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This thesis is a contribution to multivariate extreme value statistics. The tail of a multivariate distribution function is characterized by its spectral distribution, for which we propose a new semi-parametric model based on mixtures of Dirichlet distributions. To estimate the components of this model, reversible jump Monte Carlo Markov chain and EM algorithms are developed. Their performances are illustrated on real and simulated data, obtained using new representations of the extremal logistic and Dirichlet models. In parallel with the estimation of the spectral distribution, extreme value statistic machinery requires the selection of a threshold in order to classify data as extreme or not. This selection is achieved by a new method based on heuristic arguments. It allows a selection independent of the dimension of the data. Its performance is illustrated on real and simulated data. Primal scientific interests behind a multivariate extreme value analysis reside in the estimation of quantiles of rare events and in the exploration of the dependence structure, for which the estimation of the spectral measure is a means rather than an end. These two issues are addressed. For the first, a Monte Carlo method is developed based on simulation of extremes. It is compared with classical and new methods of the literature. For the second one, an original conditional dependence analysis is proposed, which enlightens various aspects of the dependence structure of the data. Examples using real data sets are given. In the last part, the semi-parametric model and the presented methods are extended to spatial extremes. It is made possible by considering the spectral distribution as the distribution of a random probability, an original viewpoint adopted throughout this thesis. Classical multivariate extremes are extended to extremes of random measures. The application is illustrated on rainfall data in China.

Abstract Many parasitic wasps that exploit herbivores as their hosts make use of herbivoreinduced plant odours to locate their victims and these wasps often exhibit an ability to learn to associate specific plant-produced odours with the presence of hosts. This associative learning is expected to allow generalist parasitoids to focus on cues that are most reliably associated with current host presence, but evidence supporting this hypothesis is ambiguous. Using a six-arm olfactometer we compared the responses of three generalist larval endoparasitoids, Cotesia marginiventris (Hymenoptera: Braconidae), Microplitis rufiventris (Hymenoptera: Braconidae) and Campoletis sonorensis (Hymenoptera: Ichneumonidae), to the induced odours of three plant species: maize (Zea mays), cowpea (Vigna unguiculata), and cotton (Gossypium hirsutum). We tested the responses of naïve females as well as of females that were first conditioned by parasitising host larvae feeding on one of the plant species. Despite similarities in biology and host range the three wasp species responded entirely differently. Naïve C. marginiventris and C. sonorensis chose equally among the induced odours of the three plants, whereas naïve M. rufiventris, which may have a somewhat more restricted host range, tended to prefer the odour of maize. After conditioning, most C. marginiventris females chose the odour of the plant species that they had experienced, but conditioned M. rufiventris showed an even stronger preference for maize odours, independently of the plant they had experienced. Cotesia sonorensis did not show any change in its preference after conditioning. We speculate that its extremely broad host range allows C. sonorensis females to use fixed responses to cues commonly associated with plants damaged by Lepidoptera. These results imply that different generalist parasitoids may employ different foraging strategies and that associative learning is not necessarily part of it.

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.

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.

The intraclass correlation coefficient rho plays a key role in the design of cluster randomized trials. Estimates of rho obtained from previous cluster trials and used to inform sample size calculation in planned trials may be imprecise due to the typically small numbers of clusters in such studies. It may be useful to quantify this imprecision. This study used simulation to compare different methods for assigning bootstrap confidence intervals to rho for continuous outcomes from a balanced design. Data were simulated for combinations of numbers of clusters (10, 30, 50), intraclass correlation coefficients (0.001, 0.01, 0.05, 0.3) and outcome distributions (normal, non-normal continuous). The basic, bootstrap-t, percentile, bias corrected and bias corrected accelerated bootstrap intervals were compared with new methods using the basic and bootstrap-t intervals applied to a variance stabilizing transformation of rho. The standard bootstrap methods provided coverage levels for 95 per cent intervals that were markedly lower than the nominal level for data sets with only 10 clusters, and only provided close to 95 per cent coverage when there were 50 clusters. Application of the bootstrap-t method to the variance stabilizing transformation of rho improved upon the performance of the standard bootstrap methods, providing close to nominal coverage.

This paper extends a previous discussion of the use of Bayesian networks for evaluating evidence in the forensic investigation of fire incidents. Bayesian networks are proposed for two casework examples and the practical implications studied in detail. Such networks were found to provide precious support in addressing some of the wide range of issues that affect the coherent evaluation of evidence.

