Spatial Statistics: Methodological Aspects and Applications

Spatial statistics has applications in geology, health, brain mapping, and image analysis. This collection of papers presents papers on both the theory and applications of this active research area.

Inhalt
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 (18901962) , 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.