In geostatistics, a common problem is to predict a spatial exceedance and its exceedance region. This is scientifically important since unusual events tend to strongly impact the environment. Here, we use classes of loss functions based on image metrics (e.g., Baddeley's loss function) to predict the spatial-exceedance region. We then propose a joint loss to predict a spatial quantile and its exceedance region. The optimal predictor is obtained by minimizing the posterior expected loss given the process parameters, which we achieve by simulated annealing. Various predictors are compared through simulation. This methodology is applied to a spatial dataset of temperature change over the Americas. This research is joint with Jian Zhang and Peter Craigmile. Noel Cressie. Director, Program in Spatial Statistics and Environmental Sciences Department of Statistics The Ohio State University. Bande son disponible au format mp3 Durée : 44 mn

Workshop on spatial statistics (SAMOS, 2007)

01 - Predicting spatial exceedance regions - Noël Cressie

Noël Cressie - Ohio State University Bande son disponible au format mp3 Durée : 10 mn

02 - Questions - Noël Cressie

Modeling space-time data often relies on parametric covariance models and various assumptions such as full symmetry and separability. These assumptions are important because they simplify the structure of the model and its inference, and ease the possibly extensive computational burden associated with spacetime data sets. We review various space-time covariance models and propose a unified framework for testing a variety of assumptions commonly made for covariance functions of stationary spatio-temporal random fields. The methodology is based on the asymptotic normality of space-time covariance estimators. We focus on tests for full symmetry and separability, but our framework naturally covers testing for isotropy, TaylorÂ's hypothesis, and the structure of cross-covariances. The proposed test successfully detects the asymmetric and nonseparable features in two sets of wind speed data. We perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on space-time covariance functions. Marc G. Genton. University of Geneva and Texas A&M University. Bande son disponible au format mp3 Durée : 46 mn

03 - Modelling and testing properties of space-time covariance functions - Marc Genton

Marc Genton - University of Geneva Bande son disponible au format mp3 Durée : 5 mn

04 - Questions - Marc Genton

We develop contrasting spatio-temporal models for two weather variables: solar radiation and rainfall. For solar radiation the aim is to assess the performance of area networks of photo-voltaic cells. Although radiation measured at a sufficiently fine temporal scale has a bimodal marginal distribution (Glasbey, 2001), averages of 10-minute or longer duration can be transformed to be approximately Gaussian, and we fit a spatio-temporal auto-regressive moving average (STARMA) process (Glasbey and Allcroft, 2007). For rainfall, the aim is to disaggregate to a finer spatial scale than that observed. To overcome the difficulty that the marginal distribution of hourly rainfall has a singularity at zero and so is highly non-Gaussian, we apply a monotonic transformation. This defines a latent Gaussian variable, with zero rainfall corresponding to censored values below a threshold, which we model using a spatio-temporal Gaussian Markov random field (Allcroft and Glasbey, 2003). For both models, computations are simplified by approximating space by a torus and using Fourier transforms. Allcroft, D.J. and Glasbey, C.A. (2003). A latent Gaussian Markov random field model for spatio-temporal rainfall disaggregation. Applied Statistics, 52, 487-498. Glasbey CA (2001). Nonlinear autoregressive time series with multivariate Gaussian mixtures as marginal distributions. Applied Statistics, 50, 143-154. Glasbey, C.A. and Allcroft, D.J. (2007). A STARMA model for solar radiation. Available at http://www.bioss.sari.ac.uk/staff/chris.html : http://www.bioss.sari.ac.uk/staff/chris.html Chris Glasbey - Biomathematics and Statistics Scotland Bande son disponible au format mp3 Durée : 51 mn

05 - Spatio-temporal weather models - Chris Glasbey

Chris Glasbey - Biomathematics and Statistics Scotland Bande son disponible au format mp3 Durée : 14 mn

06 - Questions - Chris Glasbey

Soil moisture provides the physical link between soil, climate and vegetation. It increases via the infiltration of rainfall and decreases through evapotranspiration, run-off and leakage, all these effects being dependent on the existing soil moisture level. During wet periods, soil moisture tends largely to be driven by the topography, while evapotranspiration has more influence in dry periods. In this talk, I will describe models for soil moisture dynamics in which marked Poisson processes are used to model the temporal process of rainfall input to the soil moisture dynamics, first at a fixed location and then over a spatial region. In these models, precipitation input is instantaneous so that, in the spatial-temporal version, rain storms have a spatial extent but no temporal duration. In a generalisation, storms are allowed to have both spatial and temporal extents. Losses due to evapotranspiration depend on vegetation cover and the models allow for variable, and possibly random, vegetation processes. In the spatial-temporal models, random-radius circular tree canopies are assumed, located in a homogeneous Poisson process over the region. Under arid/semi-arid conditions, many transient and equilibrium properties of these models can be determined analytically and used for comparison with data on soil moisture dynamics. Valérie Isham - University College, London Bande son disponible au format mp3 Durée : 48 mn

