Clive Anderson - Academia.edu (original) (raw)

Papers by Clive Anderson

Journal of Climate, 2002

It is often useful to make initial estimates of changing extremes without the use of a specific s... more It is often useful to make initial estimates of changing extremes without the use of a specific statistical model, though a statistical model is likely to be desirable as a second step. A proof is given of a formula used by A. F. Jenkinson in the 1970s that converts data that are ranked according to their magnitude into an estimate of the associated cumulative probability. This formula is compared to its exact equivalent, based on a beta distribution of the first kind. It is also compared to similar ranking formulas, which have been recommended, mostly in hydrology, based on similar ideas. Some results concerning the effect of serial correlation on Jenkinson's formula are reported. For initial estimates of return periods or percentiles of cumulative probability from time series of data, Jenkinson's method performs as well as many of the other methods. Empirical ranking methods are not so useful for estimating the rarest percentiles in climatology, those in the most extreme 100/N% tails of the distribution, say, where N is the data length. To estimate such extreme percentiles, distributional models are essential. However, for moderate extremes it is suggested that Jenkinson's or one of the similar methods are useful for an initial assessment of changing percentiles for a wide range of underlying data distributions.

Extremes, Aug 3, 2006

Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedance... more Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedances over high thresholds. In practice, a threshold u is fixed and a GPD is fitted to the data exceeding u. A difficulty in this approach is the selection of the threshold above which the GPD assumption is appropriate. Moreover the estimates of the parameters of the GPD may depend significantly on the choice of the threshold selected. Sensitivity with respect to the threshold choice is normally studied but typically its effects on the properties of estimators are not accounted for. In this paper, to overcome the difficulties of the fixedthreshold approach, we propose to model extreme and non-extreme data with a distribution composed of a piecewise constant density from a low threshold up to an unknown end point α and a GPD with threshold α for the remaining tail part. Since we estimate the threshold together with the other parameters of the GPD we take naturally into account the threshold uncertainty. We will discuss this model from a Bayesian point of view and the method will be illustrated using simulated data and a real data set.

Nat Geosci, 2008

The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period ha... more The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period has been extensively investigated, but the role of CO2 in temperature changes during the rest of Earth's history is less clear. The range of geological evidence for cool periods during the high CO2 Mesozoic `greenhouse world' of high atmospheric CO2 concentrations, indicated by models and fossil soils, has been particularly difficult to interpret. Here, we present high-resolution records of Mesozoic and early Cenozoic atmospheric CO2 concentrations from a combination of carbon-isotope analyses of non-vascular plant (bryophyte) fossils and theoretical modelling. These records indicate that atmospheric CO2 rose from ~420p.p.m.v. in the Triassic period (about 200 million years ago) to a peak of ~1,130p.p.m.v. in the Middle Cretaceous (about 100 million years ago). Atmospheric CO2 levels then declined to ~680p.p.m.v. by 60 million years ago. Time-series comparisons show that these variations coincide with large Mesozoic climate shifts, in contrast to earlier suggestions of climate-CO2 decoupling during this interval. These reconstructed atmospheric CO2 concentrations drop below the simulated threshold for the initiation of glaciations on several occasions and therefore help explain the occurrence of cold intervals in a `greenhouse world'.

Previous work at Sheffield on computational models of auditory scene analysis has attempted to se... more Previous work at Sheffield on computational models of auditory scene analysis has attempted to separate the acoustic evidence from simultaneous sound sources by techniques grounded in auditory grouping processes. For this work to be useful in automatic speech recognition, we need to develop recognition techniques which can cope with 'occluded' speech. The separation stage will group together components of the sound mixture which were produced by the same source, but will contain little or no information for those parts of the spectrum which were obscured by other sources.

There is a substantial literature on estimating land cover, but most authors do not address the u... more There is a substantial literature on estimating land cover, but most authors do not address the uncertainty in the resulting estimates. Our approach characterises uncertainty through a Bayesian approach which incorporates several layers of modelling. In particular, we incorporate ...