Diabetes is characterized by hyperglycemia that can result from the loss of pancreatic insulin secreting b cells in the islets of Langerhans. We analyzed ex vivo the entire gastric and duodenal lobes of a murine pancreas using extended focus Optical Coherence Microscopy (xfOCM). To identify and quantify the islets of Langerhans observed in xfOCM tomograms we implemented an active contour algorithm based on the level set method. We show that xfOCM reveals a three dimensional islet distribution consistent with Optical Projection Tomography albeit with a higher resolution that also enables the detection of the smallest islets (= 8000 µm3). Although this category of the smallest islets represents only a negligible volume compared to the total b cell volume a recent study suggests that these islets located at the periphery are the first to be destroyed when type I diabetes develops. Our results underline the capability of xfOCM to contribute to the understanding of the development of diabetes especially when considering islets volume distribution instead of the total b cell volume only.

We review sketchily bootstrap and other resampling methods for statistical inference. Topics covered include: regression problems; complex dependence; efficient resamping methods; confidence limits; bootstrap hypothesis tests; iterative resampling; and bootstrap and other empirical likelihoods.

Statistical methods are concerned with the analysis of data with an appreciable random component. Whatever the reason for an analysis, there is almost always pattern in the data, obscured to a greater or lesser extent by random variation. Both pattern and randomness can be summarized by statistical methods, but their relative importance and the eventual summary depend on the aim of the analysis. At one extreme are techniques intended solely to explore and describe the data, and at the other extreme is the analysis of data for which there is an accepted probability model based on biological or physical mechanisms. Regression methods stretch between these extremes, and are among the most widely used techniques in statistics.

Summary Various diagnostics for generalized linear models are reviewed and extended to more general models. These include some models for censored and grouped data, and regressions that are nonlinear, or where the response does not have an exponential family distribution. Among diagnostics considered are score tests, various types of residual, and approximate Cook statistics. Diagnostics for models with incidental parameters orthogonal to the regression parameters are discussed. Examples are given and the adequacy of approximations is considered.

On developpe des approximations precises et facilement calculables pour les densites conditionnelles et les distributions des statistiques exhaustives dans les modeles lineaires generalises avec des fonctions de liaison canoniques

Results generated from a detailed long-range transport model, MESOS, simulating dispersal of a large number of hypothetical releases of radionuclides in a variety of meteorological situations over Western Europe, have been used to derive a simpler statistical model, MESOSTAT. This model may be used to generate probability distributions of different levels of contamination at a receptor point 100–1000 km or so from the source (for example, across a frontier in another country) without considering individual release and dispersal scenarios. The model is embodied in a series of equations involving parameters which are determined from such factors as distance between source and receptor, nuclide decay and deposition characteristics, release duration, and geostrophic windrose at the source. Suitable geostrophic windrose data have been derived for source locations covering Western Europe. Special attention has been paid to the relatively improbable extreme values of contamination at the top end of the distribution. In this paper the MESOSTAT model and its development are described, with illustrations of its use and comparison with the original more detailed modelling techniques.

The higher-order moments and cumulants of sums of a special case of random variables having long-range dependence are investigated. Tensor methods are used to simplify the calculations. The limiting form of the second and third cumulants as the number of variables added becomes large is studied by analytical and numerical methods. The implications are discussed for the existence of non-gaussian limits of sums of random quantities of finite variance and long-range dependence.

SUMMARY We discuss the use of normal order statistics plots, based on deviance residuals, to check distributional assumptions in regression models. Continuous and discrete error distributions are considered, as are censored data. Misspecified error distributions and discrimination between competing models are discussed, with an example. Residual plots to detect inadequacies in normal linear regression models have a long history. An example is the normal scores or rankit plot: a plot of ordered residuals against normal order statistics, which is used to detect outliers and to check distributional assumptions. Under- or overdispersion in such a plot may also indicate a misspecified systematic component of the model. The purpose of this paper is to discuss such plots for regressions with nonnormal errors, such as generalized linear models, for which deviance residuals are commonly used. Deviance residuals are known to be approximately normal in many cases. In this paper we briefly describe the properties of rankit plots based on them for continuous distributions, outline analogous results for discrete and censored data, and describe a method for discriminating between competing models with different error distributions. Most roads lead to Rome for the normal distribution in the sense that many definitions of residuals are functions of (y - jt)/ o. Not so for other distributions, for which various

