9h12h30  Resste NETWORK An introduction to geostatistical analysis of spatiotemporal data with R Session 1  Handling and importing large spatiotemporal data using structured objects; projection coordinate systems for geolocated data. Session 2  Visualizing data according to their temporal, spatial or spatiotemporal structures. An introduction to geostatistical analysis of spatiotemporal data with R Chairman: Denis ALLARD, Campus du triolet TD 9.03  
12h3014h  Lunch, Cafeteria CROUS  
14h17h30  Resste NETWORK An introduction to geostatistical analysis of spatiotemporal data with R Session 3  Statistical inference for spatiotemporal models: method of moments; maximum likelihood, pairwise composite likelihoods. Session 4  Prediction and validation. An introduction to geostatistical analysis of spatiotemporal data with R Chairman: Denis ALLARD, Campus du triolet TD 9.03 
8h459h15  Welcome & registration  
9h159h30  Opening session  
9h3010h20  Thordis THORARINSDOTTIR Models vs. inference Point process data arises naturally in various fields of science such as biology, ecology, epidemiology, and environmental sciences. Point process models generally fall in the three categories: Completely random processes, or Poisson processes, where the points are assumed independent, repulsive processes where the points tend to avoid each other and clustered processes. Cluster processes commonly have the following general structure. There is a point process of cluster centers and to each cluster center is associated a random number of points forming a subsidiary process, where the points in the subsidiary process are distributed about the cluster center in some specific way. A model for such processes consists of three components; a component describing the cluster center process, a component describing the cluster sizes, and a component describing the distribution of the subsidiary points around the cluster center, the dispersion process. While a great number of different point process models are available, the modeling framework is very involved and inference can often only be performed approximately and with great care. In this talk, we discuss the dilemma that, in the point process literature, we have many more models than models we can usefully do inference with. Models vs. inference Chairman: Christian LANTUEJOUL, 002003 KourosCaryatides  
10h2010h50  Break, Jardin d'hiver  
10h5011h30  Janine ILLIAN Point processes — abstraction and practical relevance All statistical modelling of complex data structures involves an abstraction to the essential properties of interest into quantifiable units and associated random variables. In addition, it also often goes along with simplifying assumptions as part of the abstraction process, typically for practical reasons. As a result, methodology can tend to be far removed from reality and hence be of little practical relevance. In the context of point process modelling, the usual abstraction reduces the available information to locations of points in space, whose spatial structure is analysed. Classical simplifications often concern assumptions of homogeneity, isotropy and known detection probabilities, often for computational reasons. Recent computational improvement however, allows us to relax some of these assumptions. This talk provides a number of examples of how we have been able to relax these classical assumptions along with associated abstractions, leading to increased practical relevance. In particular, I will discuss how this increased practical relevance has also caused an increasing demand for the development of new methodology that has previously played a rather minor role. Point processes — abstraction and practical relevance Chairman: Jorge MATEU, 002003 KourosCaryatides  
11h3012h30 
Point processes
Point processes Carles COMAS, Sergi COSTAFREDAAUMEDES, Cristina VEGAGARCIA
During the last few decades, it has become increasingly popular the study of events that occur on a network of lines. Examples include, for instance, wildlifevehicle collisions, street crimes, traffic accidents and plant and tree spatial distribution. For all these cases, as points depend on the linear network, the analysis of such spatial configurations is focused on the description of the spatial configuration of points assuming that the whole point pattern is placed over the linear network.
However, in some cases, the dependence between a point pattern and a linear network is not always evident. In these cases, as points do not occur on the linear network, the spatial dependence between
point and line segments is not visually obvious (for instance, humancaused fires and road networks). In this work we proposed the definition of a new second order characteristic, based on the Ripley’s K
function, to analyse the spatial structure between point patterns and linear networks. Analysing the spatial structure of point patterns and linear networks
Felix BALLANI, Francisco Javier RODRÍGUEZ CORTES, Jorge MATEU, Dietrich STOYAN
Spatiotemporal point processes can be analysed statistically by considering the times as marks of the locations or the locations as marks of the times. For these marked point processes, classical secondorder characteristics yield interesting information about spatiotemporal correlations. These summary functions provide valuable information about the relations between the points over distances in space and time and on the strength and range of interaction in spatiotemporal patterns. We give statistical estimators of these summary characteristics and investigate their properties by simulation. Spatiotemporal point processes: a secondorder marked framework
María Isabel BORRAJO GARCÍA, Wenceslao GONZÁLEZMANTEIGA, María Dolores MARTÍNEZMIRANDA
The firstorder intensity function is one of the functions characterising a point process, and its study has been approached so far from different perspectives. One appealing model describes the intensity as a function of a spatial covariate, and in the recent literature estimation theory and several applications have been developed under this model. In this work we first formulate a goodnessoffit test for this intensity model, assuming a nonhomogeneous Poisson point processes, and secondly we formulate a two sample testing problem. Both tests are based on an $L^2$distance, their normal asymptotic distributions are proved and appropriate bootstrap procedures are implemented to calibrate them. The performance of the proposed techniques is analysed in extensive simulation studies and is illustrated with two real data sets: Murchison gold deposits in Western Australia and wildfire data in Canada. Testing in spatial nonhomogeneous Poisson point processes with covariates
 
12h3014h  Lunch, Cafeteria CROUS  
14h14h40  Giovanni SILVA A Bayesian modelling of spatiotemporal forest data in Portugal In the last decade, forest fires have become a natural disaster in Portugal, causing great forest devastation, leading to both economic and environmental losses and putting at risk populations and the livelihoods of the forest itself. In this work, we present Bayesian hierarchical models to analyse spatiotemporal forest fire data on the proportion of burned area in Portugal. We look for space and time effects on that proportion among Portuguese municipalities or districts over last years. Conditionally on the existence of forest fires for specific time and region, we assume different probabilistic model to the outcome of interest i.e. the proportion of burned area, especially a mixture of distributions to model jointly the proportion of area burned and the excess of no burned area for early years. For getting estimates of the model parameters, we have used Monte Carlo Markov chain methods, as well as for some short term prediction. A Bayesian modelling of spatiotemporal forest data in Portugal Chairman: Edith GABRIEL, 002003 KourosCaryatides  
14h4015h40 
Environment
Environment Edith GABRIEL, Thomas OPITZ, Florent BONNEU
