Copula Processes

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find both methods comparable. We also find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

Generalised Wishart Processes

We introduce a stochastic process with Wishart marginals: the generalised Wishart process (GWP). It is a collection of positive semi-definite random matrices indexed by any arbitrary dependent variable. We use it to model dynamic (e.g. time varying) covariance matrices. Unlike existing models, it can capture a diverse class of covariance structures, it can easily handle missing data, the dependent variable can readily include covariates other than time, and it scales well with dimension; there is no need for free parameters, and optional parameters are easy to interpret. We describe how to construct the GWP, introduce general procedures for inference and predictions, and show that it outperforms its main competitor, multivariate GARCH, even on financial data that especially suits GARCH. We also show how to predict the mean of a multivariate process while accounting for dynamic correlations.

Articulated wooden blades for a horizontal-axis wind turbine. Design, construction and testing.

A pair of blades were constructed following a Tapered Chord, Zero Twist pattern after Anderson. The construction uses the Wood Epoxy Saturation Technique, with a solid Beech main spar and leading edge joined together with laminated veneers of beech forming a D-section; the trailing edge is formed from millimetre ply skins, foam filled to resist compressive loads. This construction leads to an extremely light, flexible blade, with the centres of gravity and torsion well forward, giving good stability. Each blade has three built-in strain gauges, alowing flapwise bending to be measured. Stiffness, and natural frequencies, were measured, to input to a numerical computer model to calculate blade deformation during operation, and to determine stability boundaries of the blade. Preliminary aerodynamic performance measurements are presented and close agreement is found with theory.

Experimental and theoretical comparison between static and dynamic torsional soil tests

The dynamic properties of dry Leighton Buzzard sand have been investigated using a resonant column test apparatus. These data are compared with very low frequency cyclic tests on identical specimens of sand. The comparison indicates that the properties of dry sand are independent of frequency. A simple one-dimensional model of kinematic hardening plasticity is used to predict the dynamic behaviour of the sand. The input parameters for this model are based on the results of static tests. These may be conducted on standard laboratory equipment with only minor modifications. The predictions are in good agreement with the measured data.