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# Mathematical statistics

The mathematical statistics group concentrates on the following research fields:

### Statistical modeling of meteorological processes

Various kinds of meteorological data sampled at fine resolution become more and more available. There is research activity focused on exploiting such data in connection with analyses of climate changes. We work currently with Markov models for daily precipitation data.

The model is time inhomogeneous to account for seasonal effects and orders larger than one is considered. One important aspect of precipitation processes is the properties of the spell length distribution; e.g. the distribution of the number of consecutive wet/dry days.

These properties are also generally seasonally dependent. The Markov approach seems promising for such analyses. The research activity centers around developing methods based on the Markov model approach to study possible changes over time.

### Analysis of time to event data

Time to event data are important in many fields like medicine, engineering and social science, and this type of data require specific statistical methods due to issues like incomplete observations, skew distributions, competing risks etc.

The research activities in time to event data spans from applied work with medical and engineering data to methodological work. Some areas of interest for methodological research are flexible non-parametric modelling, residual analysis and analysis of trends in recurrent event data.

On the applied side we work e.g. with relative survival analysis of cancer registry data, multi-state modelling of emergency medicine data and exponential regression of nucleation time data.

### Statistical processes control

Statistical process control is a set of techniques for monitoring and controlling stochastic processes over time with applications in industry, medicine, environmental monitoring etc. A key method is control charts for monitoring of processes.

In applications of such charts, parameters need to be estimated and in more complex problems a model for risk adjustment have to be fitted. Current research interests are into methods for handling estimation error and methods for model choice when fitting risk adjusted control charts.  We also work on applications to medical data.

### Medical statistics

The statistics group have extensive collaborations with researchers in medical sciences, in particular at SUS but also at UiB, UiO and NTNU. In these medical research projects we analyze a wide variety of different types of data, and we also contribute to the planning of studies.

In these projects many elements of the statistical toolbox are applied, adapted and extended. Some of the work on medical problems is in collaboration with researchers in the signal-processing group at UiS as part of the research area “Health Technology”, and we also have some collaboration with researchers at the Faculty of Health Sciences at UiS.

### Computational Statistics

In many situations, non-linear statistical models are needed for an appropriate modeling of the data generating process. In such cases, computational statistical methods are typically required.

The end of such methods is typically to numerically compute integrals (as opposed to finding analytic expressions) over high-dimensional spaces, which are needed for analyzing non-linear statistical models and fitting such models to data.

Currently, the research focus in computational statistics activities are mainly centered on Hamiltonian Monte Carlo (HMC) algorithms for Bayesian hierarchical models. HMC algorithms produces random numbers with a given distribution by simulating Hamiltonian dynamical systems.

The ongoing work draws on insights from many different fields, including differential geometry and physics, numerical methods (symplectic integrators, sparse numerical linear algebra, automatic differentiation), numerical optimization as well as Bayesian statistics.

### Econometric time series analysis

Currently, the ongoing work in econometric time series analysis centers mainly around non-linear models for commodities market (e.g. crude oil, natural gas, argricultural commodities), and in particular modeling of futures markets.

The work is done in cooperation both with the UiS industrial economics researchers, and international collaborators. We consider both reduced form models (i.e. not based on economic theory) and more theoretically founded models are considered.

In many cases, such models are cast in terms of Bayesian hierarchical models, and the numerical methods required for fitting such models to data are a large part of the research activity.

### Probability theory

Probability theory is playing a prominent role in modern mathematics, as shown by the awarding of several prestigious prices in recent years, including the Abel price (won by Srinivasa S. R. Varadhan (2007) and Yakov G. Sinai (2014)) and the Fields medal (among others, won by Wendelin Werner (2006), Stanislav Smirnov (2010) and Martin Hairer (2014)). Moreover, probability theory is the foundational building block for all statistical methods.

Our group is actively involved in research on discrete probabilistic models with application areas including biology, physics and the spreading of infections. The focus of our research is on the understanding of various complex systems in which many components interact, and particularly the asymptotic behavior of such systems. More specifically, we work on models of random networks, interacting particle systems and stochastic processes in random media. Another research area in which the group is involved in is the study of stochastic processes with long (possibly infinite) memory. The group is affiliated with the research collaboration network "Stochastic Processes on Evolving Networks", financed by German Research Foundation.