Description

Mathematical models are applied to very many areas of science and social science as tools which assist industry, commerce, charities and government. Commonly, models are implemented in computer software.

Sensitivity analysis (SA) is a largely empirical approach to understanding the behaviour of a model and the consequences of uncertainty about model parameters. The key question it addresses is how changing the inputs (parameters or boundary conditions) to a model changes the output and the relative contributions of different inputs, and interactions between inputs, to changes in the output. For users of mathematical models who cannot study, or understand, the mathematics in detail, SA can deliver a lot of insight.

If you search online, you will find many examples of applications. Perhaps one will catch your interest.

There are many different methods for SA. An important distinction is between local and global SA. Deterministic, probabilistic and statistical tools all have important roles to play. Monte Carlo simulation is often used.

After developing an understanding of basic concepts, students will be expected to choose models to study, to explore suitable SA tools for those models, to learn about the underlying theory and to apply the theory using appropriate software.

Prerequisites

Statistical Concepts II is nearly essential.

It is recommended that students doing this project should also have taken Statistical Methods III.

Resources

Wikipedia article on Sensitivity Analyis and references therein.

Global sensitivity analysis : the primer, Saltelli, Ratto, Andres, Campolongo, Cariboni, Gatelli, Saisana and Tarantola, Wiley 2008 (ISBN 0470059974)

Sensitivity analysis, edited by Saltelli, Chan and Scott, Wiley 2000 (ISBN 0471998923)