Wildfires can cause important economic and ecological disasters. Their prevention begins with understanding the stochastic mechanisms governing the intensity of occurrences and the severity of fires. We focus on wildfires in the Mediterranean region BouchesduRhone (South of France) observed since 1981, with burnt area larger than one hectare. Occurrences depend on the presence and concomitance of several factors: climatic (temperature, humidity, wind speed), environmental (vegetation types, urbanization, road network) and human activity. Whilst human activity is the main direct cause of wildfires, climatic and environmental conditions are a prior condition to their outbreak and propagation. Therefore, the structure of relative risk of wildfires is highly complex and shows strong variation over space and time and is driven by numerous covariates. Statistical challenges arise from the multiscale spatiotemporal structure of data defined over various supports like fine grids for land use, coarse grids for fire position leading to positional uncertainty, and meteorological series observed at irregularly spaced measurement sites. The spatial heterogeneity of wildfires depends on the spatial distribution of current land use like vegetation type, urban zones or wetlands. We also show that changes in vegetation due to past fires affect the probability of wildfire occurrence during a regeneration period. LogGaussian Cox processes, along with the INLA method for inference and prediction, are particularly useful to model clustered events. Here, we show that they can also deal with more complex structures, allowing us to include the temporal inhibition at small spatial scales and thus providing more accurate predictions. Detecting and modeling multiscale spacetime structures of wildfire occurrences
Maxime BEAUCHAMP, Laure MALHERBE, Chantal DE FOUQUET, Marta VALSANIA, Frédérik MELEUX, Anthony UNG
The national PREV'AIR system (www2.prevair.org) delivers daily analyses and forecasts of different atmospheric pollutant concentrations over Europe and France. Forecast maps for the current and next two days (D+0, D+1, D+2) are computed by kriging statistical forecasts at the monitoring sites obtained by station specific multilinear regression models. Output data from the chemistrytransport model (CMT) CHIMERE are also used as an external drift in the kriging. In this study two kriging competitors are used: the usual spacetime covariancebased kriging with external drift (KED) involving some appropriate neighbourhood to deal with reasonable CPU time and the SPDEbased kriging approach (SPDE). The performance is assessed using 2013 daily data and CMT simulations over France. It will be shown that both local fitting of the drift by (KED) and more global estimation made by (SPDE) can be a good alternative to the former (SA) framework. A comparison of spacetime estimation methods applied to air quality forecasting
Marie DENIS, Benoît COCHARD, Indra SYAHPUTRA, Sébastien TISNE
In the field of epidemiology, studies are often focused on mapping diseases in relation to time and space. Hierarchical modeling is a common flexible and effective tool for modeling problems related to disease spread. In the context of oil palm plantations infected by the fungal pathogen Ganoderma boninense, we propose and compare two spatiotemporal hierarchical Bayesian models addressing the lack of information on propagation modes and transmission vectors. We investigate two alternative process models to study the unobserved mechanism driving the infection process. The models help gain insight into the spatiotemporal dynamic of the infection by identifying a genetic component in the disease spread and by highlighting a spatial component acting at the end of the experiment. In this challenging context, we propose models that provide assumptions on the unobserved mechanism driving the infection process while making shortterm predictions using readytouse software. Evaluation of spatiotemporal Bayesian models for the spread of infectious diseases in oil palm
 
15h4016h10  Break, Jardin d'hiver  
16h1016h50  Thomas KNEIB Modular regression  A Lego System for Building Structured Additive Distributional regression Models with tensor Product Interactions "Semiparametric regression models offer considerable flexibility concerning the specification of additive regression predictors including effects as diverse as nonlinear effects of continuous covariates, spatial effects, random effects, or varying coefficients. In this paper, we discuss a generic concept for defining interaction effects in such semiparametric distributional regression models based on tensor products of main effects. These interactions can be anisotropic, i.e. different amounts of smoothness will be associated with the interacting covariates. We study identifiability and the decomposition of interactions into main effects and pure interaction effects (similar as in a smoothing spline analysis of variance) to facilitate a modular model building process. The decomposition is based on orthogonality in function spaces which allows for considerable flexibility in setting up the effect decomposition. Inference is based on Markov chain Monte Carlo simulations with iteratively weighted least squares proposals under constraints to ensure identifiability and effect decomposition. The performance of modular regression is demonstrated along the construction of spatiotemporal interactions for the analysis of precipitation sums and extreme precipitation events." Modular regression  A Lego System for Building Structured Additive Distributional regression Models with tensor Product Interactions Chairman: Eric PARENT, 002003 KourosCaryatides  
16h5017h50 
Bayesian modeling
Bayesian modeling Giovanna JONA LASINIO, Alessio POLLICE, Thomas KNEIB, Stefan LANG, Roberta ROSSI, Mariana AMATO
The flexibility of the Bayesian approach to account for covariates with measurement error is combined with semiparametric
regression models for a class of continuous, discrete and mixed univariate response distributions with potentially all parameters depending
on a structured additive predictor. Markov chain Monte Carlo enables a modular and numerically efficient implementation of Bayesian
measurement error correction based on the imputation of unobserved errorfree covariate values. We allow for very general measurement
errors, including correlated replicates with heterogeneous variances. The proposal is applied to the assessment of a soilplant
relationship crucial for implementing efficient agricultural management practices. Observations on multidepth soil information and forage
groundcover for a seven hectares Alfalfa stand in South Italy were obtained using sensors with very refined spatial resolution. Estimating
a functional relation between groundcover and soil with these data involves addressing issues linked to the spatial and temporal
misalignment and the large data size. We propose a preliminary spatial interpolation on a lattice covering the field and subsequent
analysis by a structured additive distributional regression model accounting for measurement error in the soil covariate. Results are
interpreted and commented in connection to possible Alfalfa management strategies. Bayesian Measurement Error Correction in Structured Additive Distributional Regression with an Application to the Analysis of Sensor Data on SoilPlant Variability
Gianluca MASTRANTONIO, Giovanna JONA LASINIO, Alessio POLLICE, Giulia CAPOTORTI, Lorenzo TEODONIO, Carlo BLASI
We introduce a Bayesian multivariate hierarchical framework to estimate a spacetime process model for a joint series of monthly extreme temperatures and amounts of rainfall. Data are available for 360 monitoring stations over 60 years, with missing data affecting almost all series. Model components account for spatiotemporal correlation and annual cycles, dependence on covariates and between responses. Spatiotemporal dependence is modeled by the nearest neighbor Gaussian process, response multivariate dependencies are represented by the linear model of coregionalization and effects of annual cycles are included by a circular representation of time. The proposed approach allows imputation of missing values and interpolation of climate surfaces at the national level. It also provides a characterization of the so called Italian ecoregions, namely broad and discrete ecologically homogeneous areas of similar potential as regards the climate, physiography, hydrography, vegetation and wildlife. To now, Italian ecoregions are hierarchically classified into 4 tiers that go from 2 Divisions to 35 Subsections and are defined by informed expert judgments. The current climatic characterization of Italian ecoregions is based on bioclimatic indices for the period 19552000. A Hierarchical Multivariate SpatioTemporal Model for Clustered Climate data with Annual Cycles
Nadja KLEIN, Thomas KNEIB