The Annals of Applied Probability, 1997

It is known that maxima of independent Poisson variables cannot be normalized to converge to a no... more It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore

Novartis Foundation Symposia, 1999

In Europe the monitoring of ozone doses to growing crops is based on measurement of AOT40, the an... more In Europe the monitoring of ozone doses to growing crops is based on measurement of AOT40, the annual accumulated excess ozone concentration over a threshold of 40 ppb, aggregated over the growing season. To show the extent of ozone pollution it is desirable to construct maps of AOT40. However, data are limited and there is large inter-annual variation, so what is to be mapped is very variable, and our knowledge of it is limited. This paper describes a spatially referenced random effects model which appears able to describe many features of the data and our uncertainty about them. The problem of translating this or similar models into a map faithfully representing our knowledge is considered, as are some questions it raises about decision-makers' and the public's need for and use of technical models.

Reliability Engineering & System Safety, 2006

In this paper we present a number of recent applications in which an emulator of a computer code ... more In this paper we present a number of recent applications in which an emulator of a computer code is created using a Gaussian process model. Tools are then applied to the emulator to perform sensitivity analysis and uncertainty analysis. Sensitivity analysis is used both as an aid to model improvement and as a guide to how much the output uncertainty might be reduced by learning about specific inputs. Uncertainty analysis allows us to reflect output uncertainty due to unknown input parameters, when the finished code is used for prediction.

Theory of Probability & Its Applications, 1993

Polar Research, 1999

This paper compares the responses of two contrasting Arctic ecosystems to climate change simulati... more This paper compares the responses of two contrasting Arctic ecosystems to climate change simulations: a polar semi-desert (in Svalbard) and a dwarf shrub heath (at Abisko, northern Sweden). These ecosystems are located close to the northern-and southernmost extremes of the Arctic region, respectively. Impacts of simulated climatic changes were determined through factorial perturbation experiments, where growing season temperature, nutrient availability and water supply were manipulated. The results are compared with the impact of interannual variation in climate on the growth of a keystone moss species, Hylocoinium splendens, from the wider circumpolar area. The perturbation studies revealed that current interannual variability in temperature and the temperate tolerance of many species may exceed predicted changes in mean summer temperature over the next century. Arctic ecosystems differed in their responses to environmental manipulations, with the structure of the dwarf shrub heath being affected through shifts in competitive hierarchy, potentially leading to lower biodiversity, and the polar semi-desert being affected through invasion, potentially leading to higher diversity. H. splendeizs showed negative responses to perturbation at the sub-Arctic site, in contrast to the positive relationship between temperature and growth observed in the natural environment. This apparent discrepancy may result from: (i) artefacts arising from the perturbations, such as lower atmospheric relative humidity; (ii) non-equilibrium responses during the relatively short-term perturbation studies and/or (iii) ecotypic variation in the moss population. Thus, caution should be employed when extrapolating from perturbations studies to both longer time-scales and different ecosystems within the Arctic.

Nature Geoscience, 2008

The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period ha... more The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period has been extensively investigated, but the role of CO2 in temperature changes during the rest of Earth's history is less clear. The range of geological evidence for cool periods during the high CO2 Mesozoic `greenhouse world' of high atmospheric CO2 concentrations, indicated by models and fossil soils,

Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000

Estimates of the largest wind gust that will occur at a given location over a speci®ed period are... more Estimates of the largest wind gust that will occur at a given location over a speci®ed period are required by civil engineers. Estimation is usually based on models which are derived from the limiting distributions of maxima of stationary time series and which are ®tted to data on extreme gusts. In this paper we develop a model for maximum gusts which also incorporates data on hourly mean speeds through a distributional relationship between maxima and means. This joint model is closely linked to the physical processes which generate the most extreme values and thus provides a mechanism by which data on means can augment those on gusts. It is argued that this increases the credibility of extrapolation in estimates of long period return gusts. The model is shown to provide a good ®t to data obtained at a location in northern England and is compared with a more traditional modelling approach, which also performs well for this site. Fig. 1. Hourly records of mean wind speed and gust range during a stormy 24-h period: (a) times series of means () with gust ranges; (b) gust range versus mean

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1998

Multivariate extreme value models and associated statistical methods are developed for vector obs... more Multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction. The approach extends the multivariate threshold methodology of Coles and Tawn, Joe and co-workers and Smith and co-workers. The results are illustrated by an analysis of extreme rainfalls of different durations, and by a study of the problem of linking a long series of daily rainfall extremes with a partially overlapping shorter series of hourly extremes.

