Tony O'Hagan - Academic pages

Short course: Uncertainty in Mechanistic Models

This course provides an introduction to Bayesian methods, based particularly on the use of Gaussian process emulators, to characterise uncertainties in the outputs of mechanistic models. No background knowledge is assumed beyond very basic appreciation of statistical methods and of how mechanistic models are used to predict complex real-world processes. This is a hands-on course with exercises using the GEM-SA software. Participants will be expected to have their own laptop computers.

Learning Objectives

At the end of the course, participants should:

• understand the various sources of uncertainty in the outputs of mechanistic computer models;
• appreciate how uncertainty in model inputs may be quantified and how it propagates through the model to induce uncertainty in outputs;
• understand the approach of variance-based sensitivity analysis to quantify the relative impacts of uncertainty regarding the different inputs;
• have a clear idea of how the Gaussian process emulator is built using a sample of training runs, the roles of key parameters in its specification, and methods for designing the training sample;
• know how to use GEM-SA to build an application, to generate a suitable design and analyse model outputs to conduct uncertainty and sensitivity analyses;
• be aware of the importance of validating the emulator, and the tools available for this in GEM-SA;
• appreciate more advanced topics such as structural uncertainty, calibration and data assimilation.

Synopsis

1. Uncertainty in computer models. Mechanistic models of real-world processes. Sources of uncertainty. Uncertainty and sensitivity analyses. Computational issues.
2. Gaussian process modelling. Simulators and emulators. The Gaussian process emulator. Mean and covariance modelling. Design and validation.
3. Getting started with GEM-SA. Introduction to the software and principal options/menus. Creating a project.
4. Uncertainty analysis using GEM-SA. Input and output files. Fitting and uncertainty analysis. Validation diagnostics.
5. Elicitation of input distributions. Eliciting expert knowledge. The SHELF system. Practical exercise.
6. Sensitivity analysis in GEM-SA. Setting up and interpreting sensitivity analyses. Main, interaction and total effects.
7. More advanced topics. Structural uncertainty. Calibration and data assimilation. Dynamic and stochastic simulators. Multiple outputs.