Statistics - Mathematical Sciences
What is statistics?
Statistics is the science of collecting, presenting and learning from data — including the effects of uncertainty. It thereby provides the navigation essential for controlling the course of scientific and societal advances (Davidian & Louis 2012).
What do statisticians do?
Statisticians apply statistical thinking and methods to a wide variety of scientific, social, and business endeavours in such areas as astronomy, biology, education, economics, engineering, genetics, marketing, medicine, psychology, public health, sports, among many.
Areas of research
Areas of research
Besides population dynamics this research also covers topics as
- evolutionary biology
- population genetics
- conservation biology
- functional genomics
An important activity is statistical modelling and analysis of data from genomics, where multiple hypothesis testing is a central research topic. Ongoing research also includes exact hypothesis testing concerning parameters of discrete distributions in the presence of nuisance parameters.
The main research topics include
- Design of Experiments (DOE)
- reliability analysis
- extreme value statistics
In reliability, focus is modelling and statistical inference in connection with repairable and maintainable systems and calculation of system reliability of structural systems.
In extreme value statistics, focus is estimation of extreme responses of dynamic structures and extreme value prediction from sampled time series.
The research in Design of Experiments (DOE) is directed towards projection properties of non-regular two-level designs.
Focus is on stochastic modelling of spatial and spatio-temporal phenomena and inference of the associated model parameters. Based on indirect observations of the phenomena Bayesian inversion with prior models of the type mentioned above is performed. Various types of Gaussian random fields and Markov random fields are mostly used.
Moreover, simulation algorithms, approximations and decision analysis for complicated spatial and spatio-temporal models are being studied. The research is inspired by challenges in characterization of petroleum reservoirs.
Research is directed towards speeding up algorithms for handling complex statistical problems. Special focus is given to Gaussian Markov random fields and applications of the approach INLA which makes it possible to avoid MCMC for doing Bayesian inference for latent Gaussian models.
Topics studied include characteristic functions and choice of smoothing parameters in kernel density estimation and methods for Monte Carlo computation of conditional distributions given sufficient statistics.
More generally, the focus is on the theoretical and mathematical foundations of Bayesian, fiducial, and frequentist inference motivated by applications in artificial intelligence (e.g. deep neural networks) and statistical inference and prediction (e.g. improper priors, nuisance parameters, parametric and non-parametric models).