Journal of the Royal Statistical Society: Series A (Statistics in Society), 2007

A crucial issue in the current global warming debate is the effect of vegetation and soils on car... more A crucial issue in the current global warming debate is the effect of vegetation and soils on carbon dioxide (CO 2 ) concentrations in the atmosphere. Vegetation can extract CO 2 through photosynthesis, but respiration, decay of soil organic matter and disturbance effects such as fire return it to the atmosphere. The balance of these processes is the net carbon flux. To estimate the biospheric carbon flux for England and Wales, we address the statistical problem of inference for the sum of multiple outputs from a complex deterministic computer code whose input parameters are uncertain. The code is a process model which simulates the carbon dynamics of vegetation and soils, including the amount of carbon that is stored as a result of photosynthesis and the amount that is returned to the atmosphere through respiration. The aggregation of outputs corresponding to multiple sites and types of vegetation in a region gives an estimate of the total carbon flux for that region over a period of time. Expert prior opinions are elicited for marginal uncertainty about the relevant input parameters and for correlations of inputs between sites. A Gaussian process model is used to build emulators of the multiple code outputs and Bayesian uncertainty analysis is then used to propagate uncertainty in the input parameters through to uncertainty on the aggregated output. Numerical results are presented for England and Wales in the year 2000. It is estimated that vegetation and soils in England and Wales constituted a net sink of 7.55 Mt C (1 Mt C = 10 12 g of carbon) in 2000, with standard deviation 0.56 Mt C resulting from the sources of uncertainty that are considered.

Journal of ASTM International, 2006

The presence of multiple types of defect is a challenge for Extreme Value Inclusion Rating since ... more The presence of multiple types of defect is a challenge for Extreme Value Inclusion Rating since it can lead to serious underestimation of extreme inclusion size and it can in practice make methods less robust than expected. First the paper deals with the results being obtained by ESIS TC20 within two round-robins carried out on an automotive steel and a bearing steel. Results show the need for correct assessment of multiple types of particles. We present here a new method of analysis based on a "competing risks" model together with some practical exploitation in terms of: ͑i͒ evaluation of the minimum control area to be inspected by "block maxima" sampling; ͑ii͒ new implications for data collection based on image analysis; ͑iii͒ assessment of sensitivity to the distribution of different particles.

Journal of Climate, 2002

It is often useful to make initial estimates of changing extremes without the use of a specific s... more It is often useful to make initial estimates of changing extremes without the use of a specific statistical model, though a statistical model is likely to be desirable as a second step. A proof is given of a formula used by A. F. Jenkinson in the 1970s that converts data that are ranked according to their magnitude into an estimate of the associated cumulative probability. This formula is compared to its exact equivalent, based on a beta distribution of the first kind. It is also compared to similar ranking formulas, which have been recommended, mostly in hydrology, based on similar ideas. Some results concerning the effect of serial correlation on Jenkinson's formula are reported. For initial estimates of return periods or percentiles of cumulative probability from time series of data, Jenkinson's method performs as well as many of the other methods. Empirical ranking methods are not so useful for estimating the rarest percentiles in climatology, those in the most extreme 100/N% tails of the distribution, say, where N is the data length. To estimate such extreme percentiles, distributional models are essential. However, for moderate extremes it is suggested that Jenkinson's or one of the similar methods are useful for an initial assessment of changing percentiles for a wide range of underlying data distributions.

