nonstationarity, covariance estimation and state-space ... - EPFL

More documents

Recommendations

Info

Contents Acknowledgernents Abstract Version abrégée Kurzfassung Riassunto Contents List of Figures List of Tables Prologue Overview of Geostatistical Data Analysis and Modeling 1 ......................................... 1.1 Historical Overview 1 ............................................ 1.1.1 Genesis 1 .......................................... 1.1.2 Quo Vadis 2 ..................................... 1.2 Univariate Spatial Processes 3 ................................. 1.2.1 Stationarity and Ergodicity 4 1.2.2 Anisotropy .......................................... 5 .................................. 1.2.3 Additive Decompositions 5 ............................. 1.2.4 Characterization Using Variograms 6 ............................ 1.2.5 Characterization Using Covariograms 8 1.3 Estimation of the Second Moment Structure ............................ 9 .................................. 1.3.1 Estimation of Variograms 9 .................................. 1.3.2 Variogram Model Fitting 11 .......................................... 1.4 Spatial Prediction 12 ............................................ 1.4.1 Kriging 12 vii ix xi ... Xlll xv xix xxi xxiii
xvi Contents 1.4.2 Other Interpolation Approaches . .............................. 13 1.4.3 Stability of Kriging ..................................... 14 1.5 h9ultivariate Spatial Processes ................................... 15 1.6 Spatio-Temporal Processes ..................................... 16 2 Nonstationarity Issues in Geostatistical Modeling 19 2.1 T'rend Detection and Global Fitting . ................................ 19 2.1.1 Exploratory Examination of the Process .......................... 20 2.1.2 Fitting Parametric Models ................................. 24 2.1.3 Fitting Nonparametric Models ............................... 26 2.2 Local Trend Estimation ....................................... 27 2.2.1 Simulations ......................................... 29 2.2.2 Application ......................................... 29 2.2.3 Local Variogram estimation . ................................ 34 2.3 Covariograms of Nonstationary Spatio-Temporal Processes .................... 35 2.3.1 Spectral Representation ................................... 35 2.3.2 Simulations ......................................... 38 2.3.3 Application ......................................... 40 3 Covariance Estimation of Geostatistical Data 45 3.1 Motivation .............................................. 45 3.2 The Estimator Û .......................................... 46 3.3 Asymptotic Considerations ..................................... 49 3.3.1 Limiting Bias ........................................ 50 3.3.2 Asymptotic Bias ....................................... 53 3.3.3 Random and lrregular Locations .............................. 57 3.4 Eigenvalues and Eigenvectors of U ................................. 59 3.4.1 AsymptoticDistribution ................................... 59 3.4.2 Confidence Cones ...................................... 63 3.5 Simulations ............................................. 66 3.6 Application . ............................................. 71 4 State-Space Decomposition of Geostatistical Processes 4.1 Motivation . ............................................. 4.2 State-Space Decompositions .................................... 4.2.1 State Equation with a Degenerate Kernel ......................... 4.2.2 Other Types of State Equations .............................. 4.3 Parameter Estimation ........................................ 4.3.1 Moment Equations ..................................... 4.3.2 Consistency ......................................... 4.3.3 lnference ........................................... 4.3.4 OLS, WLS, GLS and Robust Estimation .......................... ......................................... 4.4 lllustrative Examples 4.4.1 Three Parameter Model . .................................. 4.4.2 Gaussian Process with N = 1 . ...............................
Page 1 and 2: ASPECTS OF MODERN GEOSTATISTICS: NO
Page 3 and 4: viii -- Abstract correlated. variab
Page 5 and 6: X -- Version abrégée pour la cons
Page 7 and 8: xii Kurzfassunn von korrelierten Va
Page 9: xiv Riassunto Diversi strumenti sta

nonstationarity, covariance estimation and state-space ... - EPFL

Create successful ePaper yourself

Delete template?

Save as template?