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| Preface | |
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| Introduction | |
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| Why geostatistics? | |
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| Generalizing | |
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| Description | |
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| Interpretation | |
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| Control | |
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| A little history | |
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| Finding your way | |
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| Basic Statistics | |
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| Measurement and summary | |
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| Notation | |
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| Representing variation | |
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| The centre | |
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| Dispersion | |
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| The normal distribution | |
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| Covariance and correlation | |
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| Transformations | |
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| Logarithmic transformation | |
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| Square root transformation | |
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| Angular transformation | |
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| Logit transformation | |
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| Exploratory data analysis and display | |
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| Spatial aspects | |
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| Sampling and estimation | |
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| Target population and units | |
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| Simple random sampling | |
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| Confidence limits | |
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| Student's t | |
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| The x[superscript 2] distribution | |
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| Central limit theorem | |
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| Increasing precision and efficiency | |
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| Soil classification | |
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| Prediction and Interpolation | |
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| Spatial interpolation | |
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| Thiessen polygons (Voronoi polygons, Dirichlet tessellation) | |
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| Triangulation | |
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| Natural neighbour interpolation | |
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| Inverse functions of distance | |
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| Trend surfaces | |
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| Splines | |
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| Spatial classification and predicting from soil maps | |
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| Theory | |
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| Summary | |
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| Characterizing Spatial Processes: The Covariance and Variogram | |
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| Introduction | |
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| A stochastic approach to spatial variation: the theory of regionalized variables | |
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| Random variables | |
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| Random functions | |
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| Spatial covariance | |
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| Stationarity | |
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| Ergodicity | |
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| The covariance function | |
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| Intrinsic variation and the variogram | |
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| Equivalence with covariance | |
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| Quasi-stationarity | |
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| Characteristics of the spatial correlation functions | |
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| Which variogram? | |
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| Support and Krige's relation | |
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| Regularization | |
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| Estimating semivariances and covariances | |
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| The variogram cloud | |
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| h-Scattergrams | |
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| Average semivariances | |
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| The experimental covariance function | |
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| Modelling the Variogram | |
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| Limitations on variogram functions | |
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| Mathematical constraints | |
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| Behaviour near the origin | |
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| Behaviour towards infinity | |
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| Authorized models | |
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| Unbounded random variation | |
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| Bounded models | |
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| Combining models | |
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| Periodicity | |
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| Anisotropy | |
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| Fitting models | |
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| What weights? | |
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| How complex? | |
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| Reliability of the Experimental Variogram and Nested Sampling | |
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| Reliability of the experimental variogram | |
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| Statistical distribution | |
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| Sample size and design | |
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| Sample spacing | |
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| Theory of nested sampling and analysis | |
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| Link with regionalized variable theory | |
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| Case study: Youden and Mehlich's survey | |
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| Unequal sampling | |
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| Case study: Wyre Forest survey | |
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| Summary | |
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| Spectral Analysis | |
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| Linear sequences | |
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| Gilgai transect | |
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| Power spectra | |
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| Estimating the spectrum | |
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| Smoothing characteristics of windows | |
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| Confidence | |
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| Spectral analysis of the Caragabal transect | |
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| Bandwidths and confidence intervals for Caragabal | |
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| Further reading on spectral analysis | |
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| Local Estimation or Prediction: Kriging | |
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| General characteristics of kriging | |
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| Kinds of kriging | |
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| Theory of ordinary kriging | |
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| Weights | |
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| Examples | |
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| Kriging at the centre of the lattice | |
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| Kriging off-centre in the lattice and at a sampling point | |
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| Kriging from irregularly spaced data | |
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| Neighbourhood | |
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| Ordinary kriging for mapping | |
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| Case study | |
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| Kriging with known measurement error | |
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| Summary | |
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| Regional estimation | |
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| Simple kriging | |
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| Lognormal kriging | |
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| Optimal sampling for mapping | |
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| Isotropic variation | |
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| Anisotropic variation | |
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| Cross-validation | |
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| Scatter and regression | |
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| Kriging in the Presence of Trend and Factorial Kriging | |
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| Non-stationarity in the mean | |
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| Some background | |
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| Application of residual maximum likelihood | |
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| Estimation of the variogram by REML | |
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| Practicalities | |
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| Kriging with external drift | |
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| Case study | |
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| Factorial kriging analysis | |
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| Nested variation | |
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| Theory | |
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| Kriging analysis | |
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| Illustration | |
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| Cross-Correlation, Coregionalization and Cokriging | |
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| Introduction | |
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| Estimating and modelling the cross-correlation | |
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| Intrinsic coregionalization | |
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| Example: CEDAR Farm | |
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| Cokriging | |
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| Is cokriging worth the trouble? | |
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| Example of benefits of cokriging | |
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| Principal components of coregionalization matrices | |
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| Pseudo-cross-variogram | |
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| Disjunctive Kriging | |
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| Introduction | |
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| The indicator approach | |
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| Indicator coding | |
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| Indicator variograms | |
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| Indicator kriging | |
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| Disjunctive kriging | |
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| Assumptions of Gaussian disjunctive kriging | |
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| Hermite polynomials | |
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| Disjunctive kriging for a Hermite polynomial | |
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| Estimation variance | |
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| Conditional probability | |
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| Change of support | |
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| Case study | |
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| Other case studies | |
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| Summary | |
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| Stochastic Simulation | |
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| Introduction | |
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| Simulation from a random process | |
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| Unconditional simulation | |
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| Conditional simulation | |
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| Technicalities | |
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| Lower-upper decomposition | |
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| Sequential Gaussian simulation | |
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| Simulated annealing | |
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| Simulation by turning bands | |
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| Algorithms | |
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| Uses of simulated fields | |
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| Illustration | |
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| Aide-memoire for Spatial Analysis | |
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| Introduction | |
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| Notation | |
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| Screening | |
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| Histogram and summary | |
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| Normality and transformation | |
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| Spatial distribution | |
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| Spatial analysis: the variogram | |
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| Modelling the variogram | |
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| Spatial estimation or prediction: kriging | |
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| Mapping | |
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| GenStat Instructions for Analysis | |
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| Summary statistics | |
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| Histogram | |
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| Cumulative distribution | |
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| Posting | |
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| The variogram | |
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| Experimental variogram | |
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| Fitting a model | |
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| Kriging | |
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| Coregionalization | |
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| Auto- and cross-variograms | |
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| Fitting a model of coregionalization | |
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| Cokriging | |
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| Control | |
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| References | |
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| Index | |