The selection of appropriate hyperpriors for variance parameters is an important and sensible topic in all kinds of Bayesian regression models involving the specification of (conditionally) Gaussian prior structures where the variance parameters determine a datadriven, adaptive amount of prior variability or precision. We consider the special case of structured additive distributional regression where Gaussian priors are used to enforce specific properties such as smoothness or shrinkage on various effect types combined in predictors for multiple parameters related to the distribution of the response. Relying on a recently proposed class of penalised complexity priors motivated from a general set of construction principles, we derive a hyperprior structure where prior elicitation is facilitated by assumptions on the scaling of the different effect types. The posterior distribution is assessed with an adaptive Markov chain Monte Carlo scheme and conditions for its propriety are studied theoretically. We investigate the new type of scaledependent priors in simulations and two challenging applications, in particular in comparison to the standard inverse gamma priors but also alternatives such as halfnormal, halfCauchy and proper uniform priors for standard deviations. ScaleDependent Priors for Variance Parameters in Structured Additive Distributional Regression
 
18h4523h  Gala diner, Musée Fabre 
9h9h50  Finn LINDGREN Quantifying the uncertainty of contour maps Contour maps are ubiquitous for visualising estimated spatial fields, but the uncertainty associated with such maps has been given a surprisingly small amount of attention. The question is closely connected with the dual problem of constructing credible regions for excursion sets, which leads to a more stringent formulation of the problem. With computational implementations, we can answer questions such as How many or few contours levels is it reasonable to use, given the inherent uncertainty?, in particular for Bayesian latent Gaussian models estimated with Integrated Nested Laplace Approximations. Quantifying the uncertainty of contour maps Chairman: Thomas OPITZ, 002003 KourosCaryatides  
9h5010h50 
Modeling dependence in space and time
Modeling dependence in space and time Ricardo CARRIZO VERGARA, Denis ALLARD, Nicolas DESASSIS
We present a wide class of spatiotemporal geostatistical stationary models arising from spatiotemporal Stochastic Partial Differential Equations (SPDEs) interpreted in a distributional sense. We investigate the properties of models which are stationary solutions of first order and second order evolution SPDEs. When using a white noise as source term, remarkable properties about the spatiotemporal symmetry and the spatial behaviour have been obtained in the case of the first order models, and we show that these properties can be easily controlled by a suitable manipulation of the spatial operator of the SPDE. Second order models are always symmetric, and the spatial operator of the SPDE also determines its spatial structure. We detail important cases for these classes of models that have physical and statistical interest. In particular, we exemplify advectiondiffusion equations, evolution of Matérn models, as well as the class of waving Matérn models which are stationary solutions of the homogeneous wave equation and usual Matérn models in space. We present simulations of these models, using algorithms based on PDEsolver, such as the finite difference method, the finite elements method, and Fourier methods. SpatioTemporal Geostatistical Models associated to Evolution SPDEs
Jorge CLARKE, Alfredo ALEGRÍA, Emilio PORCU
In many geoscientific applications, the phenomena of interest are observed on a large portion of the Planet Earth. When such phenomena evolve over time, a valid model for the study of these observations is to consider them as a partial realization of a spatiotemporal random field, where the spatial component is defined on a sphere, considering this last as a more realistic representation of the globe.
We Introduce a family of Gaussian random fields ({\it GRFs}) constructed by spectral methods via a double KarhunenLo\`eve type representation. Based, recent results in the literature we claim that this family represents the class of Isotropic and stationary GRFs over $\mathbb{S}^{d} \times \mathbb{R}$ and study its regularity properties. In particular, we consider two alternative spectral decompositions for a GRF on $\mathbb{S}^{d} \times \mathbb{R}$. For each decomposition, we establish regularity properties through Sobolev and interpolation spaces. We then propose a simulation method and study its level of accuracy in the $L^2$ sense. The method turns to be both fast and efficient.
Later, we propose an extension of the previous results to GRF over the spherical shell (considering altitude), and to the longitudinally isotropic case. In both situations, the random field is nonstationary in time. A family of random fields for modelling global data evolving in time: Regularity analysis and simulations
Ronny VALLEJOS, Javier PEREZ, Aaron ELLISON, Andrew D RICHARDSON
In this work we define a spatial concordance coefficient for secondorder stationary processes. This problem has been widely addressed in a nonspatial context, but here we consider a coefficient that for a fixed spatial lag allows one to compare two spatial sequences along a 45º line. The proposed coefficient is explored for the bivariate Matérn and Wendland covariance functions. The asymptotic normality of a sample version of the spatial concordance coefficient for an increasing domain sampling framework is established for the Wendland covariance function. Monte Carlo simulations are used to gain additional insights into the asymptotic properties for finite sample sizes. The results will be illustrated by real data examples to see how our method works in practice Constructing a Spatial Concordance Correlation Coefficient
 
10h5011h20  Break, Jardin d'hiver  
11h2012h  Valérie MONBET Markov Switching Multivariate Space Time model for weather variables In this talk, we propose a Markov Switching model which is based on nonseparable crosscovariance functions for multivariate spacetime data. This model is built as a stochastic weather generator and it is applied to simulate weather data on a large West part of France. Markov Switching Multivariate Space Time model for weather variables Chairman: Denis ALLARD, 002003 KourosCaryatides  
12h13h 
Models for climate
Models for climate Dionissios HRISTOPULOS, Vasiliki AGOU
Spacetime data, even spatial data, are big and difficult to handle by methods that scale poorly with size. The main roadblock in the application of
geostatistical and machine learning methods (Gaussian processes) is the storage of dense covariance matrices and the $\Or(N^3)$ scaling of the numerical covariance matrix
inversion. Efficient representations of spatial or spacetime correlations can be constructed using local dependence models, in the spirit of Gaussian Markov random fields (GMRFs).
In the case of continuum random fields, the Gaussian field theories of statistical physics provide models with local structure.
Stochastic local interaction (SLI) models are inspired both from GMRFs and Gaussian field theory. The main idea is that the correlations are generated by interactions between neighboring sites and times. The interactions are incorporated in a precision matrix with simple parametric dependence.
The strength of the interactions and the size of the neighborhood are defined by means of kernel functions and respective bandwidths.
Compactly supported kernels lead to finitesize local neighborhoods. This representation leads to sparse precision matrices. In addition, the precision matrix is
explicitly constructed at the model estimation stage, which means that optimal prediction does not require the costly matrix inversion. Consequently, computational implementations require less memory space and run faster than traditional approaches. In the case of lattice data, SLI models transform into GMRFs. We present a specific SLI formulation and consider its application to lattice and scattered data. Stochastic Local Interaction Model for Spatial and SpaceTime Data
Claudio HEINRICH, Alex LENKOSKI, Kristoffer HELLTON, Thordis THORARINSDOTTIR
Numerical weather prediction (NWP) models predict future weather by approximating solutions to the (deterministic) partial differential equations that govern the dynamics in atmosphere and oceans.
