9 Glossary

Beliefs: In Bayesian statistics, probability expresses a degree of belief in an event. Such belief can be based either on prior knowledge or on personal beliefs about the event.

Correlation lengths: The correlation lengths are hyperparameters that appear in the structure of the emulators. They determine how close two parameter sets must be in order for the corresponding residual values to be highly correlated. Large values for the correlation lenghts are chosen if the model is believed to be a smooth function of the parameters.

Emulator output: The data produced by executing an emulator. In each wave of the history matching process, a subset of the model outputs is selected to be emulated.

Ensemble variability: The variability resulting from the stochasticity of the model.

Implausibility: A measure which evaluates the distance between the targets and the model output/emulator output at any given parameter set.

Input space: The set of all possible combinations of parameters.

Model output: Any data produced by executing a model. An example of model output in this case study is the number of infectious individuals at time \(10\) (or \(15, 20, 25, 30\)).

Observed data: The data we fit our model to, which usually comes from empirical observations. Since in this case study we work with a synthetic dataset, we prefer to use the word ‘targets’ rather than ‘observed data’.

Parameter set: An element of the input space.

Points: Another word for ‘parameter set’.

SEIRS model: A model consisting of four compartments: Susceptible individuals (S), Exposed individuals (E) i.e. people that are infected but not infectious yet, Infectious individuals (I) and Recovered individuals (R). In the model four transitions are allowed: S to E, when a susceptible individual becomes infected, E to I, when an infected individual becomes infectious, I to R, when an infectious individual recovers, and R to S, when a recovered individual becomes susceptible again.

Targets: A list of pairs of the form (val, sigma), one per emulated output, used to evaluate implausibility. The ‘val’ component represents the mean value of the output and ‘sigma’ represents our uncertainty about it.

Training data: The data used to train the emulators. It is obtained by running the model at a given number of parameter sets.

Validation data: The data used to validate the emulators. It is obtained by running the model at a given number of parameter sets (different from those used for the training data).

Wave: An iteration of the history matching process.