A. C. Davison

Statistical Modeling of Spatial Extremes

The areal modeling of the extremes of a natural process such as rainfall or temperature is important in environmental statistics; for example, understanding extreme areal rainfall is crucial in flood protection. This article reviews recent progress in the statistical modeling of spatial extremes, starting with sketches of the necessary elements of extreme value statistics and geostatistics. The main types of statistical models thus far proposed, based on latent variables, on copulas and on spatial max-stable processes, are described and then are compared by application to a data set on rainfall in Switzerland. Whereas latent variable modeling allows a better fit to marginal distributions, it fits the joint distributions of extremes poorly, so appropriately-chosen copula or max-stable models seem essential for successful spatial modeling of extremes.

Assessment and analysis of mechanical allodynia-like behavior induced by spared nerve injury (SNI) in the mouse

Abstract Experimental models of peripheral nerve injury have been developed to study mechanisms of neuropathic pain. In the spared nerve injury (SNI) model in rats, the common peroneal and tibial nerves are injured, producing consistent and reproducible pain hypersensitivity in the territory of the spared sural nerve. In this study, we investigated whether SNI in mice is also a valid model system for neuropathic pain. SNI results in a significant decrease in withdrawal threshold in SNI‐operated mice. The effect is very consistent between animals and persists for the four weeks of the study. We also determined the relative frequency of paw withdrawal for each of a series of 11 von Frey hairs. Analysis of response frequency using a mixed‐effects model that integrates all variables (nerve injury, paw, gender, and time) shows a very stable effect of SNI over time and also reveals subtle divergences between variables, including gender‐based differences in mechanical sensitivity. We tested two variants of the SNI model and found that injuring the tibial nerve alone induces mechanical hypersensitivity, while injuring the common peroneal and sural nerves together does not induce any significant increase in mechanical sensitivity in the territory of the spared tibial nerve. SNI induces a mechanical allodynia‐like response in mice and we believe that our improved method of assessment and data analysis will reveal additional internal and external variability factors in models of persistent pain. Use of this model in genetically altered mice should be very effective for determining the mechanisms involved in neuropathic pain.

Entrainment and motion of coarse particles in a shallow water stream down a steep slope

We investigate the entrainment, deposition and motion of coarse spherical particles within a turbulent shallow water stream down a steep slope. This is an idealization of bed-load transport in mountain streams. Earlier investigations have described this kind of sediment transport using empirical correlations or concepts borrowed from continuum mechanics. The intermittent character of particle transport at low-water discharges led us to consider it as a random process. Sediment transport in this regime results from the imbalance between entrainment and deposition of particles rather than from momentum balance between water and particles. We develop a birth–death immigration–emigration Markov process to describe the particle exchanges between the bed and the water stream. A key feature of the model is its long autocorrelation times and wide, frequent fluctuations in the solid discharge, a phenomenon never previously explained despite its ubiquity in both nature and laboratory experiments. We present experimental data obtained using a nearly two-dimensional channel and glass beads as a substitute for sediment. Entrainment, trajectories, and deposition were monitored using a high-speed digital camera. The empirical probability distributions of the solid discharge and deposition frequency were properly described by the theoretical model. Experiments confirmed the existence of wide and frequent fluctuations of the solid discharge, and revealed the existence of long autocorrelation time, but theory overestimates the autocorrelation times by a factor of around three. Particle velocity was weakly dependent on the fluid velocity contrary to the predictions of the theoretical model, which performs well when a single particle is moving. For our experiments, the dependence of the solid discharge on the fluid velocity is entirely controlled by the number of moving particles rather than by their velocity. We also noted significant changes in the behaviour of particle transport when the bed slope or the water discharge was increased. The more vigorous the stream was, the more continuous the solid discharge became. Moreover, although 90% of the energy supplied by gravity to the stream is dissipated by turbulence for slopes lower than 10 %, particles dissipate more and more energy when the bed slope is increased, but surprisingly, the dissipation rate is nearly independent of fluid velocity. A movie is available with the online version of the paper.

