial applications (e.g. design of pension systems, insurance, etc.) to the management and protection of species threatened with extinction.
High-dimensional statistics
Recent developments have made large amounts of data with very high dimension available and have led to new challenges in statistics. One central problem is referred to as “p larger n problem” and refers to situations where the number of variables in a dataset largely exceeds the number of observations. In this case, many classical statistical methods break down, e.g. the estimation of covariance matrices requires special techniques such as shrinkage approaches. The notion of sparsity refers to models where only few parameters or weights differ from zero and has become a major paradigm in highdimensional statistics. Based on sparsity assumptions, the error-controlled selection of variables is one of several central problems.
Functional data analysis
The field of functional data analysis has expanded rapidly in the last couple of decades as more and more data is recorded at a fine time scale due to the advance of modern technology. Precise information allows us to consider data as curves instead of numbers or vectors. Functional data analysis deals with the analysis and theory of the data that is in the form of curves or even more general objects (surfaces, sets, images, etc.).
Applied statistics
Along with steady developments in theoretical statistics goes the need to support application and implementation of up-to-date methods in other communities and interdisciplinary collaborations such as in life and health sciences, natural sciences, social sciences, ....