Many scientific and business problems revolve around understanding data that is in some way uncertain or ambiguous. The challenge is generally to squeeze as much useful information as possible from the data, and at the same time maintain a clear and quantified understanding of the final accuracy. Uncertainty may arise from noisy sensors, imperfect models, or the inherently stochastic nature of biological systems and experiments – in all cases the key need is to understand and manage uncertainty.
Sometimes the requirement is to choose actions on the basis of the available information – a good example is management of a utilities network given an uncertain weather forecast. When a sequence of decisions is needed, each choice can have complex and far-reaching consequences; making good decisions in this situation is challenging from both a mathematical and a computational perspective. In addition, human insight and judgement cannot be replaced – any computer systems must enhance and not reduce the ability of human decision makers to stay in control.
Our experience and expertise includes the following:
- Bayesian methods: Use of Bayesian statistical methods for inference problems.
- Monte Carlo techniques: Stochastic simulation methods to analyse the impact of uncertainty or randomness.
- Stochastic calculus: Analytical methods to model processes which are inherently stochastic.
- Optimal decision making under uncertainty: Mathematical methods to support good decision making using uncertain data, such as ensemble forecasts.