Multivariate emulation of computer simulators: model selection and diagnostics with application to a humanitarian relief model

We present a common framework for Bayesian emulation methodologies for multivariate-output simulators, or computer models, that employ either parametric linear models or nonparametric Gaussian processes. Novel diagnostics suitable for multivariate covariance-separable emulators are developed and techniques to improve the adequacy of an emulator are discussed and implemented. A variety of emulators are compared for a humanitarian relief simulator, modelling aid missions to Sicily after a volcanic eruption and earthquake, and a sensitivity analysis is conducted to determine the sensitivity of the simulator output to changes in the input variables. The results from parametric and nonparametric emulators are compared in terms of prediction accuracy, uncertainty quantification and scientific interpretability

Bayesian Optimal Design for Ordinary Differential Equation Models

Bayesian optimal design is considered for experiments where it is hypothesised that the responses are described by the intractable solution to a system of non-linear ordinary differential equations (ODEs). Bayesian optimal design is based on the minimisation of an expected loss function where the expectation is with respect to all unknown quantities (responses and parameters). This expectation is typically intractable even for simple models before even considering the intractability of the ODE solution. New methodology is developed for this problem that involves minimising a smoothed stochastic approximation to the expected loss and using a state-of-the-art stochastic solution to the ODEs, by treating the ODE solution as an unknown quantity. The methodology is demonstrated on three illustrative examples and a real application involving estimating the properties of human placentas

Functional programming framework for GRworkbench

The software tool GRworkbench is an ongoing project in visual, numerical General Relativity at The Australian National University. Recently, the numerical differential geometric engine of GRworkbench has been rewritten using functional programming techniques. By allowing functions to be directly represented as program variables in C++ code, the functional framework enables the mathematical formalism of Differential Geometry to be more closely reflected in GRworkbench . The powerful technique of `automatic differentiation' has replaced numerical differentiation of the metric components, resulting in more accurate derivatives and an order-of-magnitude performance increase for operations relying on differentiation

Design of experiments for non-manufacturing processes : benefits, challenges and some examples

Design of Experiments (DoE) is a powerful technique for process optimization that has been widely deployed in almost all types of manufacturing processes and is used extensively in product and process design and development. There have not been as many efforts to apply powerful quality improvement techniques such as DoE to improve non-manufacturing processes. Factor levels often involve changing the way people work and so have to be handled carefully. It is even more important to get everyone working as a team. This paper explores the benefits and challenges in the application of DoE in non-manufacturing contexts. The viewpoints regarding the benefits and challenges of DoE in the non-manufacturing arena are gathered from a number of leading academics and practitioners in the field. The paper also makes an attempt to demystify the fact that DoE is not just applicable to manufacturing industries; rather it is equally applicable to non-manufacturing processes within manufacturing companies. The last part of the paper illustrates some case examples showing the power of the technique in non-manufacturing environments

Reconstructing ice-sheet accumulation rates at ridge B, East Antarctica

Understanding how ice sheets responded to past climate change is fundamental to forecasting how they will respond in the future. Numerical models calculating the evolution of ice sheets depend upon accumulation data, which are principally available from ice cores. Here, we calculate past rates of ice accumulation using internal layering. The englacial structure of the East Antarctic ice divide at ridge B is extracted from airborne ice-penetrating radar. The isochronous surfaces are dated at their intersection with the Vostok ice-core site, where the depth–age relationship is known. The dated isochrons are used as input to a one-dimensional ice-flow model to investigate the spatial accumulation distribution. The calculations show that ice-accumulation rates generally increase from Vostok lake towards ridge B. The western flank of the ice divide experiences markedly more accumulation than in the east. Further, ice accumulation increases northwards along the ice divide. The results also show the variability of accumulation in time and space around the ridge B ice divide over the last 124 000 years

Numerical wave optics and the lensing of gravitational waves by globular clusters

We consider the possible effects of gravitational lensing by globular clusters on gravitational waves from asymmetric neutron stars in our galaxy. In the lensing of gravitational waves, the long wavelength, compared with the usual case of optical lensing, can lead to the geometrical optics approximation being invalid, in which case a wave optical solution is necessary. In general, wave optical solutions can only be obtained numerically. We describe a computational method that is particularly well suited to numerical wave optics. This method enables us to compare the properties of several lens models for globular clusters without ever calling upon the geometrical optics approximation, though that approximation would sometimes have been valid. Finally, we estimate the probability that lensing by a globular cluster will significantly affect the detection, by ground-based laser interferometer detectors such as LIGO, of gravitational waves from an asymmetric neutron star in our galaxy, finding that the probability is insignificantly small.Comment: To appear in: Proceedings of the Eleventh Marcel Grossmann Meetin

Robust Bayesian detection of unmodelled bursts

A Bayesian treatment of the problem of detecting an unmodelled gravitational wave burst with a global network of gravitational wave observatories reveals that several previously proposed statistics have implicit biases that render them sub-optimal for realistic signal populations.Comment: 9 pages, 1 figure, submitted to CQG Amaldi proceedings special issu

An approach for finding fully Bayesian optimal designs using normal-based approximations to loss functions

The generation of decision-theoretic Bayesian optimal designs is complicated by the significant computational challenge of minimising an analytically intractable expected loss function over a, potentially, high-dimensional design space. A new general approach for approximately finding Bayesian optimal designs is proposed which uses computationally efficient normal-based approximations to posterior summaries to aid in approximating the expected loss. This new approach is demonstrated on illustrative, yet challenging, examples including hierarchical models for blocked experiments, and experimental aims of parameter estimation and model discrimination. Where possible, the results of the proposed methodology are compared, both in terms of performance and computing time, to results from using computationally more expensive, but potentially more accurate, Monte Carlo approximations. Moreover, the methodology is also applied to problems where the use of Monte Carlo approximations is computationally infeasible

Bayesian Optimal Design for Ordinary Differential Equation Models

Bayesian optimal design is considered for experiments where it is hypothesised that the responses are described by the intractable solution to a system of non-linear ordinary differential equations (ODEs). Bayesian optimal design is based on the minimisation of an expected loss function where the expectation is with respect to all unknown quantities (responses and parameters). This expectation is typically intractable even for simple models before even considering the intractability of the ODE solution. New methodology is developed for this problem that involves minimising a smoothed stochastic approximation to the expected loss and using a state-of-the-art stochastic solution to the ODEs, by treating the ODE solution as an unknown quantity. The methodology is demonstrated on three illustrative examples and a real application involving estimating the properties of human placentas