Food and Chemical Toxicology, 2011

The number of residue measurements in an individual field trial, carried out to provide data for ... more The number of residue measurements in an individual field trial, carried out to provide data for a pesticide registration for a particular crop, is generally too small to estimate upper tails of the residue distribution for that crop with any certainty. We present a new method, using extreme value theory, which pools information from various field trials, with different crop and pesticide combinations, to provide a common model for the upper tails of residue distributions generally. The method can be used to improve the estimation of high quantiles of a particular residue distribution. It provides a flexible alternative to the direct fitting of a distribution to each individual dataset, and does not require strong distributional assumptions. By using a hierarchical Bayesian model, our method also accounts for parameter uncertainty. The method is applied to a range of supervised trials containing residues on individual items (e.g. on individual apples), and the results illustrate the variation in tail properties amongst all commodities and pesticides. The outputs could be used to select conservative high percentile residue levels as part of a deterministic risk assessment, taking account of the variability between crops and pesticides and also the uncertainty due to relatively small datasets.

Extremes, 2006

Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedance... more Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedances over high thresholds. In practice, a threshold u is fixed and a GPD is fitted to the data exceeding u. A difficulty in this approach is the selection of the threshold above which the GPD assumption is appropriate. Moreover the estimates of the parameters of the GPD may depend significantly on the choice of the threshold selected. Sensitivity with respect to the threshold choice is normally studied but typically its effects on the properties of estimators are not accounted for. In this paper, to overcome the difficulties of the fixedthreshold approach, we propose to model extreme and non-extreme data with a distribution composed of a piecewise constant density from a low threshold up to an unknown end point α and a GPD with threshold α for the remaining tail part. Since we estimate the threshold together with the other parameters of the GPD we take naturally into account the threshold uncertainty. We will discuss this model from a Bayesian point of view and the method will be illustrated using simulated data and a real data set.

Journal of Climate, 2002

It is often useful to make initial estimates of changing extremes without the use of a specific s... more It is often useful to make initial estimates of changing extremes without the use of a specific statistical model, though a statistical model is likely to be desirable as a second step. A proof is given of a formula used by A. F. Jenkinson in the 1970s that converts data that are ranked according to their magnitude into an estimate of the associated cumulative probability. This formula is compared to its exact equivalent, based on a beta distribution of the first kind. It is also compared to similar ranking formulas, which have been recommended, mostly in hydrology, based on similar ideas. Some results concerning the effect of serial correlation on Jenkinson's formula are reported. For initial estimates of return periods or percentiles of cumulative probability from time series of data, Jenkinson's method performs as well as many of the other methods. Empirical ranking methods are not so useful for estimating the rarest percentiles in climatology, those in the most extreme 100/N% tails of the distribution, say, where N is the data length. To estimate such extreme percentiles, distributional models are essential. However, for moderate extremes it is suggested that Jenkinson's or one of the similar methods are useful for an initial assessment of changing percentiles for a wide range of underlying data distributions.

Extremes, Aug 3, 2006

Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedance... more Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedances over high thresholds. In practice, a threshold u is fixed and a GPD is fitted to the data exceeding u. A difficulty in this approach is the selection of the threshold above which the GPD assumption is appropriate. Moreover the estimates of the parameters of the GPD may depend significantly on the choice of the threshold selected. Sensitivity with respect to the threshold choice is normally studied but typically its effects on the properties of estimators are not accounted for. In this paper, to overcome the difficulties of the fixedthreshold approach, we propose to model extreme and non-extreme data with a distribution composed of a piecewise constant density from a low threshold up to an unknown end point α and a GPD with threshold α for the remaining tail part. Since we estimate the threshold together with the other parameters of the GPD we take naturally into account the threshold uncertainty. We will discuss this model from a Bayesian point of view and the method will be illustrated using simulated data and a real data set.