These models oftentimes exhibit bias and miscalibration and therefore require statistical postprocessing based on training data.
We consider NWP forecasts for sea surface temperature on the entire globe issued by the Norwegian Climate Prediction Model NorCPM.
Challenges for statistical postprocessing of sea surface temperature are, among others, strong seasonality effects, trends in the bias caused by global warming, and a nonstationary spatial error correlation.
Moreover, as we consider a fine grid spanning the entire globe, the dimension of the forecast variable is much higher than the sample size. In order to overcome this issue we apply principal component analysis to regularize the covariance matrix of the forecasting distribution.
Statistical postprocessing of sea surface temperature forecasts
Sheng CHEN, Etienne LEBLOIS, Sandrine ANQUETIN, Sara MARTINO
In this contribution, a geostatistically sound approach inspired by a soil simulation strategy known as the ``pilot point'' technique is proposed to simulate heterogeneous spatial fields respecting average values known over large scale domains.
It typically allows the disaggregation of atmospheric reanalysis, GCMs outputs or large scale stochastic weather simulations.
The disaggregation is based on an "a priori" smallscale simulation over the final grid, conducted as in Leblois and Creutin (2013).
The two main components of this "a priori" simulation are a first Gaussian field thresholded to get a 0/1 rainfall indicator field and a second Gaussian field to get a nonzero rainfall field, the nonzero rainfall field is then multiplied by the indicator field.
The novelty is that the Gaussian fields are iteratively modified so that the final simulation will reach the wished largescale values.
The disaggregation is not deterministic and reintroduces smallscale variability implicit in the largescale data, giving an instrumental picture of the conditional uncertainty.
The technique was developed within a stochastic weather simulation project led by Sintef; it is presently tested under Norwegian and French climates. Disaggregation of largescale atmospheric data: a nondeterministic geostatisticallybased approach
 
13h14h30  Lunch, Cafeteria CROUS  
14h3015h10  Miguel A. MARTINEZ BENEITO An heteroscedastic proposal for highly multivariate disease mapping Highly multivariate disease mapping has been recently proposed as an enhancement of traditional multivariate studies, making it possible to perform the joint analysis of a large number of diseases. This line of research has an important potential as it integrates information of many diseases into a single model yielding richer and more accurate risk maps. In this work we show how some of the proposals already put forward in this area display particular problems when applied to small regions of study. Specifically, the homoscedasticity of these proposals may produce evident misfits and distorted risk maps. We propose two new models to deal with varianceadaptivity problems in multivariate disease mapping studies and give some theoretical insights on their interpretation. An heteroscedastic proposal for highly multivariate disease mapping Chairman: Lola UGARTE, 002003 KourosCaryatides  
15h1016h10 
Small area
Small area Cécile HARDOUIN, Noel CRESSIE
A spatial lattice model for binary data is constructed from two spatial scales
linked through conditional probabilities. A coarse grid of lattice locations
is specified and all remaining locations (which we call the background)
capture finescale spatial dependence. Binary data on the coarse grid are
modelled with an autologistic distribution, conditional on the binary process
on the background. The background behaviour is captured through a hidden
Gaussian process after a logit transformation on its Bernoulli success
probabilities. The parameters of the new model come from both spatial scales, and are estimated with likelihoodbased methods. We introduce the Spatial oddsratio, which is more appropriate in the binary context than the spatial correlation.
Presenceabsence data of corn borers in the roots of corn plants are used to
illustrate how the model is fitted. TwoScale Spatial Models for Binary Data
Helena BAPTISTA, Jorge M. MENDES, Peter CONGDON
Conditionally specified Gaussian Markov random field (GMRF) models with adjacencybased neighborhood weight matrix, commonly known as neighborhoodbased GMRF models, have been the mainstream approach to spatial smoothing in Bayesian disease mapping. However, there are cases when there is no evidence of positive spatial correlation or the appropriate mix between local and global smoothing is not constant across the region being study. Two models have been proposed for those cases, a conditionally specified Gaussian random field (GRF) model using a similaritybased nonspatial weight matrix to facilitate nonspatial smoothing in Bayesian disease mapping, and a spatially adaptive conditional autoregressive prior model. The former model, named similaritybased GRF, is motivated for modeling disease mapping data in situations where the underlying small area relative risks and the associated determinant factors do not varying systematically in space, and the similarity is defined by similarity with respect to the associated disease determinant factors. In the presence of disease data with no evidence of positive spatial correlation, a simulation study showed a consistent gain in efficiency from the similaritybased GRF, compared with the adjacencybased GMRF with the determinant risk factors as covariate. The latter model considers a spatially adaptive extension of Leroux et al.~\cite{9} prior to reflect the fact that the appropriate mix between local and global smoothing may not be constant across the region being studied. Local smoothing will not be indicated when an area is disparate from its neighbours (e.g. in terms of social or environmental risk factors for the health outcome being considered). The prior for varying spatial correlation parameters may be based on a regression structure which includes possible observed sources of disparity between neighbours. We will compare the results of the two models. Comparing two models for disease mapping data not varying systematically in space
Soraia PEREIRA, Kamil TURKMAN, Luís CORREIA, Haavard RUE
In Portugal, the Portuguese National Statistical Institute publishes quarterly labour market figures at national level and for both NUTS I and NUTS II regions. Over recent years it has become increasingly important to know these figures at more disaggregated levels. However, using the current estimation method, it is not possible to produce satisfactorily precise estimates. This problem is known in the literature as `small area estimation'. Some alternative methods have subsequently been proposed, one of which  and perhaps the most important  is the FayHerriot model, an areal model which assumes normality of the data. However, the assumptions made in this model are very restrictive and do not appear to be suitable in the context of unemployment. From the 4th quarter of 2014 onwards, all the sampling units (the residential buildings) of the Portuguese Labour Force Survey (PLFS) were georeferenced. To take advantage of this, the authors proposed using this new data, along with the information regarding the inhabitants themselves. Thus, the method we propose is based on a point referenced data model, also described as a geostatistical model. This model assumes that the points in the population are fixed and the interest is to model the spatial variation of the marks. Here, the points are the residential buildings, whereas the associated marks are the number of unemployed people residing in these buildings. The inference will be based on the Integrated Nested Laplace approximations (INLA). Spatiotemporal models for georeferenced unemployment data
 
16h1016h40  Break, Jardin d'hiver  
16h4017h10  Luigi IPPOLITI Simple spatiotemporal models for complex spatial data This work is concerned with the specification of a simple hierarchical generalized spatiotemporal model which warrants consideration when data sets with different types of spatial complexities are available. Especially under Gaussian assumptions, the model is simple to estimate and particularly useful when reliable estimates of the parameters of a covariance function are difficult to obtain. Details on data analysis in several research fields will be given in an extended version of the present abstract. Simple spatiotemporal models for complex spatial data Chairman: Alessio POLLICE, 002003 KourosCaryatides  
17h1018h10 
Hierarchical Spatiotemporal models
Hierarchical Spatiotemporal models Unai PEREZGOYA, Ana F MILITINO, María Dolores UGARTE, Marc GENTON
Time series of satellite imagery is nowadays essential for monitoring the evolution of land use, land cover, vegetation trends, and climatological or phenological changes. However, but some of these images could be useless because of the presence of clouds.
