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Research Programme 2.3: Mathematical and Applied Statistics

Programme leader: R. Gill

Staff

(situation at November 1, 2008)

permanent staff

emeritus

PhD student

Guest researchers

Description of the project

Statistics is the art of drawing conclusions about phenomena in which chance plays a role. Randomness may arise through a variety of reasons: the intrinsic random nature of a phe-nomenon, unavoidable noise in an experiment, conscious randomization of experimental or measurement units, or as a best approximation to reality. Chance phenomena occur in a broad range of situations. This has rendered Statistical Science a highly multidisciplinary undertak-ing, but with a core body of concepts and methods that are common to the diverse applica-tions. In the stochastics group at MI we concentrate on a few of the many strands in Statisti-cal Science. Those chosen have in common that they represent areas of rapid development and strong relevance to science and society, and have substantial and challenging mathematical components. These are: forensic statistics; high throughput "omics" data; statistical and ma-chine learning; and quantum statistics.

Forensic statistics is developing into a field of statistics with a rather special flavour, where neither classical frequentist nor classical Bayesian approaches fit the need to communicate the weight of evidence of some crime-related findings to a judge or jury. The focus lies on the likelihood ratio, and in the cases that the statistical analysis is really significant, this involves extrapolation into the tails of distributions, small data sets, and unreliable modelling. A par-ticular example is given by estimating the probability of a random match of a DNA profile. Here the research relies also on statistical genetics and the probability models used in that area.

Development and applications of multivariate analysis/statistical learning techniques have especially been directed toward the field of systems biology, particularly genomics, tran-scriptomics, proteomics and metabolomics, where there is a high demand for data analysis techniques for high-volume data sets. These high-throughput "omics" data can be character-ized as consisting of few objects compared to very many variables. Objects (e.g., patients) may cluster on small subsets of variables (e.g., measurements obtained by LC-mass spec-trometry). Other interest is in the structure of fluorescence intensity data of SNP arrays. Modeling of this structure may result in parameter estimates that can be used to improve the results of "calling algorithms" that assign alleles to one of three genotypes.

In statistical learning/machine learning one deals with data arising from complex, often ill-understood phenomena. The aim is to find patterns in such data, and use these to predict fu-ture data, based on robust methods that make only few assumptions. Such methods can be very different in nature: they include structural risk minimization for classification and re-gression, but also nonparametric Bayesian methods. One may also use more traditional unions of parametric models combined with model selection and/or averaging procedures and analyze their behaviour under the assumption that they are all wrong, yet still useful in prediction. The research concerns both theoretical analysis of such methods and development of new, practical methods that combine the advantages of several existing ones.

Quantum statistics refers to the role of statistical inference for data on measurements from quantum systems. This field is making a rapid transition from a theoretical academic exercise to the laboratory and beyond, to technology, fueled by the rise of quantum information and quantum communication.