Nat Geosci, 2008

The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period ha... more The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period has been extensively investigated, but the role of CO2 in temperature changes during the rest of Earth's history is less clear. The range of geological evidence for cool periods during the high CO2 Mesozoic `greenhouse world' of high atmospheric CO2 concentrations, indicated by models and fossil soils, has been particularly difficult to interpret. Here, we present high-resolution records of Mesozoic and early Cenozoic atmospheric CO2 concentrations from a combination of carbon-isotope analyses of non-vascular plant (bryophyte) fossils and theoretical modelling. These records indicate that atmospheric CO2 rose from ~420p.p.m.v. in the Triassic period (about 200 million years ago) to a peak of ~1,130p.p.m.v. in the Middle Cretaceous (about 100 million years ago). Atmospheric CO2 levels then declined to ~680p.p.m.v. by 60 million years ago. Time-series comparisons show that these variations coincide with large Mesozoic climate shifts, in contrast to earlier suggestions of climate-CO2 decoupling during this interval. These reconstructed atmospheric CO2 concentrations drop below the simulated threshold for the initiation of glaciations on several occasions and therefore help explain the occurrence of cold intervals in a `greenhouse world'.

Previous work at Sheffield on computational models of auditory scene analysis has attempted to se... more Previous work at Sheffield on computational models of auditory scene analysis has attempted to separate the acoustic evidence from simultaneous sound sources by techniques grounded in auditory grouping processes. For this work to be useful in automatic speech recognition, we need to develop recognition techniques which can cope with 'occluded' speech. The separation stage will group together components of the sound mixture which were produced by the same source, but will contain little or no information for those parts of the spectrum which were obscured by other sources.

There is a substantial literature on estimating land cover, but most authors do not address the u... more There is a substantial literature on estimating land cover, but most authors do not address the uncertainty in the resulting estimates. Our approach characterises uncertainty through a Bayesian approach which incorporates several layers of modelling. In particular, we incorporate ...

The Annals of Applied Probability, 1997

It is known that maxima of independent Poisson variables cannot be normalized to converge to a no... more It is known that maxima of independent Poisson variables cannot be normalized to converge to a nondegenerate limit distribution. On the other hand, the Normal distribution approximates the Poisson distribution for large values of the Poisson mean, and maxima of random samples of Normal variables may be linearly scaled to converge to a classical extreme value distribution. We here explore

Novartis Foundation Symposia, 1999

In Europe the monitoring of ozone doses to growing crops is based on measurement of AOT40, the an... more In Europe the monitoring of ozone doses to growing crops is based on measurement of AOT40, the annual accumulated excess ozone concentration over a threshold of 40 ppb, aggregated over the growing season. To show the extent of ozone pollution it is desirable to construct maps of AOT40. However, data are limited and there is large inter-annual variation, so what is to be mapped is very variable, and our knowledge of it is limited. This paper describes a spatially referenced random effects model which appears able to describe many features of the data and our uncertainty about them. The problem of translating this or similar models into a map faithfully representing our knowledge is considered, as are some questions it raises about decision-makers' and the public's need for and use of technical models.

Reliability Engineering & System Safety, 2006

In this paper we present a number of recent applications in which an emulator of a computer code ... more In this paper we present a number of recent applications in which an emulator of a computer code is created using a Gaussian process model. Tools are then applied to the emulator to perform sensitivity analysis and uncertainty analysis. Sensitivity analysis is used both as an aid to model improvement and as a guide to how much the output uncertainty might be reduced by learning about specific inputs. Uncertainty analysis allows us to reflect output uncertainty due to unknown input parameters, when the finished code is used for prediction.