In this paper we propose filling these clouds through a thinplate spline (Tps) model that accommodates spatiotemporal dependence among images. The performance of the method is illustrated with a simulation study where the Tps procedure is compared with other alternatives. The scenario of the simulation study consists in introducing at random seven sizes of clouds in three time series of composite MODIS Terra and Aqua images of Navarre (Spain) between 2011 and 2013. The remote sensing data are the normalized difference vegetation index (NDVI) and the land surface temperature (LST) day and night. The results show that the thinplate spline model outperforms Timesat, Hants and Gapfill in small, moderate, and big clouds in LST day and night and it is equally competitive with NDVI. Thinplate splines for cloud filling in satellite imagery
Philipp OTTO, Wolfgang SCHMID, Robert GARTHOFF
Otto, Schmid, and Garthoff (2016) introduce a new spatial model that incorporates heteroscedastic variance depending on neighboring locations. The proposed process is regarded as the spatial equivalent to the temporal autoregressive conditional heteroscedasticity (ARCH) model.
In contrast to the temporal ARCH model, in which the distribution is known given the full information set of the prior periods, the distribution is not straightforward in spatial and spatiotemporal settings. However, it is possible to estimate the parameters of the model using the maximumlikelihood approach. Moreover, we introduce an exponential spatial ARCH models and propose a maximumlikelihood estimator for this kind of spatial ARCH model. In the talk, I focus on the estimation from a computational and practical point of view. From this perspective, the loglikelihood function is usually sufficient to get accurate parameter estimates by using any nonlinear, numerical optimization function. To compute the likelihood for a certain set of parameters, the determinant of the Jacobian matrix must be computed, which often requires large computationally capacities, especially for large data sets. In particular, I show the implementation of the estimation approach in the Rpackage \texttt{spGARCH}. Eventually, the function for estimation is demonstrated by an illustrative example. Estimation of spatial autoregressive conditional heteroscedasticity models
Francesco LAGONA, Monia RANALLI
Motivated by segmentation issues in marine studies, a novel hidden Markov model is proposed for the analysis of cylindrical spacetime series, that is, bivariate spacetime series of intensities and angles. The model is a multilevel mixture of cylindrical densities, where the parameters of the mixture vary across space according to a latent Markov field, while the parameters of this hidden Markov random field evolve over time according to the states of a hidden Markov chain. It segments the data within a finite number of latent classes that represent the conditional distributions of the data under environmental conditions that vary across space and time, simultaneously accounting for unobserved heterogeneity and spacetime autocorrelation. It parsimoniously accommodates specific features of environmental cylindrical data, such as circularlinear correlation, multimodality and skewness. Due to the numerical intractability of the likelihood function, parameters are estimated by a computationally efficient EM algorithm based on the maximization of a weighted composite likelihood. The effectiveness of the proposal is tested in a case study that involves speeds and directions of marine currents in the Gulf of Naples, where the model was capable to cluster cylindrical data according to a finite number of intuitively appealing latent classes.
A multilevel hidden Markov model for spacetime cylindrical data
 
18h3020h30 
Posters
Posters Julie LOUVRIER, Julien PAPAIX, Christophe DUCHAMP, Olivier GIMENEZ
Species distribution models (SDMs) are a family of statistical tools for ecologists to understand and predict species range. SDMs suffer from several limitations including the difficulty i) to incorporate ecological theory like, e.g., dispersal and ii) to account for imperfect species detectability. Ignoring these issues can lead to bias in inferring species distribution.
Here, we adopt the theory of ecological diffusion that has recently been introduced in ecological statistics to incorporate in ecological models spatiotemporal processes like dispersal or invasion. As a case study, we focus on wolves (Canis lupus) that have been recolonizing France through dispersal from the Apennines since the last 20 years.
We developed a Bayesian hierarchical model to combine a mathematical formulation of the temporal dynamics of species distribution with data collected in the field. The observation process led to detection/nondetection data that were used to estimate occupancy while accounting for heterogeneity in detection due to variation in abundance. Detection was mainly driven by the sampling effort which we measured as the number of observers per sampling unit. We used differential equations for modelling species diffusion and growth in a fragmented landscape.
We found that our model accurately described the recolonization process of wolves in France. The Bayesian framework was particularly useful to quantify parameter uncertainty in the observation and the ecological processes, and to propagate this uncertainty in the forecasting step. A dynamic mechanistic species distribution model of wolf recolonization in France
Luciano TELESCA , Tony A. STABILE
Seismicity induced by the human activity has been observed and documented since at least the 1920s. Various energy technologies have been claimed as responsible for it, like water reservoir impoundment, mining activity, underground nuclear tests, enhanced geothermal systems, injection/withdrawal of fluids into/from the ground associated with the gas storage, the CO2 sequestration, and the exploitation of oil and gas.
The HAV hosts the biggest onshore oil field in west Europe, with an average production of about 3.6 × 109 kg of oil per year and 9.6 × 108 m3 of gas per year. The HAV is also one of the most important areas of Italy from a seismotectonic point of view, as a NESW extensional stress regime is ongoing, with a seismogenic fault system capable of producing large earthquakes.
On 2 June 2006 the wastewater produced during the oil and gas field exploitation started to be disposed of by pumping the fluids back into a 4km deep injection well; and after only 4 days the seismic activity around increased significantly.
Combining the results of the Schuster’s spectrum of the earthquake point process generated around the injection well with those of the singular spectrum analysis of the fluid injection variables (volume, pressure and energy), the correlation between fluid disposal and seismicity was investigated and discussed.
The present study was supported by the project “INduced Seismicity in Italy: Estimation, Monitoring, and sEismic risk mitigation (INSIEME)” funded by MIURItaly.
