METHODOLOGICAL RESEARCH: * Forecasting (PP) Short: Methodological developments related to forecasting encompass statistical modeling aspects, communication of the forecasts, and subsequent decisionmaking. Long: The ultimate objective of any kind of mathematical modeling is to have the ability to forecast the future behavior of the system considered. This is thus also the case when developing statistical models. Forecasting is however a peculiar research area, since developing a model describing the observed behavior of a system, may not be enough for insuring sufficient forecast ability. For instance, understanding how and why oil prices increased so suddenly in the last few years is certainly not enough for forecasting when will be the next time this will happen. Forecasting can then be seen as a combination of mathematical modeling and expert knowledge. Methodological research related to forecasting includes probabilistic forecasting, extreme event detection (and issuing of warnings/alarms), etc. While forecasting is common when talking about the weather, oil prices or more generally stock exchange markets, few may know that forecasting is also necessary for a wide range of industrial applications (eg. production and maintenance management, transportation planning, product development), as well as social and political issues. Optimal decision-making is today generally based on forecasts. Methodological developments therefore also include optimal communication of forecasts, and stochastic decision-making. * Data Assimilation (PP) Short: Development in the field of data assimilation focuses on nonparametric Bayesian methods such as particle filtering. Long: Data assimilation is the process of accounting for new data, describing the state of a system, for the initialization (or recalibration) of a mathematical model describing the evolution of such a system. The most known areas using data assimilation are weather and hydrological forecasting, for which analysis cycles permit to regularly update the estimated state of the atmosphere and oceans. Approaches to data assimilation may range from simple spatial interpolation techniques to more complex recursive Bayesian estimation techniques. The most famous of those approaches is certainly Kalman filtering, related to which significant research developments are still on the way (eg. ensemble Kalman filtering), and which has a broad range of applications for system modeling, forecasting and control. Today, research efforts at DTU Informatics concentrates on newly developed methods such as particle filtering for instance. * Modelling using Stochastic Differential Equation (LEC) Short: Stochastic differential equations are used to describe many systems with true noise and simplified models. Its application opens for a wide range of tools for model building and selection. Long: Stochastic differential equations (SDEs) are used within many fields to model systems that are too complex to be described perfectly using ordinary differential equations and for systems with noise. One of the advantages relative to ordinary differential equations (ODEs) is that it is possible to separate measurement noise from system noise and hence gaining more insight into the origin of the noise. A large part of the work on SDEs at DTU Informatics is related to discretely observed continuous time stochastic state space models. Allowing for parameter estimation in a likelihood framework. And using likelihood ratio tests for model comparison. The group currently have two software packages within these topics: CTSM (www.imm.dtu.dk/~ctsm) and PSM (www.imm.dtu.dk/projects/psm) where the latter is expected to replace CTSM as it is further developed. Topics of interest include the use of additional random walk states in suggesting functional relationships, methods for model evaluation, and estimation of linear and non-linear mixed-effects models using stochastic differential equations. * Model Evaluation (PP og LEC) Short: Model evaluation is one of the kernels of the statistical methodology, and is fundamental for model building, hypothesis checking, and for the forecasting application. Long: While model evaluation may be seen in an engineering sense as a simple check of the fitting of a model to observation data, the overall statistical framework of model evaluation is much more complex. It may involve the combined use of a number of statistical criteria permitting to balance model fit and complexity. It may also translate to hypothesis testing… When considering the forecasting application for nonlinear processes, model evaluation requires the developments of complete frameworks permitting to assign a level of quality to the forecasting models developed, but also to point towards weaknesses of existing models and necessary future developments. Especially in the young field of probabilistic forecasting, researchers at DTU Informatics are active in proposing evaluation methods and frameworks. * Modelling of Spatial and Spatio-temporal Processes (LEC og PP) Short: Some processes require the development of specific spatial or spatio-temporal approaches. This may involve clustering, spatial smoothing (kriging), and spatiotemporal dynamic modeling Long: Importance of focusing on spatial processes has been stressed by geosciences few decades ago. However now, it is recognized that complete methodologies have to be developed for spatial and spatio-temporal processes, beyond the sole application of geosciences. Applications may range for weather or climate modeling, to pollution and disease spreading, and even to wind power forecast uncertainty. For such processes, dimension reduction aspects are crucial in view of the potential size of datasets considered. In parallel, simultaneous consideration of both spatial and temporal components may require the proposal of new filtering techniques, semi-parametric and non-parametric frameworks to spatial covariance modeling, and new types of dynamical models applied to lattices. * Nonlinear and Nonparametric Methods in Time Series Analysis (PP og LEC) Short: Improving models and methods for time series analysis requires constant developments, which may derive from eg. new regression methods, varyingcoefficient models, regime-switching concepts, or mixtures of models. Long: In contrast to linear time-series analysis which is a fairly established area, nonlinear time-series analysis still requires the proposal of new models and development of new methodologies. Forgetting about linearity and the Gaussian assumption requires new ways of conceiving the statistical methodology. This translates to the development of data-driven (nonparametric) approaches to regression and estimation, data transformation aspects, new correlation concepts, etc. These new statistical modeling techniques are then applied to a wide range of practical problems, for which they prove their superiority in terms of model fitting, resulting forecast accuracy, and in their ability to explain the underlying processes. APPLIED RESEARCH: * Wind Power Forecasting (PP) Short: Wind power forecasting is a significant area of expertise at DTU Informatics, which research efforts concentrated on forecasting at different time scales, and optimal decision-making (management, trading, maintenance planning) based on forecasts. Long: Wind power generation is a nonlinear and bounded process. In addition, the fact that wind generation is directly related to wind speed, the characteristics of this process are constantly – though slowly – changing with time: it may be seen as nonstationary. All these aspects make the forecasting of wind power generation a complex task, whatever the time-scale considered (ie. from few minutes to few days ahead). Today, wind power forecasting is recognized as a research field of its own, with connections to meteorology, mathematical modeling, and power system engineering. Forecasts of wind generation are used on a daily basis by wind power producers, energy traders, maintenance planners, regulating authorities, etc. As wind generation takes a more and more significant part of the electricity mix, using forecasts will become a basis to decision-making A specificity of wind power generation is its highly volatile and hardly predictable nature. In addition, many researchers have shown that optimal decisions in terms of trading or management of wind power cannot be made from a single forecast only. This is the reason why a large part of research efforts are focused on probabilistic forecasting (see Figure below), spatio-temporal aspects of forecast uncertainty, and stochastic decision-making. At DTU Informatics, the research related to the wind power application deals with these various topics: Point forecasting of wind power (for horizons from few minutes to several days ahead) Spatio-temporal modeling of wind generation at the level of a region or a country (as well as the forecast uncertainty) Probabilistic forecasting of wind power (up to few days ahead): quantile forecasting, prediction intervals and density forecasts, or alternatively scenarios Skill forecasting, indicating the confidence to have in provided forecasts * Electricity Price Forecasting (PP) Short: The research on electricity price forecasting mainly focuses on aspects related to the effects of stochastic generation on electricity prices and competitive bidding. Long: The liberalization of electricity markets, especially in Scandinavian countries, has led to certain changes in the way electricity is traded. In addition, the significant share of renewable energies such as wind and hydro power with their inherent characteristics, results in external forces acting on the electricity prices. Trading power generation via liberalized electricity markets makes the value of each unit of produced energy tightly linked to the variations of prices in the various electricity markets. And, if focusing on renewable generation such as wind power for instance, the final revenue on the market may then be a complex function of revenues on markets with different gate closures (day-ahead, intraday, etc.) and of the penalties coming from non-respect of settled bids. While forecasting of renewable generation is crucial for trading, it is also important to be able to forecast prices on the various markets, accounting for the potential influence of external factors. In that context, research at DTU Informatics puts emphasis on the following issues: Forecasting of prices on spot, intraday, and regulation markets, accounting for the influence of wind generation on such electricity prices Probabilistic forecasting of prices and penalties, in order to seize their uncertainty Modeling of the interaction of stochastic generation sources with the various markets Stochastic decision-making methods, ie. stochastic optimization or stochastic programming, in order to design optimal management and trading strategies Possibly stochastic decision-making methods accounting for combined systems eg. wind-storage, wind-hydro, or wind -CHP * Financial Modelling (HM) Short: Long: * Pharmaceutical (PK/PD) Modelling (LEC et al.) Short: Development of new drugs involves many experiments and including very costly clinical trials. So proper modelling of pharmacokinetics and pharmacodynamics is an important tool increasing the knowledge gain from the experiments. Long: Missing – I guess Søren and Stig should contribute here ... * Bacterial Growth and Evolution Modelling (LEC) Short: The main focus is on using stochastic mathematical modelling to acquire new insights in bacterial life in collaboration with microbiologists. Long: Selection of bacteria happens all the time. Bacteria mutate and adjust to the environment also when exposed to antimicrobial agents such as antibiotics. Doctors, microbiologists, and epidemiologists produce and gather data that is important in describing these processes. One of our main focuses is to use this data in model development and thereby through close collaboration acquire new insights into bacterial growth and evolution. Traditionally these systems are modelled using ordinary differential equations thereby implicitly assuming that the