Theory of Probability & Its Applications, 1993

Polar Research, 1999

This paper compares the responses of two contrasting Arctic ecosystems to climate change simulati... more This paper compares the responses of two contrasting Arctic ecosystems to climate change simulations: a polar semi-desert (in Svalbard) and a dwarf shrub heath (at Abisko, northern Sweden). These ecosystems are located close to the northern-and southernmost extremes of the Arctic region, respectively. Impacts of simulated climatic changes were determined through factorial perturbation experiments, where growing season temperature, nutrient availability and water supply were manipulated. The results are compared with the impact of interannual variation in climate on the growth of a keystone moss species, Hylocoinium splendens, from the wider circumpolar area. The perturbation studies revealed that current interannual variability in temperature and the temperate tolerance of many species may exceed predicted changes in mean summer temperature over the next century. Arctic ecosystems differed in their responses to environmental manipulations, with the structure of the dwarf shrub heath being affected through shifts in competitive hierarchy, potentially leading to lower biodiversity, and the polar semi-desert being affected through invasion, potentially leading to higher diversity. H. splendeizs showed negative responses to perturbation at the sub-Arctic site, in contrast to the positive relationship between temperature and growth observed in the natural environment. This apparent discrepancy may result from: (i) artefacts arising from the perturbations, such as lower atmospheric relative humidity; (ii) non-equilibrium responses during the relatively short-term perturbation studies and/or (iii) ecotypic variation in the moss population. Thus, caution should be employed when extrapolating from perturbations studies to both longer time-scales and different ecosystems within the Arctic.

Nature Geoscience, 2008

The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period ha... more The relationship between atmospheric carbon dioxide (CO2) and climate in the Quaternary period has been extensively investigated, but the role of CO2 in temperature changes during the rest of Earth's history is less clear. The range of geological evidence for cool periods during the high CO2 Mesozoic `greenhouse world' of high atmospheric CO2 concentrations, indicated by models and fossil soils,

Journal of the Royal Statistical Society: Series C (Applied Statistics), 2000

Estimates of the largest wind gust that will occur at a given location over a speci®ed period are... more Estimates of the largest wind gust that will occur at a given location over a speci®ed period are required by civil engineers. Estimation is usually based on models which are derived from the limiting distributions of maxima of stationary time series and which are ®tted to data on extreme gusts. In this paper we develop a model for maximum gusts which also incorporates data on hourly mean speeds through a distributional relationship between maxima and means. This joint model is closely linked to the physical processes which generate the most extreme values and thus provides a mechanism by which data on means can augment those on gusts. It is argued that this increases the credibility of extrapolation in estimates of long period return gusts. The model is shown to provide a good ®t to data obtained at a location in northern England and is compared with a more traditional modelling approach, which also performs well for this site. Fig. 1. Hourly records of mean wind speed and gust range during a stormy 24-h period: (a) times series of means () with gust ranges; (b) gust range versus mean

Journal of the Royal Statistical Society: Series B (Statistical Methodology), 1998

Multivariate extreme value models and associated statistical methods are developed for vector obs... more Multivariate extreme value models and associated statistical methods are developed for vector observations whose components are subject to an order restriction. The approach extends the multivariate threshold methodology of Coles and Tawn, Joe and co-workers and Smith and co-workers. The results are illustrated by an analysis of extreme rainfalls of different durations, and by a study of the problem of linking a long series of daily rainfall extremes with a partially overlapping shorter series of hourly extremes.

Journal of the Royal Statistical Society: Series A (Statistics in Society), 2007

A crucial issue in the current global warming debate is the effect of vegetation and soils on car... more A crucial issue in the current global warming debate is the effect of vegetation and soils on carbon dioxide (CO 2 ) concentrations in the atmosphere. Vegetation can extract CO 2 through photosynthesis, but respiration, decay of soil organic matter and disturbance effects such as fire return it to the atmosphere. The balance of these processes is the net carbon flux. To estimate the biospheric carbon flux for England and Wales, we address the statistical problem of inference for the sum of multiple outputs from a complex deterministic computer code whose input parameters are uncertain. The code is a process model which simulates the carbon dynamics of vegetation and soils, including the amount of carbon that is stored as a result of photosynthesis and the amount that is returned to the atmosphere through respiration. The aggregation of outputs corresponding to multiple sites and types of vegetation in a region gives an estimate of the total carbon flux for that region over a period of time. Expert prior opinions are elicited for marginal uncertainty about the relevant input parameters and for correlations of inputs between sites. A Gaussian process model is used to build emulators of the multiple code outputs and Bayesian uncertainty analysis is then used to propagate uncertainty in the input parameters through to uncertainty on the aggregated output. Numerical results are presented for England and Wales in the year 2000. It is estimated that vegetation and soils in England and Wales constituted a net sink of 7.55 Mt C (1 Mt C = 10 12 g of carbon) in 2000, with standard deviation 0.56 Mt C resulting from the sources of uncertainty that are considered.