Investigating the relationship between fluid injection and triggered seismicity in southern Italy
Maria FRANCOVILLORIA, Massimo VENTRUCCI, Haavard RUE
We discuss the use of penalized complexity priors for spatially varying coefficient models, introducing a natural base model choice that corresponds to a constant coefficient (no variation in space). Preliminary results on the use of these priors in a case study on air pollution and hospital admissions in Turin (Italy) are presented. Varying coefficient models for areal data
Giada ADELFIO, Marcello CHIODI
The paper proposes a stochastic process that improves the assessment of seismic events in space and time, considering a contagion model (branching process) within a regressionlike framework. The proposed approach develops the Forward Likelihood for prediction (FLP) method including covariates in the epidemic component.
A spacetime branching process with covariates
Carlos DÍAZAVALOS, Pablo JUAN, Laura SERRASAURINA, Pau ARAGÓ
The objective of the present study is first, the last developments and validation results of modeling the evolution of wildfires using random spread process. Second, a sensitivity analysis was conducted to identify the most influential covariates for controlling fire propagation. The model combines the features of a network model with those of a quasiphysical model of the interaction between burning and nonburning cells, which strongly depends on covariates. The models applied to different wildfires in Spain, including the different temporal states. In the same way, the possible predictions for compare the experiments in terms of rate of spread, area and shape of the burn and it is studied the environmental risk during the fire propagation. Finally, the sensitivity of the model outcomes to input parameters is modeled.
In this work, the idea of random set modeling of fire spread is developed, including the covariates. Some facts indicating the stochastic nature of fire spread are reviewed. A brief survey of deterministic and stochastic models of spread and a description of random set models based on a Markov process called Random Spread Process (RSP) is developed. Modelling the environmental risk of the evolution wildfires using random spread process including covariates
Crescenza CALCULLI, Alessio POLLICE, Letizia SION, Porzia MAIORANO
In recent years, marine litter has become a recognized
global ecological concern, although its distribution and influence
on deepsea habitats are still not wellknown. This study focuses on the
analysis of abundance data for litter categories, collected
during trawl surveys regularly conducted at local scale, in the
Central Mediterranean. Multivariate abundance data have spacetime
structure and come with additional environmental continuous
covariates, such as distances to the coastline or to the nearest
harbor. Here marine litter data are modeled in order to estimate the
effects affecting the dynamics of litter assemblages at different
spatio/temporal scales. We propose a correlated response model with
latent variables, that proves to be particularly suitable to infer
potential environmental covariates while controlling for correlation
between litter categories and providing a method for residual
ordination. MCMC estimation is implemented within the Bayesian
hierachical framework that allows to integrate environmental and
anthropogenic processes into a single model. Bayesian spacetime modeling of multivariate marine litter abundance
Mario SANTORO, Gianluca MASTRANTONIO, Giovanna JONA LASINIO
CircSpaceTime is going to be a new R package that eventually will implement most of the models recently developed for spatial and spatiotemporal interpolation of circular data. Such data are often found in applications where, among the many, wind directions, animal movement directions, and wave directions are involved. To analyze such data we need models for observations at locations $\mathbf{s}$ and times $t$, socalled geostatistical models providing structured dependence which is assumed to decay in distance and time. For example for wave directions in a body of water, we imagine a wave direction at every location and every time. Thus, the challenge is to introduce structured dependence into angular data. The approach we take begins with models for linear variables over space and time using Gaussian processes. Then, we use either wrapping or projection to obtain Gaussian processes for circular data. Altogether, this package will implement in its first version the proposals by Mastrantonio, Jona Lasinio, and Gelfand. The models are cast as hierarchical models, with fitting and inference within a Bayesian inference framework. All procedures are written using Rcpp and whenever possible, the computation is parallelized. We use a wave direction dataset as a running example. CircSpaceTime: an R package for spatial and spatiotemporal modeling of Circular data
Pilar GARCIASOIDAN, Tomas R. COTOS YANEZ
Prediction of a spatial variable at an unsampled location can be addressed through the kriging methodology. Furthermore, the resulting predictor can incorporate data from secondary variables, correlated with the target one, when using cokriging techniques. This issue demands characterizing the multivariate dependence structure, which is not an easy task, due to the number of functions that must be approximated and the conditions required to the estimators so as to be valid for prediction. In addition, the accuracy of the resulting predicted values is highly dependent on different factors, such as the data correlation level and the limitations of the diagnostic techniques. Thus, in the current work, we suggest a nonparametric kernel alternative for prediction, designed to avoid the aforementioned problems when including data from auxiliary variables. Consistency of the proposed predictor will be checked, under the assumption of different hypotheses. For choice of the bandwidth parameters involved, balloon selectors will be suggested. We will also deal with the estimation of the remaining unknown terms in the kernel predictor, by proceeding through parametric and nonparametric approaches. Simulation studies will be developed in different scenarios to check the performance of the new methodology for prediction. Finally, the nonparametric approach will be applied to a real data set to illustrate its practical implementation. Nonparametric approach for spatial prediction incorporating information from correlated auxiliary variables
Maria Antonia AMARAL TURKMAN, Kamil Feridun TURKMAN, Paula PEREIRA
Wildfires, particularly in Portugal, are a relevant public policy issue due to the significant economical and social damage they cause. Most wildfires are extinguished upon ignition and do not have significant effect. However, it is generally an established fact that a small number of fires cause most of the damage, often expressed by the phrase "1 % of the fires do 99% percent of the damage" .
Therefore, It is very important to understand the causes of extreme fires, their spatial distribution as well as predicting the onset of a possible extreme wildfires. Probability maps indicating where ignition is most likely to take place and the consequent fire scar sizes, are very important administrative tools in managing wildfires. In this talk, we will define the concept of probability maps for wildfires, describe different types of data that are commonly available for the purpose and the consequent different spatiotemporal modeling strategies, using Bayesian hierarchical methods. Probability maps for extreme wildfires
Sergio CASTILLOPAEZ, Ruben FERNANDEZCASAL, Pilar GARCIASOIDAN
The aim of this work is to provide a nonparametric resampling method for approximating the (unconditional) probability that a spatial variable exceeds a prefixed threshold value, from the available data. Then, a risk map of the target variable can be obtained, which is of great applicability in the environmental setting, for instance, to assess the contamination risk by any pollutant. Other approaches suggested for the same issue require stationarity from the random process or relax this hypothesis to admit the presence of a deterministic trend, although all of them assume constant variance throughout the observation region. However, our proposal has been designed to be valid under heteroscedasticity of the spatial process. For this purpose, local linear estimates of the trend, variance and variogram functions must be derived, where the two latter ones are corrected to reduce the bias due to the use of residuals. These estimates are employed in the implementation of a bootstrap procedure, whose replicates allow the approximation of the aforementioned risk. The performance of this mechanism is checked through numerical studies with simulated and real data. Nonparametric bootstrap approach for risk mapping under heteroscedasticity
Álvaro BRIZ, Francisco MARTÍNEZ, Francisco MONTES
In the last decade, research on traffic accidents is increasing and expanding with the design of a wide variety of methodologies and techniques. In order to properly capture the distribution of accidents within an area of interest, spatial models have become required, focusing on two main objectives: the detection of zones of high crash risk (hotspots) and the explicability of accidents incidence from a set of related variables of different nature. These include geometric features and traffic information of the roads being studied, but also socioeconomic and demographic issues.
