Statistical Methods for Trend Detection and Analysis in the Environmental Sciences

by Chandler, Richard; Scott, Marian

• ISBN13: 9780470015438
• ISBN10: 0470015438
• Edition: 1st
• Format: Hardcover
• Copyright: 2011-04-11
• Publisher: Wiley

Summary

Statistical methodology itself has made some significant developments in areas that are highly relevant to the problems faced by environmentalists; thus this book fills a gap in the market in which there is currently a lot of interest. Split into two parts, part 1 - Theory and methods - introduces the basis for and scope of the book, and covers amongst others the chief topics of exploratory analysis, non-parametric estimation and testing, and parametric modeling. Part 2 - Case Studies - introduces a number of co-authors, specialists in their own areas of environmental science, to illustrate the application of the theory and methods in practice. The accompanying website develops the practical aspects raised in the book, and provides a useful complementary tool.

Author Biography

Richard E Chandler, Lecturer in Statistical Science, Department of Statistical Science, University College London
Researcher in the area of stochastic processes and time series, with specific applications in hydrology and climate modeling. Work previously published by Wiley in the Encyclopaedia of Biostatistics.

E. Marian Scott, Professor of Environmental Statistics, Department of Statistics, University of Glasgow
Marian Scott is the editor of the Earth & Environmental Sciences section of Statistics in Practice for Wiley. She has 49 published articles. Her reputation within the community is evidenced by her associate editorship for 2 external journals (Radiocarbon and the Journal of Environmental Radioactivity); she is also honorary secretary for the Royal Statistical Society's Environmental Statistics Study Group.

