Workshop on spatial statistics (SAMOS, 2007‪)‬ Université Paris 1 Panthéon-Sorbonne

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

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

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

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

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

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