Most of the studies on traffic accidents have been developed over an areal region subject to a certain administrative division. However, recent studies have employed the specific network structure of roads of the region of interest, which are known as linear networks in the field of spatial statistics. These are like graphs made of edges and vertex that accurately represent the geographical space where accidents take place.
In this work, a collection of accidents registered by the Local Police Department of the city of Valencia (Spain) in the period 20052017 are projected to a linear network, which represents a zone of this city with more than 30 km of road structure. Furthermore, the linear network has been endowed with a direction according to the traffic flow. Several models including various road features as variables and different definitions of neighbourhoods have been analyzed and compared with explanatory and methodological objectives. Spatial analysis of crash data in the road network of the city of Valencia
Jonatan A. GONZÁLEZ, Jorge MATEU
We formulate statistical tests to check for interaction effects under the twoway ANOVA models when the observations are secondorder descriptors of spatial point patterns. The data involved come from a metallurgy procedure related to flotation cells. In particular, we analyse the interaction effect between the frother concentration and the volumetric air flow factors in the spatial distribution of bubbles. Random permutation test in factorial models for spatial point patterns
Isabel FUENTES SANTOS, Wenceslao GONZÁLEZMANTEIGA, Jorge MATEU
The pair correlation function can be considered one of the most informative secondorder characteristic of spatial point processes. Nonparametric estimators of the pair correlation function are useful tools to identify the type, aggregation or inhibition, and strength of spatial interaction in observed spatial point patterns. Kernel smoothing is the most popular nonparametric estimator of the pair correlation function for both homogeneous and inhomogeneous point processes. The performance of any kernel estimator depends on the bandwidth parameter. Several procedures, such as crossvalidation, semiparametric bootstrap or an adaptive plugin rule, have been proposed for bandwidth
selection in the stationary framework. To our knowledge, leastsquares cross validation is the only datadriven bandwidth selector available for the inhomogenous case. This work analyzes the asymptotic properties of the kernel estimator of the pair correlation function for secondorder intensity reweighted stationary (SOIRS) point processes. We propose a nonparametric bootstrap to estimate the asymptotic mean square error (AMISE), and develop a bandwidth selector based on the minimization
of the bootstrap AMISE. We compare the performance of our proposal with the leastsquares bandwidth selector in a simulation study, and through its application to the secondorder analysis of wildfire patterns in Galicia (NW Spain). Bootstrap bandwidth selection for kernel estimation of the pair correlation function in inhomogeneous spatial point processes
Rubén FERNÁNDEZCASAL, Sergio CASTILLOPÁEZ, Mario FRANCISCOFERNÁNDEZ
In this work, a nonparametric procedure to approximate the conditional probability that a regionalized variable exceeds a certain threshold value is proposed. The method consists of a bootstrap algorithm that combines conditional simulation techniques with nonparametric estimations of the trend and the variogram of the spatial process. For the local linear estimation of the mean, a bandwidth selection method that takes the spatial dependence into account is used. The variogram is approximated by a flexible estimator based on the residuals, previously correcting its bias due to the estimation of the trend. The proposed method allows obtaining estimates of the exceedance risk in nonobserved spatial locations, and its behavior will be analyzed through simulation studies and with the application to a real data set. Nonparametric approximation of conditional risk in nonstationary geostatistical processes
Angel GUTIERREZPRIETO, Nancy MEJIADOMINGUEZ, Carlos DIAZAVALOS
Obesity has become ahealth problem worldwide .According to the WHO,
the tren of obesity prevalence in México is one of the highest worldwide. The association of obesity as a risk factor to hipertensive diseases and diabetes makes it necessary to analise the spatial distribution of its prevalence in the country. Such analyses provide information necessary to plan the level of health care that will be needed in the short and mid term. In this work we present the results of a preliminary analysis using the data provided by the 2012 National Health Survey. We fit a hierarchical poisson model to asses the relative prevalence at a municipality level. Our results show that the prevalence does not show any clear trend, an that there exist several hot spots associated to very particular municipalities. Prevalence of obesity in Mexico: model for input values
Johann OSPÍNAGALÍNDEZ, Ramón GIRALDO, Mercedes ANDRADEBAJARANO
We show an extension of the functional regression model to the case of spatially correlated errors. The estimation of the parameters is obtained by feasible generalized least squares. Functional geostatistics and particularly the tracevariogram function is proposed as a method for estimating the spatial dependence Functional regression with spatially correlated errors
Haifa FEKI, Julie CARREAU
Tunisia is suffering from intense and persistent drought episodes characterized by significant
rainfall deficit. The country’s historical memory confirms the abundance of drought sequences and
their aggressiveness, particularly in arid zones. This study presents the interest of certain statistical
and geostatistical methods for the spatial and temporal variability of the drought at different time
steps. This drought would be characterized and quantified based on the triptych: "intensity, duration
and geographical extent". The data used concern 67 raingauges covering the Tunisian territory and
spreading over the period (19002015) and over which SPI indices are calculated. The PCA showed
three similar areas in terms of drought, the average SPI for each region is then calculated. Spatial
variability is analyzed based on the semivariogram and the trend of the series is analyzed by the
Mann Kendall test.
Spatial and temporal drought variability in Tunisia
Mounia ZAOUCHE, Liliane BEL, Jessica TRESSOU, Emmanuelle VAUDOUR
Organic carbon is a good indicator of soil fertility and enables to mitigate gas emissions. Having at our disposal a precise mapping of its content is therefore essential. In this study we aim at spatially estimate the soil carbon content (SOC) in the Versailles plain and the Alluets plateau, a 221 km2 agricultural area.