Table of Contents

Preface	p. xi
Contributing authors	p. xiii
Methodology	p. 1
Introduction	p. 3
What is a trend?	p. 4
Why analyse trends?	p. 5
Some simple examples	p. 6
Dutch wind speeds	p. 6
North Sea haddock stocks	p. 8
Alkalinity in the Round Loch of Glenhead	p. 10
Atmospheric ozone in eastern England	p. 12
Considerations and difficulties	p. 14
Autocorrelation	p. 14
Effect of other variables	p. 15
Lack of designed experiments	p. 15
Consideration of auxiliary information	p. 16
The necessity of extrapolation	p. 17
Scope of the book	p. 19
Further reading	p. 20
References	p. 21
Exploratory analysis	p. 25
Data visualisation	p. 25
Time series plots	p. 26
Boxplots	p. 28
The autocorrelation function	p. 30
Irregularly spaced data - the variogram	p. 35
Relationships between variables	p. 38
Simple smoothing	p. 41
Moving averages	p. 41
Local polynomial fitting	p. 42
Further considerations	p. 43
Linear filters	p. 45
Frequency considerations	p. 46
The convolution theorem and filter design	p. 48
Dealing with end effects	p. 50
Other applications	p. 51
Classical test procedures	p. 54
Concluding comments	p. 57
References	p. 58
Parametric modelling - deterministic trends	p. 61
The linear trend	p. 63
Checking the model assumptions	p. 65
Choosing the time index	p. 69
An overview of least squares	p. 70
Extrapolation	p. 74
Influential observations	p. 76
Other methods of model fitting	p. 79
Multiple regression techniques	p. 82
Representing seasonality in regression models	p. 83
Interactions	p. 86
Model building and selection	p. 87
Violations of assumptions	p. 94
Dealing with heteroscedasticity	p. 94
Dealing with non-normality	p. 96
Dealing with autocorrelation	p. 97
Nonlinear trends	p. 105
Nonlinear least squares	p. 105
Cycles	p. 106
Changepoints and interventions	p. 108
Generalised linear models	p. 111
Parameter estimation	p. 113
Model comparison	p. 115
Model checking	p. 116
Prediction with GLMs	p. 117
Extensions and refinements	p. 118
Inference with small samples	p. 120
References	p. 122
Nonparametric trend estimation	p. 127
An introduction to nonparametric regression	p. 127
Linear smoothing	p. 128
Local linear regression	p. 129
Spline smoothing	p. 130
Choice of smoothing parameter	p. 131
Variance estimators	p. 135
Standard errors for the regression function	p. 135
Testing for consistency with parametric models	p. 136
Multiple covariates	p. 140
Additive, semiparametric and bivariate models	p. 140
The backfitting algorithm	p. 142
Inference for additive models	p. 144
Handling autocorrelation	p. 148
Other nonparametric estimation techniques	p. 151
Lowess smoothing	p. 151
Wavelets	p. 154
Varying coefficient models	p. 160
Discontinuity detection	p. 161
Quantile regression	p. 162
Parametric or nonparametric?	p. 166
References	p. 167
Stochastic trends	p. 171
Stationary time series models and their properties	p. 171
Autoregressive processes	p. 171
Moving average processes	p. 174
Mixed ARMA processes	p. 174
Model identification	p. 175
Parameter estimation	p. 177
Model checking	p. 182
Forecasting	p. 186
The backshift operator	p. 190
Trend removal via differencing	p. 193
ARIMA models	p. 194
Spurious regressions	p. 199
Long memory models	p. 201
Models for irregularly spaced series	p. 205
State space and structural models	p. 207
Simple structural time series models	p. 207
The state space representation	p. 209
The Kalman filter	p. 213
Parameter estimation	p. 217
Connection with nonparametric smoothing	p. 219
Nonlinear models	p. 228
References	p. 231
Other issues	p. 235
Multisite data	p. 235
Visualisation	p. 236
Modelling	p. 239
Multivariate series	p. 241
Dimension reduction	p. 241
Multivariate models	p. 244
Point process data	p. 245
Poisson processes	p. 246
Other point process models	p. 249
Marked point processes	p. 250
Trends in extremes	p. 250
Approaches based on block maxima	p. 251
Approaches based on threshold exceedances	p. 253
Modern developments	p. 256
Censored data	p. 257
References	p. 260
Case Studies	p. 265
Additive models for sulphur dioxide pollution in Europe	p. 267
Introduction	p. 267
Additive models with correlated errors	p. 269
An introduction to additive models	p. 269
Smoothing techniques	p. 270
Smoothing correlated data	p. 272
Fitting additive models	p. 273
Comparing nonparametric models	p. 276
Models for the SO2 data	p. 277
Conclusions	p. 281
Acknowledgement	p. 282
References	p. 282
Rainfall trends in southwest Western Australia	p. 283
Motivation	p. 283
The study region	p. 285
Data used in the study	p. 285
Modelling methodology	p. 289
Generalised linear models for daily rainfall	p. 289
Temporal and spatial dependence	p. 290
Covariates considered	p. 291
Modelling strategy	p. 292
Results	p. 293
Diagnostics	p. 294
Trends in wet-day precipitation amounts	p. 295
Trends in precipitation occurrence	p. 296
Combined trends in occurrence and amounts	p. 302
Summary and conclusions	p. 303
References	p. 304
Estimation of common trends for trophic index series	p. 307
Introduction	p. 307
Data exploration	p. 311
Common trends and additive modelling	p. 314
Adding autocorrelation to the additive model	p. 316
Combining the data from the eight stations	p. 319
Doing it all within a parametric model	p. 323
Dynamic factor analysis to estimate common trends	p. 324
The underlying model	p. 324
Discussion	p. 328
Acknowledgement	p. 329
References	p. 329
A space-time study on forest health	p. 333
Forest health: survey and data	p. 333
Regression models for longitudinal data with ordinal responses	p. 336
Spatiotemporal models	p. 340
Penalised splines	p. 341
Interaction surfaces	p. 343
Spatial trends	p. 344
Inference in spatiotemporal models	p. 346
Spatiotemporal modelling and analysis of forest health data	p. 348
Acknowledgements	p. 357
References	p. 357
Index	p. 359
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