Journal of ASTM International, 2006

The presence of multiple types of defect is a challenge for Extreme Value Inclusion Rating since ... more The presence of multiple types of defect is a challenge for Extreme Value Inclusion Rating since it can lead to serious underestimation of extreme inclusion size and it can in practice make methods less robust than expected. First the paper deals with the results being obtained by ESIS TC20 within two round-robins carried out on an automotive steel and a bearing steel. Results show the need for correct assessment of multiple types of particles. We present here a new method of analysis based on a "competing risks" model together with some practical exploitation in terms of: ͑i͒ evaluation of the minimum control area to be inspected by "block maxima" sampling; ͑ii͒ new implications for data collection based on image analysis; ͑iii͒ assessment of sensitivity to the distribution of different particles.

Journal of Climate, 2002

It is often useful to make initial estimates of changing extremes without the use of a specific s... more It is often useful to make initial estimates of changing extremes without the use of a specific statistical model, though a statistical model is likely to be desirable as a second step. A proof is given of a formula used by A. F. Jenkinson in the 1970s that converts data that are ranked according to their magnitude into an estimate of the associated cumulative probability. This formula is compared to its exact equivalent, based on a beta distribution of the first kind. It is also compared to similar ranking formulas, which have been recommended, mostly in hydrology, based on similar ideas. Some results concerning the effect of serial correlation on Jenkinson's formula are reported. For initial estimates of return periods or percentiles of cumulative probability from time series of data, Jenkinson's method performs as well as many of the other methods. Empirical ranking methods are not so useful for estimating the rarest percentiles in climatology, those in the most extreme 100/N% tails of the distribution, say, where N is the data length. To estimate such extreme percentiles, distributional models are essential. However, for moderate extremes it is suggested that Jenkinson's or one of the similar methods are useful for an initial assessment of changing percentiles for a wide range of underlying data distributions.

Food and Chemical Toxicology, 2011

The number of residue measurements in an individual field trial, carried out to provide data for ... more The number of residue measurements in an individual field trial, carried out to provide data for a pesticide registration for a particular crop, is generally too small to estimate upper tails of the residue distribution for that crop with any certainty. We present a new method, using extreme value theory, which pools information from various field trials, with different crop and pesticide combinations, to provide a common model for the upper tails of residue distributions generally. The method can be used to improve the estimation of high quantiles of a particular residue distribution. It provides a flexible alternative to the direct fitting of a distribution to each individual dataset, and does not require strong distributional assumptions. By using a hierarchical Bayesian model, our method also accounts for parameter uncertainty. The method is applied to a range of supervised trials containing residues on individual items (e.g. on individual apples), and the results illustrate the variation in tail properties amongst all commodities and pesticides. The outputs could be used to select conservative high percentile residue levels as part of a deterministic risk assessment, taking account of the variability between crops and pesticides and also the uncertainty due to relatively small datasets.

Extremes, 2006

Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedance... more Tail data are often modelled by fitting a generalized Pareto distribution (GPD) to the exceedances over high thresholds. In practice, a threshold u is fixed and a GPD is fitted to the data exceeding u. A difficulty in this approach is the selection of the threshold above which the GPD assumption is appropriate. Moreover the estimates of the parameters of the GPD may depend significantly on the choice of the threshold selected. Sensitivity with respect to the threshold choice is normally studied but typically its effects on the properties of estimators are not accounted for. In this paper, to overcome the difficulties of the fixedthreshold approach, we propose to model extreme and non-extreme data with a distribution composed of a piecewise constant density from a low threshold up to an unknown end point α and a GPD with threshold α for the remaining tail part. Since we estimate the threshold together with the other parameters of the GPD we take naturally into account the threshold uncertainty. We will discuss this model from a Bayesian point of view and the method will be illustrated using simulated data and a real data set.