Learning curves for Gaussian processes models: fluctuations and universality

Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves and their sample fluctuations for Gaussian process regression models. We give examples for the Wiener process and show that universal relations (that are independent of the input distribution) between error measures can be derived.

Using a group support system to aid input-output identification in DEA

In data envelopment analysis (DEA), operating units are compared on their outputs relative to their inputs. The identification of an appropriate input-output set is of decisive significance if assessment of the relative performance of the units is not to be biased. This paper reports on a novel approach used for identifying a suitable input-output set for assessing central administrative services at universities. A computer-supported group support system was used with an advisory board to enable the analysts to extract information pertaining to the boundaries of the unit of assessment and the corresponding input-output variables. The approach provides for a more comprehensive and less inhibited discussion of input-output variables to inform the DEA model. © 2005 Operational Research Society Ltd. All rights reserved.

Monthly fluctuations in radial growth of individual lobes of the lichen Parmelia conspersa (Erhr. ex Ach.) Ach.

The radial growth (RG) of 120 lobes from 35 thalli of the foliose lichen Parmelia conspersa (Ehrh. ex Ach.) Ach. was studied monthly over 22 months in south Gwynedd, Wales, UK. Autocorrelation analysis of each lobe identified three patterns of fluctuation: 1) random fluctuations (58% of lobes), 2) a cyclic pattern of growth (23% of lobes), and 3) fluctuating growth interrupted by longer periods of very low or zero growth (19% of lobes). In 80% of thalli, two or three patterns of fluctuation were present within the same thallus. Growth fluctuations were correlated with climatic variables in 31% of lobes, most commonly with either total rainfall or number of rain days per month. Lobes correlated with climate were not associated with a particular type of growth fluctuation. RG of a lobe was positively correlated with the degree of bifurcation of the lobe tip. It is hypothesised that lobes of P. conspersa exhibit a cyclic pattern of growth due in part to lobe division. The effects of climate, periods of zero growth, and microvariations in the environment of a lobe are superimposed on this cyclic pattern resulting in the random growth of many lobes. Random growth fluctuations may contribute to the maintenance of thallus symmetry in P. conspersa.

Emulation of random output simulators

Computer models, or simulators, are widely used in a range of scientific fields to aid understanding of the processes involved and make predictions. Such simulators are often computationally demanding and are thus not amenable to statistical analysis. Emulators provide a statistical approximation, or surrogate, for the simulators accounting for the additional approximation uncertainty. This thesis develops a novel sequential screening method to reduce the set of simulator variables considered during emulation. This screening method is shown to require fewer simulator evaluations than existing approaches. Utilising the lower dimensional active variable set simplifies subsequent emulation analysis. For random output, or stochastic, simulators the output dispersion, and thus variance, is typically a function of the inputs. This work extends the emulator framework to account for such heteroscedasticity by constructing two new heteroscedastic Gaussian process representations and proposes an experimental design technique to optimally learn the model parameters. The design criterion is an extension of Fisher information to heteroscedastic variance models. Replicated observations are efficiently handled in both the design and model inference stages. Through a series of simulation experiments on both synthetic and real world simulators, the emulators inferred on optimal designs with replicated observations are shown to outperform equivalent models inferred on space-filling replicate-free designs in terms of both model parameter uncertainty and predictive variance.

Emulation of dynamic computer models with multivariate output

This preliminary report describes work carried out as part of work package 1.2 of the MUCM research project. The report is split in two parts: the ?rst part (Sections 1 and 2) summarises the state of the art in emulation of computer models, while the second presents some initial work on the emulation of dynamic models. In the ?rst part, we describe the basics of emulation, introduce the notation and put together the key results for the emulation of models with single and multiple outputs, with or without the use of mean function. In the second part, we present preliminary results on the chaotic Lorenz 63 model. We look at emulation of a single time step, and repeated application of the emulator for sequential predic- tion. After some design considerations, the emulator is compared with the exact simulator on a number of runs to assess its performance. Several general issues related to emulating dynamic models are raised and discussed. Current work on the larger Lorenz 96 model (40 variables) is presented in the context of dimension reduction, with results to be provided in a follow-up report. The notation used in this report are summarised in appendix.

Pulse tail suppression in laser diode output by tunable notch filter

Efficient suppression of relaxation oscillations in the output signal from an overdriven gain-switched laser diode was demonstrated. Several quantum-well distributed feedback laser diodes from different manufacturers were used for experimental analysis. A five-fold increase in the peak power was achieved for the tail-free operation. It was found that spectral filtering removed the nonlinearly chirped components resulting in pulse shortening by a factor of three.