SUMMARY A predictive likelihood is given which approximates both Bayes and maximum likeli- hood predictive inference by expansion of a posterior likelihood. This synthesizes and extends previous results and is widely applicable. The approximation usually differs from exact Bayes posterior predictive density by Op(n-2), and from exact predictive likelihood by Op(n-1), but does not depend on the availability of prior information and is applicable when exact predictive likelihood cannot be found. The results are applied to the prediction Various treatments of the likelihood function form the basis of parametric inference, but until recently few non-Bayesian attempts have been made to define versions of it suitable for prediction. However Lauritzen (1974), Hinkley (1979), and more recently Butler (1986) have proposed rather similar definitions of predictive likelihood based on the idea of conditioning on the value of a sufficient statistic. Unfortunately they apply only when sufficiency provides a genuine reduction of the data. Moreover, even if for a given problem an exact predictive likelihood exists, the calculations needed to derive it can be onerous. This paper provides approximations to Hinkley-Lauritzen predictive likelihood accur- ate to Op(n-1) in many cases, which are applicable in situations where maximum likelihood estimation is regular. They also apply to problems which admit no exact predictive likelihood because sufficiency provides no real reduction of the data. The approximations are derived from a posterior predictive density and may if prior informa- tion is available be regarded as Bayesian procedures. Their construction requires only the repeated maximization of a likelihood and evaluation of the observed information matrix at the maximum, and is fast and accurate using usual numerical maximization methods. There is a close connexion with the approximations to posterior moments and marginal densities given by Tierney & Kadane (1986), who suggest the same approxima- tion as used here but give no detailed results for prediction. Section 2 of this paper shows how Laplace's method for integrals may be applied to a posterior predictive density to yield approximate predictive likelihood. Section 3 discusses a connection with conditional inference: essentially the same approximation

SUMMARY Saddlepoint approximations are shown to be easy to use and accurate in a variety of simple bootstrap and randomization applications. Examples include mean estimation, ratio estimation, two-sample comparisons, and autoregressive estimation.

Two methods are proposed to deal with missing observations, which frequently pose problems in the statistical analysis of ambient ozone data. The first is based on exceedances of the data over thresholds and provides a flexible and general class of models for statistical analysis of air pollution data. The second uses the measured values of related variables to impute missing observations. They are applied to data for three sites in E Texas.

In this paper results obtained with a more complex Lagrangian model, MESOS, developed to study long-range effects of atmospheric releases of radioactivity from nuclear installations, will be compared with results from simpler models based on extrapolating Gaussian plume models out to longer distances using only meteorological conditions at the source.

In many areas of application the extremes of some process may be modelled by considering only its exceedances of a high threshold level. The natural parametric family for such excesses for continuous parent random variables, the generalized Pareto distribution, is closely related to the classical extreme-value distributions. Here its basic properties are discussed, with some ideas for graphical exploration of data. Maximum likelihood estimation of parameters in the presence of covariates is considered, and techniques for checking fit based on residuals and a score test developed.

The paper gives a highly personal sketch of some current trends in statistical inference. After an account of the challenges that new forms of data bring, there is a brief overview of some topics in stochastic modelling. The paper then turns to sparsity, illustrated using Bayesian wavelet analysis based on a mixture model and metabolite profiling. Modern likelihood methods including higher order approximation and composite likelihood inference are then discussed, followed by some thoughts on statistical education.

Genton et al. (2011) investigated the gain in efficiency when triplewise, rather than pairwise, likelihood is used to fit the popular Smith max-stable model for spatial extremes. We generalize their results to the Brown--Resnick model and show that the efficiency gain is substantial only for very smooth processes, which are generally unrealistic in applications. Copyright 2013, Oxford University Press.

Keywords: Hydrologie Reference HYDRAM-ARTICLE-2001-001doi:10.1029/2001WR000295 Record created on 2005-10-11, modified on 2017-05-12

SUMMARY Combined inference for heterogeneous high-dimensional data is critical in modern biology, where clinical and various kinds of molecular data may be available from a single study. Classical genetic association studies regress a single clinical outcome on many genetic variants one by one, but there is an increasing demand for joint analysis of many molecular outcomes and genetic variants in order to unravel functional interactions. Unfortunately, most existing approaches to joint modeling are either too simplistic to be powerful or are impracticable for computational reasons. Inspired by Richardson and others (2010, Bayesian Statistics 9), we consider a sparse multivariate regression model that allows simultaneous selection of predictors and associated responses. As Markov chain Monte Carlo (MCMC) inference on such models can be prohibitively slow when the number of genetic variants exceeds a few thousand, we propose a variational inference approach which produces posterior information very close to that of MCMC inference, at a much reduced computational cost. Extensive numerical experiments show that our approach outperforms popular variable selection methods and tailored Bayesian procedures, dealing within hours with problems involving hundreds of thousands of genetic variants and tens to hundreds of clinical or molecular outcomes.

