On-line since November 2006.


Our everyday activities involve predictions on a regular basis. In most cases, these predictions involve some degree of uncertainty - hence stochastic predictions. This project originates from a work on predictability of epidemics. However, the same approach can be used to other systems.


Many natural systems are inherently variable and when replicated their behaviour often differs even when occurring under apparently identical conditions. Traditionally, an ensemble of actual or potential courses of behaviour is studied in order to describe population behaviour and the following question is asked: What would a typical behaviour of a system be, were we to repeat the experiment many times? Based on the answer, we can study general properties of the system and, for example, develop strategies designed to control the dynamics. However, in many cases we encounter a different problem, as we need to analyse and predict a single realisation. In particular, many control strategies for new emerging diseases must deal with individual replicates and provide parameter estimation and predictions in real time. Central to this approach is the question: How would the particular system behave in the future?

The above graph shows a realisation of a simple stochastic process. 10 points are assumed to be known to us (marked by large red dots) but otherwise the history and the future of it (thick red line) are not known. We also do not know what parameters were used to generate this data. Ensemble forecasting is based upon running a large number of realisations of a model with randomly chosen parameters (thin blue lines). Out of these random realisations we pick up those realisations that pass very close to the known 10 points of the known replicate (thick black lines). Their history and future give us a prediction on what our known replicate could have been doing in the past (hindcasting) or will be doing in the future (forecasting). The predictions can be further narrowed using Bayesian techniques.

Predictions are mainly made for an ensemble of replicates. This makes sense if subsequent measurements are unrelated so that we only know an average behaviour of a population of replicates. However, in practical applications we are often interested in predictions for a particular population or subpopulation – based on partial observations of this particular population and on complete past observations of an ensemble of similar populations. A hierarchical Bayesian approach is a natural choice for a prediction method, enabling us to combine partial information about a particular realisation with behaviour of other realisations.

The ensemble prediction is commonly used in weather predictions, but is also used in ecology. We successfully use it in epidemiology to predict future outbreaks.


Adam Kleczkowski has an MSc and a PhD in Physics and over 27 years experience in working as a statistician and modeller in Physics, Biology and Ecology. He has written 32 scientific papers in leading international journals. He specialises in mathematical biology and his main current interest is in Markov-chain Monte-Carlo Bayesian methods. He is a Senior Lecturer in Applied Mathematics at University of Stirling, fellow of the Royal Statistical Society and The Institute of Mathematics and its Applications .

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