Data collected from c orrelated processes arise in many diverse applicat ion areas including both computer and physical exp eriments\, and studies in environmental science. O ften\, such data are used for prediction and optim isation of the process under study. For example\, we may wish to construct an emulator of a computat ionally expensive computer model\, or simulator\, and then use this emulator to find settings of the controllable variables that maximise the predicte d response. The design of the experiment from whi ch the data are collected may strongly influence t he quality of the model fit and hence the precisio n and accuracy of subsequent predictions and decis ions. We consider Gaussian process models that are typically defined by a correlation structure that may depend upon unknown parameters. This parametr ic uncertainty may affect the choice of design poi nts\, and ideally should be taken into account whe n choosing a design. We consider a decision-theore tic Bayesian design for Gaussian process models wh ich is usually computationally challenging as it r equires the optimization of an analytically intrac table expected loss function over high-dimensional design space. We use a new approximation to the e xpected loss to find decision-theoretic optimal de signs. The resulting designs are illustrated throu gh a number of simple examples. LOCATION:Seminar Room 1\, Newton Institute CONTACT:INI IT END:VEVENT END:VCALENDAR