List of tables and displays |
Preface |
Acknowledgements |
Introduction to issues in the analysis of spatially referenced data / Part A: |
Introduction / 1: |
Notes |
Issues in analysing spatial data / 2: |
Spatial data: sources, forms and storage / 2.1: |
Sources: quality and quantity / 2.1.1: |
Forms and attributes / 2.1.2: |
Data storage / 2.1.3: |
Spatial data analysis / 2.2: |
The importance of space in the social and environmental sciences / 2.2.1: |
Measurement error / 2.2.1 (a): |
Continuity effects and spatial heterogeneity / 2.2.1 (b): |
Spatial processes / 2.2.1 (c): |
Types of analytical problems / 2.2.2: |
Problems in spatial data analysis / 2.3: |
Conceptual models and inference frameworks for spatial data / 2.3.1: |
Modelling spatial variation / 2.3.2: |
Statistical modelling of spatial data / 2.3.3: |
Dependency in spatial data / 2.3.3 (a): |
Spatial heterogeneity: regional subdivisions and parameter variation / 2.3.3 (b): |
Spatial distribution of data points and boundary effects / 2.3.3 (c): |
Assessing model fit / 2.3.3 (d): |
Distributions / 2.3.3 (e): |
Extreme data values / 2.3.3 (f): |
Model sensitivity to the areal system / 2.3.3 (g): |
Size-variance relationships in homogeneous aggregates / 2.3.3 (h): |
A statistical framework for spatial data analysis / 2.4: |
Data adaptive modelling / 2.4.1: |
Robust and resistant parameter estimation / 2.4.2: |
Robust estimation of the centre of a symmetric distribution / 2.4.2 (a): |
Robust estimation of regression parameters / 2.4.2 (b): |
Parametric models for spatial variation / Part B: |
Statistical models for spatial populations / 3: |
Models for spatial populations: preliminary considerations / 3.1: |
Spatial stationarity and isotropy / 3.1.1: |
Second order (weak) stationarity and isotropy / 3.1.1 (a): |
Second order (weak) stationarity and isotropy of differences from the mean / 3.1.1 (b): |
Second order (weak) stationarity and isotropy of increments / 3.1.1 (c): |
Order relationships in one and two dimensions / 3.1.2: |
Population models for continuous random variables / 3.2: |
Models for the mean of a spatial population / 3.2.1: |
Trend surface models / 3.2.1 (a): |
Regression model / 3.2.1 (b): |
Models for second order or stochastic variation of a spatial population / 3.2.2: |
Interaction models for V of a MVN distribution / 3.2.2 (a): |
Interaction models for other multivariate distributions / 3.2.2 (b): |
Direct specification of V / 3.2.2 (c): |
Intrinsic random functions / 3.2.2 (d): |
Population models for discrete random variables / 3.3: |
Boundary models for spatial populations / 3.4: |
Edge structures, weighting schemes and the dispersion matrix / 3.5: |
Conclusions: issues in representing spatial variation / 3.6: |
Simulating spatial models / Appendix: |
Statistical analysis of spatial populations / 4: |
Model selection / 4.1: |
Statistical inference with interaction schemes / 4.2: |
Parameter estimation: maximum likelihood (ML) methods / 4.2.1: |
[mu] unknown; V known / 4.2.1 (a): |
[mu] known; V unknown / 4.2.1 (b): |
[mu] and V unknown / 4.2.1 (c): |
Models with non-constant variance / 4.2.1 (d): |
Parameter estimation: other methods / 4.2.2: |
Ordinary least squares and pseudo-likelihood estimators / 4.2.2 (a): |
Coding estimators / 4.2.2 (b): |
Moment estimators / 4.2.2 (c): |
Parameter estimation: discrete valued interaction models / 4.2.3: |
Properties of ML estimators / 4.2.4: |
Large sample properties / 4.2.4 (a): |
Small sample properties / 4.2.4 (b): |
A note on boundary effects / 4.2.4 (c): |
Hypothesis testing for interaction schemes / 4.2.5: |
Likelihood ratio tests / 4.2.5 (a): |
Lagrange multiplier tests / 4.2.5 (b): |
Statistical inference with covariance functions and intrinsic random functions / 4.3: |