Both marginal and dependence features must be described when modelling the extremes of a stationary time series. There are standard approaches to marginal modelling, but long- and short-range dependence of extremes may both appear. In applications, an assumption of long-range independence often seems reasonable, but short-range dependence, i.e., the clustering of extremes, needs attention. The extremal index $0, Comment: 30 pages, 5 figures

Wine production is an important industry in Western Switzerland, but vineyards must contend with grape vine and grape berry moths, the larval stages of which feed on grape flower buds and berries. This paper proposes a stochastic model for prediction of the emergence times of the moths, in order to aid treatment aimed at their control. Observed moth counts are treated as a realization of an inhomogeneous Poisson process whose probabilities are related to the distribution of time to emergence. We use a hierarchical model to account for the variability of this distribution between sites and years. Maximum likelihood and Bayesian fitting of the model to data are described, the latter using Markov chain Monte Carlo simulation, and the Bayesian approach is used for forecasting in future years. Grape vine moth flights proved much more variable than grape berry moth flights among sites and years; depending on the site, the flights of the two species can overlap or be completely distinct. Credibility intervals are provided for each site for a random future year, and the predictions can be updated and refined once 15–20% of the flight for a new year has emerged. The paper ends with discussion of the role of such models in similar applications.

In fields such as biology, medical sciences, sociology, and economics researchers often face the situation where the number of available observations, or the amount of available information, is sufficiently small that approximations based on the normal distribution may be unreliable. Theoretical work over the last quarter-century has led to new likelihood-based methods that lead to very accurate approximations in finite samples, but this work has had limited impact on statistical practice. This book illustrates by means of realistic examples and case studies how to use the new theory, and investigates how and when it makes a difference to the resulting inference. The treatment is oriented towards practice and comes with code in the R language (available from the web) which enables the methods to be applied in a range of situations of interest to practitioners. The analysis includes some comparisons of higher order likelihood inference with bootstrap or Bayesian methods.

Regionalization methods have long been used to estimate high return levels of river discharges at ungauged locations on a river network. In these methods, discharge measurements from a homogeneous group of similar, gauged, stations are used to estimate high quantiles at a target location that has no observations. The similarity of this group to the ungauged location is measured in terms of a hydrological distance measuring differences in physical and meteorological catchment attributes. We develop a statistical method for estimation of high return levels based on regionalizing the parameters of a generalized extreme value distribution. The group of stations is chosen by optimizing over the attribute weights of the hydrological distance, ensuring similarity and in-group homogeneity. Our method is applied to discharge data from the Rhine basin in Switzerland, and its performance at ungauged locations is compared to that of other regionalization methods. For gauged locations we show how our approach improves the estimation uncertainty for long return periods by combining local measurements with those from the chosen group.

We apply methods from extreme value theory to identify extreme events in high (termed EHOs) and low (termed ELOs) total ozone and to describe the distribution tails (i.e. very high and very low values) of five long-term European ground-based total ozone time series. The influence of these extreme events on observed mean values, long-term trends and changes is analysed. The results show a decrease in EHOs and an increase in ELOs during the last decades, and establish that the observed downward trend in column ozone during the 1970–1990s is strongly dominated by changes in the frequency of extreme events. Furthermore, it is shown that clear ‘fingerprints’ of atmospheric dynamics (NAO, ENSO) and chemistry [ozone depleting substances (ODSs), polar vortex ozone loss] can be found in the frequency distribution of ozone extremes, even if no attribution is possible from standard metrics (e.g. annual mean values). The analysis complements earlier analysis for the world's longest total ozone record at Arosa, Switzerland, confirming and revealing the strong influence of atmospheric dynamics on observed ozone changes. The results provide clear evidence that in addition to ODS, volcanic eruptions and strong/moderate ENSO and NAO events had significant influence on column ozone in the European sector.DOI: 10.1111/j.1600-0889.2011.00575.x

Olfactometer experiments are used to study the responses of arthropods to potential attractants, for purposes such as understanding natural defenses of plants against their herbivores. Such experiments typically lead to multivariate data consisting of small correlated counts, which are overdispersed relative to standard models. In this paper models that account for the overdispersion under different hypotheses on insect behavior are described and illustrated with an example, and a graphical approach to discriminating among them is briefly discussed. Supplementary files giving technical computations, data and code are available online.