A six-arm olfactometer permitting simultaneous observation of insect attraction and odour trapping

Abstract.  Behavioural assays to study insect attraction to specific odours are tedious, time consuming and often require large numbers of replications. Olfactometer and flight tunnel tests can usually only be conducted with one or two odour sources at a time. Moreover, chemical information on the odour sources has to be obtained in separate analytical studies. An olfactometer was developed in which six odours can be tested simultaneously for their relative attractiveness while during the assays, part of each test odour can be trapped for further analyses. The effectiveness of this six‐arm olfactometer was tested by observing the responses of the solitary endoparasitoid Cotesia marginiventris (Cresson) to host‐induced odours from young maize plants. For statistical analyses, we used log‐linear models were adapted to account for overdispersion and possible positional biases. Female wasps responded extremely well in tests where they were offered a single odour source, as well as in tests with multiple choices. The responses of wasps released in groups were the same as those released individually and it was found that females did not attract or repel each other, but males preferred arms in which females had been released. Dose–response tests with varying numbers of plants or host larvae on plants revealed that the wasps responded in a dose‐related manner, thus showing that the system is well suited to measure relative preference. The clear choices of the insects amongst six possibilities provided substantial statistical power. Gas chromatographic analyses of sampled air revealed clean and effective odour trapping, which largely facilitates the comparison of results from behavioural assays with the actual blends of volatiles that were emitted by the various odour sources. Advantages and disadvantages compared to other methods are discussed.

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 sample 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 3000 m race.

SPATIAL MODELING OF EXTREME SNOW DEPTH

The spatial modeling of extreme snow is important for adequate risk management in Alpine and high altitude countries. A natural approach to such modeling is through the theory of max-stable processes, an infinite-dimensional extension of multivariate extreme value theory. In this paper we describe the application of such processes in modeling the spatial dependence of extreme snow depth in Switzerland, based on data for the winters 1966--2008 at 101 stations. The models we propose rely on a climate transformation that allows us to account for the presence of climate regions and for directional effects, resulting from synoptic weather patterns. Estimation is performed through pairwise likelihood inference and the models are compared using penalized likelihood criteria. The max-stable models provide a much better fit to the joint behavior of the extremes than do independence or full dependence models.

Geostatistics of Extremes

We describe a prototype approach to flexible modelling for maxima observed at sites in a spatial domain, based on fitting of max-stable processes derived from underlying Gaussian random fields. The models we propose have generalized extreme-value marginal distributions throughout the spatial domain, consistent with statistical theory for maxima in simpler cases, and can incorporate both geostatistical correlation functions and random set components. Parameter estimation and fitting are performed through composite likelihood inference applied to observations from pairs of sites, with occurrence times of maxima taken into account if desired, and competing models are compared using appropriate information criteria. Diagnostics for lack of model fit are based on maxima from groups of sites. The approach is illustrated using annual maximum temperatures in Switzerland, with risk analysis proposed using simulations from the fitted max-stable model. Drawbacks and possible developments of the approach are discussed.

Estimating value-at-risk: a point process approach

We consider the modelling of extreme returns in financial time series, and introduce a marked point process model for the exceedances of a high threshold. This model has a self-exciting, Hawkes-process structure in which recent events affect the current intensity of threshold exceedances more than distant ones. Estimates of value-at-risk are derived for real datasets and the success of the estimation method is evaluated in backtests.

Rapid classification of phenotypic mutants of Arabidopsis via metabolite fingerprinting.

We evaluated the application of gas chromatography-mass spectrometry metabolic fingerprinting to classify forward genetic mutants with similar phenotypes. Mutations affecting distinct metabolic or signaling pathways can result in common phenotypic traits that are used to identify mutants in genetic screens. Measurement of a broad range of metabolites provides information about the underlying processes affected in such mutants. Metabolite profiles of Arabidopsis (Arabidopsis thaliana) mutants defective in starch metabolism and uncharacterized mutants displaying a starch-excess phenotype were compared. Each genotype displayed a unique fingerprint. Statistical methods grouped the mutants robustly into distinct classes. Determining the genes mutated in three uncharacterized mutants confirmed that those clustering with known mutants were genuinely defective in starch metabolism. A mutant that clustered away from the known mutants was defective in the circadian clock and had a pleiotropic starch-excess phenotype. These results indicate that metabolic fingerprinting is a powerful tool that can rapidly classify forward genetic mutants and streamline the process of gene discovery.

Local models for exploratory analysis of hydrological extremes

Trend analysis is widely used for detecting changes in hydrological data. Parametric methods for this employ pre-specified models and associated tests to assess significance, whereas non-parametric methods generally apply rank tests to the data. Neither approach is suitable for exploratory analysis, because parametric models impose a particular, perhaps unsuitable, form of trend, while testing may confirm that trend is present but does not describe its form. This paper describes semi-parametric approaches to trend analysis using local likelihood fitting of annual maximum and partial duration series and illustrates their application to the exploratory analysis of changes in extremes in sea level and river flow data. Bootstrap methods are used to quantify the variability of estimates.