### Bayesian experimental design for stochastic dynamical models

Gibson, GJ *(Heriot-Watt University)*

Thursday 21 July 2011, 11:30-12:30

Seminar Room 1, Newton Institute

#### Abstract

Advances in Bayesian computational methods have meant that it is now possible to fit a broad range of stochastic, non-linear dynamical models (including spatio-temporal formulations) within a rigorous statistical framework. In epidemiology these methods have proved particularly valuable for producing insights into transmission dynamics on historical epidemics and for assessing potential control strategies. On the other hand, there has been less attention paid to the question how future data should be collected most efficiently for the purpose of analysis with these models. This talk will describe how the Bayesian approach to experimental design can be applied with standard epidemic models in order to identify the most efficient manner for collecting data to provide information on key rate parameters. Central to the approach is the representation of the design as a 'parameter' in an extended parameter space with the optimal design appearing as the marginal mode for an appropriately specified joint distribution. We will also describe how approximations, derived using moment-closure techniques, can be applied in order to make tractable the computational of likelihood functions which, given the partial nature of the data, would be prohibitively complex using methods such as data augmentation. The talk will illustrate the ideas in the context of designing microcosm experiments to study the spread of fungal pathogens in agricultural crops, where the design problem relates to the particular choice of sampling times used. We will examine the use of utility functions based entirely on information measures that quantify the difference between prior and posterior parameter distributions, and also discuss how economic factors can be incorporated in the construction of utilities for this class of problems. The talk will demonstrate how, if sampling times are appropriately selected, it may be possible to reduce drastically the amount of sampling required in comparison to designs currently used, without compromising the information gained on key parameters. Some challenges and opportunities for future research on design with stochastic epidemic models will also be discussed.

#### Presentation

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