model is perfect – however these models only approximates the complex life of bacteria and thus we focus on applying stochastic differential equations and stochastic simulation models instead. Examples of the cases we work with include modelling: Adaptation of P. aeruginosa to ciprofloxacin – an important antibiotic in many treatments including cystic fibrosis patients. Competition between different bacteria when exposed to antimicrobial agents such as detergents and conservatives – does the disease causing bacteria win? * Environmental Modelling (JKL kan få JKM til at skrive) Short: Long: Real life ecosystems nature complex dynamic system and measurements of these systems are often difficult and expensive, as a consequence data are often few and noisy. Different components of ecosystems are often characterized by different time-constant, an example from the ocean is that algae might double within hours or days, whereas eelgrass covering the seabed uses years or decades. These timescales should be covered in models which capture the interactions between species, because of the complexity of the systems statistical rather than mechanistic methods are needed described these systems. In the above example a question that should be answered could be, how much pressure in terms of nutrient (from agriculture and cities) can a marine ecosystem absorb and remain healthy? The answer to this question should be given in a statistical sense, that is we should be able to give an estimate of the risk of a break down. The Kalman filter and the extended Kalman filter provide tools for reconstructions of the state of a system, and provide an estimate of the variance of the point estimate, the assumption in this filtering problem is however that noise is additive and Gaussian. For biological systems it is however known that noise very often scale with the number of individuals or amount of biomass. To describe this behavior noise should be multiplicative and non-Gaussian, a natural choice for the distribution is the log-normal distribution. How to include such models in Kalman filter like set up is however not part of the standard toolbox, and techniques for handling this is under development. The challenge described above apply for discrete time models as well as for Stochastic Differential Equation (SDE) models. In addition to scale dependent noise realistic models for ecosystems will often involve highly nonlinear terms like thresholds, and the behavior of non-linear stochastic models can differ significantly from the deterministic skeleton of the stochastic models. * Population modeling (MWP + LEC) Short: Our research includes models for spread of disease and tracing animals, e.g. fish. (Skal omformuleres) Long: Spatially explicit simulation models for exotic diseases such as foot and mouth disease, swine pest, and blue tongue are important both for increasing the preparedness while waiting for the arrival and for evaluating the effect of possible interventions and changes in the regulation, e.g. animal movement restrictions and use of vaccines. One of our challenges is how to maximize the benefit of the additional data that is collected in Denmark. (Mere hvis MWP skal med) * Well Field Modelling (JKL kan få Fannar til at skrive) Short: Long: Well field modelling refers to models for groundwater flow, penetrated by wells for infiltration and/or discharge from corresponding aquifer, combined with a water distribution model. The physical model of groundwater flow is essentially described by partial differential equation, which considers the water elevation in the aquifer in both time and space. The measurement error between the model and the measurements from the operating wells in the field needs to be reduced for the model to be adequate for both simulation and prediction of the groundwater system. Therefore, the groundwater flow equation is formulated in a stochastic dynamic framework, such that the model is corrected to sufficiently reflect the real-time monitoring management system. The core of this framework consist of stochastic differential equations, or so-called grey box models since derived for the well field system to combine physical knowledge (referred to as white box models) and information in observed data series (black box). DTU Informatics, mathematical statistics, participates in the research project Wellfield Optimization, which includes development and integration of modelling, data assimilation, optimization, control, and sensor technologies into a real-time well field operation and management system. An integrated, dynamically coupled hydrological and hydraulic well field modelling system is developed for modelling the flow of water from the aquifer to the waterworks. More interesting and informative details on well field optimization can be found on the project website: http://wellfield.dhigroup.com. * Modelling and Forecasting for District Heating Systems (PP) Short: District heating is a specificity of Scandinavian countries, the optimal management of which requires advanced nonlinear models of the network dynamics, for forecasting and control purposes. Long: Owing to the importance of district heating in the Northern European countries, the group also focuses on modeling and prediction problems in central district heating systems. The final objective when considering this problem is, given fluxes and temperature losses in the network, but also the consumption pattern of water consumers, to optimize the water flux and temperature at the central water supply point. For that purpose, it may necessary to forecast both loads and water temperature at critical points of the district heating network. The research works at DTU Informatics concentrate on: Load forecasting Nonlinear modeling of the dynamics of the networks (see Figure below) Forecasting of the temperature at critical points Model Predictive Control (MPC) by embedding forecasts in existing controllers implemented at the supply point * Modelling of Thermal Dynamical Systems (HM) Short: Long: Building energy signature, PV system modeling, etc.