Parameter estimation: maximum likelihood methods / 4.3.1: |
Properties of estimators and hypothesis testing / 4.3.2: |
Validation in spatial models / 4.4: |
The consequences of ignoring spatial correlation in estimating the mean / 4.5: |
Spatial data collection and preliminary analysis / Part C: |
Sampling spatial populations / 5: |
Spatial sampling designs / 5.1: |
Point sampling / 5.2.1: |
Quadrat and area sampling / 5.2.2: |
Sampling spatial surfaces: estimating the mean / 5.3: |
Fixed populations with trend or periodicity / 5.3.1: |
Populations with second order variation / 5.3.2: |
Results for one-dimensional series / 5.3.2 (a): |
Results for two-dimensional surfaces / 5.3.2 (b): |
Standard errors for confidence intervals and selecting sample size / 5.3.3: |
Sampling spatial surfaces: second order variation / 5.4: |
Kriging / 5.4.1: |
Scales of variation / 5.4.2: |
Sampling applications / 5.5: |
Concluding comments / 5.6: |
Preliminary analysis of spatial data / 6: |
Preliminary data analysis: distributional properties and spatial arrangement / 6.1: |
Univariate data analysis / 6.1.1: |
General distributional properties / 6.1.1 (a): |
Spatial outliers / 6.1.1 (b): |
Spatial trends / 6.1.1 (c): |
Second order non-stationarity / 6.1.1 (d): |
Regional subdivisions / 6.1.1 (e): |
Multivariate data analysis / 6.1.2: |
Data transformations / 6.1.3: |
Preliminary data analysis: detecting spatial pattern, testing for spatial autocorrelation / 6.2: |
Available test statistics / 6.2.1: |
Constructing a test / 6.2.2: |
Interpretation / 6.2.3: |
Choosing a test / 6.2.4: |
Describing spatial variation: robust estimation of spatial variation / 6.3: |
Robust estimators of the semi-variogram / 6.3.1: |
Robust estimation of covariances / 6.3.2: |
Concluding remarks / 6.4: |
Modelling spatial data / Part D: |
Analysing univariate data sets / 7: |
Describing spatial variation / 7.1: |
Non-stationary mean, stationary second order variation: trend surface models with correlated errors / 7.1.1: |
Non-stationary mean, stationary increments: semi-variogram models and polynomial generalised covariance functions / 7.1.2: |
Discrete data / 7.1.3: |
Interpolation and estimating missing values / 7.2: |
Ad hoc and cartographic techniques / 7.2.1: |
Distribution based techniques / 7.2.2: |
Sequential approaches (sampling a continuous surface) / 7.2.2 (a): |
Simultaneous approaches / 7.2.2 (b): |
Extensions / 7.2.3: |
Obtaining areal properties / 7.2.3 (a): |
Reconciling data sets on different areal frameworks / 7.2.3 (b): |
Categorical data / 7.2.3 (c): |
Other information for interpolation / 7.2.3 (d): |
Analysing multivariate data sets / 8: |
Measures of spatial correlation and spatial association / 8.1: |
Correlation measures / 8.1.1: |
Measures of association / 8.1.2: |
Regression modelling / 8.2: |
Problems due to the assumptions of least squares not being satisfied / 8.2.1: |
Problems of model specification and analysis / 8.2.2: |
Model discrimination / 8.2.2 (a): |
Specifying W / 8.2.2 (b): |
Parameter estimation and inference / 8.2.2 (c): |
Model evaluation / 8.2.2 (d): |
Interpretation problems / 8.2.3: |
Problems due to data characteristics / 8.2.4: |
Numerical problems / 8.2.5: |
Regression applications / 8.3: |
Model diagnostics and model revision (a) new explanatory variables / Example 8.1: |
Model diagnostics and model revision (b) developing a spatial regression model / Example 8.2: |
Regression modelling with census variables: Glasgow health data / Example 8.3: |
Identifying spatial interaction and heterogeneity: Sheffield petrol price data / Example 8.4: |
Robust estimation of the parameters of interaction schemes |
Postscript |
Glossary |
References |
Index |
List of tables and displays |
Preface |
Acknowledgements |