07 - Space-time models for soil moisture dynamics - Valérie Isham

Valérie Isham - University College, London Bande son disponible au format mp3 Durée : 8 mn

08 - Questions - Valérie Isham

The fields of geographical epidemiology and public health surveillance have benefited from combined advances in hierarchical model building and in geographical information systems. Exploring and characterising a variety of spatial patterns of diseases at a fine geographical resolution has become possible (Banerjee, Carlin and Gelfand 2004). Insight into the sensitivity of the resulting inference to the choice of the structure of the different components of the hierarchical model has been gained through the use of simulation studies (Best, Richardson and Thomson, 2005) and numerous case studies. Baseline results on how to use the posterior distribution of relative risk estimates to detect areas of increased risks have been discussed (Richardson, Thomson, Best and Elliott, 2004) Extending hierarchical disease mapping models to models that simultaneously consider space and time and/or several diseases leads to a number of benefits in terms of interpretation and potential for detection of localised excesses. Such extension is accompanied by an increase of the complexity of the model structures that might be specified. The presentation will first outline classes of hierarchical space time models that can be used to characterise the patterns of chronic diseases. Space-time analysis of related diseases that that tease out common and specific space and time structures will be discussed next and illustrated on an example related to male and female lung cancer (Richardson, Abellan and Best, 2006). Finally, the use of space-time models to better characterise the stability of spatial patterns and to highlight atypical areas with unusual variability in their risk time pattern will be discussed and illustrated in a number of realistic scenarios. In particular, we will show how to model the space-time interactions and exploit their posterior distributions in order to classify the areas' risk pattern over time as 'predictable/ repeatable' or 'atypical/ highly variable'. References Banerjee S, Carlin B and Gelfand A (2004.) Hierarchical modelling and analysis of spatial data. Chapman and Hall, New York. Best N, Richardson S and Thompson A. (2005) A comparison of Bayesian spatial models for disease mapping. Statistical Methods in Medical Research. 14:35-59. Richardson S, Thomson A, Best N & Elliott P. Interpreting posterior relative risk estimates in disease mapping studies. Environmental Health Perspective , 2004, 112: 1016-25 S. Richardson, J-J. Abellan and N. Best. Bayesian spatio-temporal analysis of joint patterns of male and female lung cancer risks in Yorkshire (UK). Statistical Methods in Medical Research, 15: 385-407, (2006). Sylvia Richardson - Imperial College, London Bande son disponible au format mp3 Durée : 57 mn

09 - Analysis of spacetime patterns of disease risk - Sylvia Richardson

Sylvia Richardson - Imperial College, London Bande son disponible au format mp3 Durée : 13 mn

10 - Questions - Sylvia Richardson

Gaussian models are frequently used within spatial statistics and often as a latent Gaussian model is hierachical formulations. The devellopment of Markov chain Monte Carlo methods also allow for spatial analysis of non-Gaussian observations like spatial count and survial data. Although MCMC is doable it is not without practical hassle like long computing time and slow convergence.In this talk, I will present an alternative strategy, for which the aim is to approximate all posterior marginals for the hyperparameters and the latent field. The new approach is deterministic and make use of nested integrated nested Laplace approximations. The result is, that we can directly compute very accurate approximations to the posterior marginals. It is our experience that these are in practice exact, meaning that a well-designed MCMC algorithm has to run much longer than usual to detect any error. The main benefit is the dramatic cut in computational costs: where MCMC algorithms need hours and days to run, our approximations provide more precise estimates in seconds and minutes. This talk is based on joint work with Sara Martino (NTNU), Nicolas Chopin (ENSAE) and Jo Eidsvik (NTNU). Havard Rue - Norwegian University of Science and Technology Bande son disponible au format mp3 Durée : 44 mn

11 - Approximate Bayesian inference for latent Gaussian spatial models - Havard Rue

Havard Rue - Norwegian University of Science and Technology Bande son disponible au format mp3 Durée : 18 mn

12 - Questions - Havard Rue

Bande son disponible au format mp3 Durée : 19 mn

13 - Discussion

Ce workshop organisé sur une journée était consacré aux modèles spatio et spatio temporels. Six chercheurs étrangers de renommée internationale dans le domaine, ont été invités : N. Cressie, M. Genton, C. Glasbey, V. Isham, S. Richardson, H. Rue. Le thème plus précis du workshop était sur la modélisation hiérarchique à l'aide de processus latents. Les exposés ont abordé aussi bien les problèmes théoriques que les aspects méthodologiques, avec applications à des données réelles. Les supports de présentation sont disponibles sur l'Espace pédagogique interactif (http://epi.univ-paris1.fr/samos-workshop-spatial-statistic). Recommandé à : étudiant de la discipline, chercheur - Catégorie : conférences - Année de réalisation : 2007

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Workshop on spatial statistics (SAMOS, 2007)

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