TUM Library

"This handbook focuses on the enormous literature applying statistical methodology and modelling to environmental and ecological processes. The statistics community has become increasingly interdisciplinary, bringing a large collection of modern tools to all areas of application in the environmental processes. In addition, the environmental community has substantially increased its scope of data collection including, e.g., observational data, satellite-derived data, and computer model output. The resultant impact in this latter community has been substantial. The contribution of this handbook is to assemble, in roughly 35 chapters, a state-ofthe-art view of this interface"--Provided by publisher.

Cover; Half Title; Title Page; Copyright Page; Table of Contents; Preface; 1: Introduction; I: Methodology for Statistical Analysis of Environmental Processes; 2: Modeling for environmental and ecological processes; 2.1 Introduction; 2.2 Stochastic modeling; 2.3 Basics of Bayesian inference; 2.3.1 Priors; 2.3.2 Posterior inference; 2.3.3 Bayesian computation; 2.4 Hierarchical modeling; 2.4.1 Introducing uncertainty; 2.4.2 Random effects and missing data; 2.5 Latent variables; 2.6 Mixture models; 2.7 Random effects; 2.8 Dynamic models; 2.9 Model adequacy; 2.10 Model comparison

2.10.1 Bayesian model comparison2.10.2 Model comparison in predictive space; 2.11 Summary; 3: Time series methodology; 3.1 Introduction; 3.2 Time series processes; 3.3 Stationary processes; 3.3.1 Filtering preserves stationarity; 3.3.2 Classes of stationary processes; 3.3.2.1 IID noise and white noise; 3.3.2.2 Linear processes; 3.3.2.3 Autoregressive moving average processes; 3.4 Statistical inference for stationary series; 3.4.1 Estimating the process mean; 3.4.2 Estimating the ACVF and ACF; 3.4.3 Prediction and forecasting; 3.4.4 Using measures of correlation for ARMA model identification

3.4.5 Parameter estimation3.4.6 Model assessment and comparison; 3.4.7 Statistical inference for the Canadian lynx series; 3.5 Nonstationary time series; 3.5.1 A classical decomposition for nonstationary processes; 3.5.2 Stochastic representations of nonstationarity; 3.6 Long memory processes; 3.7 Changepoint methods; 3.8 Discussion and conclusions; 4: Dynamic models; 4.1 Introduction; 4.2 Univariate Normal Dynamic Linear Models (NDLM); 4.2.1 Forward learning: the Kalman filter; 4.2.2 Backward learning: the Kalman smoother; 4.2.3 Integrated likelihood; 4.2.4 Some properties of NDLMs

4.2.5 Dynamic generalized linear models (DGLM)4.3 Multivariate Dynamic Linear Models; 4.3.1 Multivariate NDLMs; 4.3.2 Multivariate common-component NDLMs; 4.3.3 Matrix-variate NDLMs; 4.3.4 Hierarchical dynamic linear models (HDLM); 4.3.5 Spatio-temporal models; 4.4 Further aspects of spatio-temporal modeling; 4.4.1 Process convolution based approaches; 4.4.2 Models based on stochastic partial differential equations; 4.4.3 Models based on integro-difference equations; 5: Geostatistical Modeling for Environmental Processes; 5.1 Introduction; 5.2 Elements of point-referenced modeling

5.2.1 Spatial processes, covariance functions, stationarity and isotropy5.2.2 Anisotropy and nonstationarity; 5.2.3 Variograms; 5.3 Spatial interpolation and kriging; 5.4 Summary; 6: Spatial and spatio-temporal point processes in ecological applications; 6.1 Introduction -- relevance of spatial point processes to ecology; 6.2 Point processes as mathematical objects; 6.3 Basic definitions; 6.4 Exploratory analysis -- summary characteristics; 6.4.1 The Poisson process-a null model; 6.4.2 Descriptive methods; 6.4.3 Usage in ecology; 6.5 Point process models

6.5.1 Modelling environmental heterogeneity -- inhomogeneous Poisson processes and Cox processes

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