Large Structured Models in Applied Sciences; Challenges for Statistics

Abstract

The first session of invited papers at the 18th Nordic Conference on Mathematical Statistics held from 5 to 8 June 2000 in Grimstad, Norway, ran under the title structured models in applied sciences; challenges for The economist Jansen, the meteorologist Gustafsson and the fishery scientists Gavaris and lanelli gave papers that were discussed by statisticians. These papers and the discussions are presented in this issue of SJS. The programme committee, which I chaired, wanted to expose Nordic statisticians to current use of large structured models. By working together with the applied scientists, statisticians can surely help to solve problems and to improve practices. This is done in many branches of science today, but the scope for co-operation is wide and the demand for skilled statisticians that are willing to dive into applied fields is increasing. Statisticians can also contribute as go-betweens. Much of the advance in the field of statistics results from applied work, either by innovations within the field as such, or by co-operation involving statisticians. These advances are often useful in other applied areas as well. The statistician can help to spread new ideas by formulating the specific innovations in the general language of statistics. To be successful go-betweens, statisticians must thus keep a sufficient foothold in their mother field of statistics. Large structured models are used in many sciences and for various purposes. In addition to economics, fisheries and meteorology, one could mention epidemiology, physiology, ecology, oceanography, and climatology. Large structured models describe complex processes. In order to represent the multivariate nature of the process, the model must be sufficiently rich in variables and parameters, and thus is large. Linear or non-linear difference or differential equations, definitional equations, and other structural restrictions are imposed on variables and parameters to represent the dynamics in time and space of the system as postulated by the substantive theory in question. Take the climatic system of the earth as an example. In order to represent the climate in its spatial and temporal diversity, the model needs to be large. Geophysics, assisted with other relevant branches of the natural sciences, provides physical laws and other regularities that give structure to the overarching model. Although smaller partial models are useful to study separate aspects of the system, large structured models are needed to describe and measure the system as a whole, with its interactions, simultaneity, delayed reaction, non-linearity, chock propagation and other complexities. The non-linearities might be severe, even bifurcations (e.g. epochs of rapid cooling or heating of the north Atlantic region, as inferred from glacial cores from Greenland). Large structured models are used for forecasting and prediction. They might be useful in making sense of data (e.g. Greenland ice-core data), and to assess the current state of the system. Policy analyses are carried out in many fields, and to account for indirect effects, delays, and non-linearities, large structured models are often required. Addressing statisticians, Gustafsson, Jansen and Gavaris & lanelli use their space primarily on statistical issues associated with large structured models in their fields of meteorology, economics, and fisheries rather than on the many issues associated with the use and utility of such models. Current and potential use should, however, be kept in mind when reading their papers.