The novel Bayesian inference approach called Integrated Nested Laplace Approximation with Stochastic Partial Differential Equation (INLASPDE) allows us to ensure consistency between various available sources of information (soil samples and optical satellite image) and to produce in a short time a posteriori estimations of the parameters and the SOC field, considered as a latent field. Two models were evaluated and compared using the elevation covariate stemming from a Digital Elevation Model (DEM), including or not the data from the satellite image. Adding the image improves the prediction quality in terms of RMSE (Root Mean Square Error RMSE) since the RMSE goes from 4.48 g/Kg to 3.81 g/Kg using a validation set of 75 locations. Overall the carbon prediction map from the joint model represents more realistically the spatial structure and variability of the carbon field. Soil Organic Carbon joint modelling using jointly different sources
Luigi IPPOLITI, Eugenia NISSI
Spatiotemporal modelling has received more and more attention from academic researchers
for its promising applicability to complex data containing both spatial and temporal patterns. In
this work, we discuss the modelling of Particulate Matter (PM10) data by using a frequency domain
approach. We show that our model has several computational advantages, and that it is able to provide
good predictions and can be used for descriptive purposes. Spatialtemporal pattern analysis and prediction of air quality using Discrete Fourier Transform
Conceição RIBEIRO, Paula PEREIRA
The study of the evolution of crime, whether in a temporal level or in a space level, presents a great importance in the definition of measures to improve the welfare of the population. Usually, to analyze the evolution of crime in a given region, it resorts to compare rates of several years. This work aims to extend this analysis and use spatial and temporal models that allow to characterize the trend of crime in the spatial level and in the temporal level. These models are applied to data crime observed in the municipalities of mainland Portugal, from 2011 to 2016. SpatioTemporal Modelling of Criminal data in Portugal
Angie VILLAMIL, Martha BOHORQUEZ, Ramon GIRALDO, Jorge MATEU
The aim of this paper is to introduce an R package that carries out spatial prediction of univariate and multivariate functional data and optimal sampling. The kriging and cokriging methods used here are based on the scalar fields resulting from the scores associated to the representation of the functional data with the empirical functional principal components. Based on this representation the predictors only depend on the autocovariance and crosscovariance of the associated score vectors. In addition, design criteria are given for all predictors derived. The examples of the package are developed for networks of air quality. Spatialfd: A package for functional kriging, functional cokriging and optimal sampling of functional data

9h9h50  Carlo GAETAN On statistical modelling of spacetime extremes The statistical modelling of spacetime extremes in environmental applications is key to understanding the complex extremal dependence structures in original event data and to realistic scenario generation for impact models. While classical limit models based on maxstability fail to appropriately capture relatively fast joint decay rates between asymptotic dependence and classical independence, empirical evidence in recent studies motivates the use of more flexible subasymptotic models. In this talk I (partially) review some recent attempts to model higher threshold exceedances defined over continuous space and time. Then I introduce a novel hierarchical model by embedding a spacetime Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through spacetime according to a velocity vector. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France. On statistical modelling of spacetime extremes Chairman: JeanNoël BACRO, 002003 KourosCaryatides  
9h5010h50 
Covariance modeling
Covariance modeling Christian LANTUÉJOUL
In several domains of the Geosciences (climatology, cosmology, geodesy or paleomag
netism), data are supported by spheres. As they often exhibit spatial strutures, it may be interesting
to examine them using a geostatistical approach. At first some background is provided on several
geometric and stochasic features of the sphere that make it so different from Euclidean spaces (spher
ical harmonics, Schoenberg representation of covariance functions). Then an algorithm is proposed
to perform continuous simulations of isotropic Gaussian random fields on the sphere. This algorithm
requires knowledge of the spectral measure of the covariance function. Besides a few examples, par
ticular attention is paid to the spectral measures of the Yadrenko class of covariance functions.
Simulation of isotropic Gaussian random Fields on Spheres
Emilio PORCU, Stefano CASTRUCCIO, Alfred ALEGRIA, Paola CRIPPA
This paper revisits axial symmetry for spatial data, putting special emphasis on results obtained recently by the same group of authors. Then, axial symmetry for spacetime data is discussed and new models for this characterization are proposed. We illustrate our findings on applications to climate models. Axial Symmetry Covariance Models for Climate Data
Francisco CUEVAS, Emilio PORCU, Moreno BEVILACQUA
We offer a dual view of the dimple problem related to spacetime correlation functions in
terms of their contours. We find that the dimple property in the Gneiting class of correlations
is in onetoone correspondence with nonmonotonicity of the parametric curve describing the associated
contour lines. Further, we show that, given such a non monotonic parametric curve associated
to a given level set, all the other parametric curves at smaller levels inherit the property of non monotonicity.
We finally propose a modified Gneiting class of correlations having monotonically decreasing
parametric curves and no dimple along the temporal axis.
Contours and dimple for the Gneiting class of spacetime correlation functions
 
10h5011h20  Break, Jardin d'hiver  
11h2012h  Jenny WADSWORTH Conditional modelling of spatial extremes Conditional extreme value theory enables a flexible approach to modelling multivariate extremes. We extend the conditional approach to the modelling of spatial extremes, proposing different models that allow for both asymptotically dependent and asymptotically independent processes. Tractable likelihoods permit inference on spatial extremes observed at a large number of sites, whilst simulation of new extreme events at existing and new sites allows inference on quantities of interest via Monte Carlo. Conditional modelling of spatial extremes Chairman: Gwladys TOULEMONDE, 002003 KourosCaryatides  
12h12h40 
Extremes
Extremes Fátima PALACIOSRODRÍGUEZ, Gwladys TOULEMONDE, Julie CARREAU, Thomas OPITZ
Flash floods in France are highly destructive natural phenomena, not only by creating material
damage but also by threatening the safety of human life. To anticipate the impact of such disasters,
it is crucial to propose stochastic simulation methods of realistic scenarios for spatiotemporal extreme
fields. Pareto processes are justified because they model phenomena that exceed a certain extreme
threshold. Therefore, they are promising models for the aforementioned challenge. Nonparametric and
parametric approaches in this framework have been provided over last years, but the proposed models
do not establish a direct link to Pareto processes. A semiparametric method for simulation of extreme
spacetime generalized Pareto processes is introduced. A key benefit of the proposed method is that it
allows to generate an unlimited number of realizations of such extreme fields. Our simulation method
is applied to a rainfall dataset to model flash floods in a region in Mediterranean France. Spacetime extreme processes simulation for flash floods in Mediterranean France
Julie CARREAU, Gwladys TOULEMONDE
Extremevalue copulas are justified by the theory of multivariate extremes. However, most highdimensional copulas are too simplistic for applications. Recently, a class of flexible extremevalue copulas was put forward by combining two extremevalue copulas with a weight parameter in the unit hypercube. In a multisite study, the copula dimension being the number of sites, this extraparametrized approach quickly becomes overparametrized. In addition, interpolation is not straightforward. The aim of this work is to extend this approach to a spatial framework. By taking the weight parameter as a function of covariates, model complexity is reduced. Moreover, the model is defined at every point of the space and can be interpreted in terms of distances. We focus on the spatial extension based on Gumbel copulas and describe its possible extremal dependence structures. The proposed spatial model is applied on both synthetic and precipitation data in the French Mediterranean. ExtraParametrized Extreme Value Copula: Extension to a Spatial Framework
 
12h4012h50  Closure  
12h5014h  Lunch, Cafeteria CROUS 