Mathematical statistics is, in the present context, a term in the Swedish academic system meaning probability and statistics. These scientific disciplines both deal with variation and randomness, and provide tools to deal with these concepts in a systematic and coherent way. Since variation appears in almost any other discipline, probability and statistics have applications as good as anywhere.
Probability generally concerns the study and construction of mathematical theories and models for random phenomena and systems, whereas statistics takes its starting point in data, with the aim to understand, quantify and model variation in the data. Often a goal is to separate random variation from systematic differences between say different disease therapies, production processes, etc.
The research in probability and statistics at the centre covers theoretical probability topics such as stochastic calculus and dynamic random graphs, applied probabilistic modelling for financial markets, insurance and epidemic spread, but also theoretical statistics and applications to, for example, life sciences and survey sampling.
My research, in close collaboration with a climate researcher, concerns prediction problems related to climate reconstruction, using proxy data (e.g. tree rings) to reconstruct temperature during the past millenium. For this a calibration period is needed, during which both actual temperature data and proxy data are available. This can be viewed as a regression problem, but complications arise due to e.g. various non-linearities, the use of filtered or otherwise preprocessed data, temporal and spatial autocorrelation between errors, and errors in both temperature and proxy measurements.
My research interests lie in applied probability models and statistical inference for such, in particular epidemic models, networks and applications towards genetics and molecular biology including phylogenetics.
My research interests are within probability theory, with emphasis on discrete spatial structures and random graphs. During the last decade there has been a large interest in random graph models aimed at describing various types of complex networks. The majority of the proposed models however do not take spatial aspects into account while, in reality, spatial aspects are often likely to play a role for the structure of a network. Introducing spatial structure in random graph models is therefore a step towards making the models more realistic. It also leads to questions of profound mathematical interest.
In my research I like to work in the intersection between between inference theory, probability theory and various applications of statistics, in particular genetics, but also insurance mathematics and signal processing.
Right now, one of my main areas of interest is population genetics, in particular computing the effective size of various populations, using mathematical tools such as coalescence theory and quasi equilibrium. This has implications for conservation biology, and I am cooperating with population geneticists on these topics.
I have always liked statistics as the bridge between deductive science (mathematics and logic) and inductive experimental science. For me, much of the beauty of mathematics is revealed when phenomena in different fields of applications are modeled in a succinct and hopefully general
Statistical learning theory and Bayesian networks, probabilistic bioinformatics, discrete probability and stochastic processes.