Local likelihood smoothing of sample extremes

Trends in sample extremes are of interest in many contexts, an example being environmental statistics. Parametric models are often used to model trends in such data, but they may not be suitable for exploratory data analysis. This paper outlines a semiparametric approach to smoothing example extremes, based on local polynomial fitting of the generalized extreme value distribution and related models. The uncertainty of fits is assessed by using resampling methods. The methods are applied to data on extreme temperatures and on record times for the womens 3000m race.

Model sensitivity and uncertainty analysis using roadside air quality measurements

Most of the air quality modelling work has been so far oriented towards deterministic simulations of ambient pollutant concentrations. This traditional approach, which is based on the use of one selected model and one data set of discrete input values, does not reflect the uncertainties due to errors in model formulation and input data. Given the complexities of urban environments and the inherent limitations of mathematical modelling, it is unlikely that a single model based on routinely available meteorological and emission data will give satisfactory short-term predictions. In this study, different methods involving the use of more than one dispersion model, in association with different emission simulation methodologies and meteorological data sets, were explored for predicting best CO and benzene estimates, and related confidence bounds. The different approaches were tested using experimental data obtained during intensive monitoring campaigns in busy street canyons in Paris, France. Three relative simple dispersion models (STREET, OSPM and AEOLIUS) that are likely to be used for regulatory purposes were selected for this application. A sensitivity analysis was conducted in order to identify internal model parameters that might significantly affect results. Finally, a probabilistic methodology for assessing urban air quality was proposed.

Semi-Parametric Analysis of Extreme Forest Fires

Forest fires can cause extensive damage to natural resources and properties. They can also destroy wildlife habitat, affect the forest ecosystem and threaten human lives. In this paper incidences of extreme wildland fires are modelled by a point process model which incorporates time-trend. A model based on a generalised Pareto distribution is used to model data on acres of wildland burnt by extreme fire in the US since 1825. A semi-parametric smoothing approach, which is very useful in exploratory analysis of changes in extremes, is illustrated with the maximum likelihood method to estimate model parameters.

Uncertainty analysis to minimise risk in designing micro-electronics manufacturing processes

A design methodology based on numerical modelling, integrated with optimisation techniques and statistical methods, to aid the process control of micro and nano-electronics based manufacturing processes is presented in this paper. The design methodology is demonstrated for a micro-machining process called Focused Ion Beam (FIB). This process has been modelled to help understand how a pre-defined geometry of micro- and nano- structures can be achieved using this technology. The process performance is characterised on the basis of developed Reduced Order Models (ROM) and are generated using results from a mathematical model of the Focused Ion Beam and Design of Experiment (DoE) methods. Two ion beam sources, Argon and Gallium ions, have been used to compare and quantify the process variable uncertainties that can be observed during the milling process. The evaluations of the process performance takes into account the uncertainties and variations of the process variables and are used to identify their impact on the reliability and quality of the fabricated structure. An optimisation based design task is to identify the optimal process conditions, by varying the process variables, so that certain quality objectives and requirements are achieved and imposed constraints are satisfied. The software tools used and developed to demonstrate the design methodology are also presented.