The statistics and mathematical economics section is passionate about data science, applications of statistics and computational aspects of statistics and has a broad expertise in fields such as graphical models, time series, survival analysis and mixed models. The group contributes with statistical expertise to interdisciplinary research projects in for example medicine, engineering, biology and pedagogy.

Modern statistics is intimately connected with computing due to large data sets and modern computationally intensive methods such as bootstrap, Monte Carlo and Markov chain Monte Carlo in Bayesian statistics.  Section  members are prominent contributors to the open source statistical analysis and programming environment R with contributed R packages regarding for example graphical models and spatial statistics.

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Econometrics is short for the analysis of economics using mathematical and statistical methods. In finance, econometrics is useful for testing financial theories, determining asset prices or returns, testing hypotheses concerning relationships between variables, examining the effect on financial markets of changes in economic conditions, forecasting future values of financial variables and for financial decision-making.

Econometrics also plays an important role in macroeconomics for studying economic trends, in principle in all areas of economics.

Financial risk management concerns the theories and methods that firms use to handle risks e.g. due to changes in commodity prices or exchange rates. From a statistical and econometric perspective, risk management involves topics such as volatility modeling, correlation modeling, extreme value problems, simulation based methods and modeling of option risk.

• Specific topics considered by the mathematical economics group are
• Time series analysis of prices and returns from financial markets and specifically commodities markets.
• Energy and weather derivatives.
• Long memory in Time Series specifically for Climate Change models
• Asset pricing in continuous time: Stochastic differential equations.
• Quantitative Finance: Derivatives modeling and stochastic volatility.
• Financial risk management.

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Forensic DNA evidence is essential in modern societies to solve crime cases and legal disputes regarding paternity and family reunions. A central problem in these contexts is to calculate the evidential weight of the DNA evidence. This requires that the genetics and statistics of the DNA profiles are well understood. Modelling the genetic part of the evidence as well as the biotechn­ol­og­ical processes calls for statistical models.

When DNA evidence is used in crime cases, statistical models are crucial to account for various complex features of the data. It is for example needed to deal with mixtures of  DNA, allelic drop-out and/or degradation of the biological material. Other challenges are the introduction of newer and more sensitive biotechnological methods, e.g. sequencing, which means that models must be continuously improved and refined.

In some applications of forensic genetics, the genetic component is less well understood and fundamental problems need to be addressed. Lineage markers (i.e. Y-chromosome and mitochondrial markers) which are passed from generation to generation with no or few recombinations impose a challenge due to their structural form. Therefore research has focused on improving the understanding of these haplotypes in the Y-chromosome and mitochondrial DNA.

With more genetic markers becoming available through the introduction of DNA sequencing, methods for predicting phenotypes and physical appearance for investigative leads is being used more and more. Using genetic markers it is to some extent possible to predict features such as eye, skin and hair colour as well as age and ancestry.

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Spatial statistics is mainly concerned with statistical analysis of point pattern data or geostatistical data.

Point pattern data arise at many spatial scales. Examples are observations of random locations of tumor and immune system cells in microscopy images of lymph nodes, locations of crime scenes or epicentres and times of earth quakes. Important hypotheses concern how occurrences of points depend on environmental variables and whether point patterns are clustered or regular. For crime scene data, for example, a key question is how crime events depend on socio-economic variables or policing strategies. It is also of interest to study how crimes cluster in space as well as the spatial dependence between different types of crimes.

Geostatistical data are georeferenced observations of some variable of interest, e.g. measurements of a soil nutrient across a field where the spatial locations of the soil samples are a crucial part of the data. For geostatistical data, the sampling locations are usually regarded as fixed and the objective is to analyse the variation of the measured variable over space.

The research of the spatial statistics group is mainly concerned with spatial and space-time point pattern data. Key research topics are construction of flexible parametric statistical models for spatial point patterns as well as computational and theoretical aspects of parameter estimation and inference procedures for such models. Another important topic is non-parametric summary statistics that allow to study scientific hypotheses without having to specify a model for the data. The spatial statistics group also conducts research in stochastic geometry which is concerned with probabilistic aspects of random geometric structures.

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