Spatial Statistics: Methodological Aspects and Applications de Marc Moore

Spatial Statistics: Methodological Aspects and Applications: Lecture Notes in Statistics, cartea 159

Marc Moore

During the past twenty years spatial statistics has experienced important developments and has been applied in many fields of science. In view of these facts, spatial statistics was an important topic during the theme year on statistics at the CRM in 1997-98. This volume contains 13 papers based on presentations by eminent researchers at four workshops during that year: Statistical Inference for Spatial Processes; Image Analysis; Applications of Spatial Statistics in Earth, Environmental, and Health Sciences; and Statistics of Brain Mapping. These papers range from asymptotic considerations for spatial processes to practical considerations related to particular applications including important methodological aspects. Many contributions concern image analysis, mainly images related to brain mapping.

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Cuprins

1 Asymptotic Distribution of t he Empirical Cumulative Distribution Function Predictor under N onstationarity.- 1 Introduction.- 2 Th e Asymptotic Framework.- 3 Main Results.- 4 Proofs.- 5 References.- 2 Robustness Problems in the Analysis of Spatial Data.- 1 Introduction.- 2 Highly Robust Variogram Estimation.- 3 Variogram Model Selection.- 4 Variogram Fitting by Generalized Least Squares.- 5 Conclusion.- 6 References.- 3 Standards Adoption Dynamics and Test for Nonspatial Coordination.- 1 Introduction.- 2 Models with out Spatial Coordination.- 3 Models with Spatial Coordination.- 4 Tests for Nonspatial Coordination : the Case of a Regular Lattice with v Nearest Neighbours.- 5 References.- 4 Random Fields on Zd, Limit Theorems and Irregular Sets.- 1 Introduction.- 2 CLT for Weakly Dependent Stationary Random Fields over Irregular Sets.- 3 CLT for % MathType!MTEF!2!1!+-% feaagCart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiwamaaBa% aaleaacaWGUbaabeaakiabg2da9iabeA8aQnaabmaabaGaeqOVdG3a% aSbaaSqaaiaad6gaaeqaaOGaaiilaiaadMfadaWgaaWcbaGaamOBaa% qabaaakiaawIcacaGLPaaaaaa!41E9!$${X_n} = \varphi \left( {{\xi _n},{Y_n}} \right)$$.- 4 The Same Program for High-Level Exceedances.- 5 References.- 5 Multiscale Graphical Modeling in Space: Applications to Command and Control.- 1 Introduction.- 2 Tree-Struct ured Markov Models.- 3 Graphical Markov Models.- 4 Multiscale Graphical Models.- 5 Discussion.- 6 References.- 6 Unsupervised Image Segmentation Using a Telegraph Parameterization of Pickard Random Field.- 1 Introduction.- 2 Approach.- 3 EM ReestimationFormulas for Parameter Estimation 119.- 4 3D extension.- 5 Telegraph model.- 6 Mixture of Gaussians.- 7 Results.- 8 Conclusion.- 9 References.- 7 Estimation of Motion from Sequences of Images.- 1 Introduction.- 2 Data.- 3 The Continuity Equation.- 4 Projection from t he Sphere to th e Plane.- 5 Parametrization of the Displacement Field.- 6 Discretization of the Continuity Equation.- 7 Penalized Least Squares Estimation.- 8 Estimation of the Variance of the Observation Error.- 9 Asymptotics.- 10 Application to Ozone Images.- 11 Conclusion.- 12 References.- 8 Applications of Random Fields in Human Brain Mapping.- 1 Introduction.- 2 Test Statistics.- 3 Distribution of the Test Statistics Based on Random Field Theory.- 4 Results.- 5 Conclusion.- 6 References.- 9 In Praise of Tedious Permutation.- 1 R.A. Fisher (1890–1962) , the Anthropologist s and Darwin’s Peas.- 2 Permutation Tests in Human Brain Mapping.- 3 Permutation Tests of Spatial Statistics.- 4 Some Limitations of Permutation Testing.- 5 Conclusion.- 6 References.- 10 Group Analysis of Individual Activation Maps Using 3D Scale-Space Primal Sketches and a Markovian Random Field.- 1 Introduction.- 2 Method.- 3 Results.- 4 Conclusion.- 5 References.- 11 Some Statistical Aspects of Magnetoencephalography.- 1 Introduction.- 2 Outlines of MEG Source Analysis.- 3 Spatial Statistics of the Measurement Noise.- 4 Localized Averages.- 5 Selected Aspects of Nonlinear Parameter Estimation Problems.- 6 Concluding Remarks.- 7 References.- 12 Statistics of Nonlinear Spatial Distortions in Histological Images.- 1 Introduction.- 2 Theory.- 3 Concerning the Application of the Central Limit Theorem.- 4 Conclusion.- 5 References.- 13 Statistical Analysis of Brain Maps: Some Lessons from Morphometries.- 1 Introduction.- 2 The Coreof Modern Morphometries: An Overview.- 3 Partial Least Squares for Correlations of Shape.- 4 Symmetry.- 5 Varieties of “Localization” for Image Phenomena.- 6 Concluding Remarks.- 7 References.