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Models for Ecological Data : An Introduction - James S. Clark

Models for Ecological Data

An Introduction

Hardcover Published: 15th April 2007
ISBN: 9780691121789
Number Of Pages: 632

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The environmental sciences are undergoing a revolution in the use of models and data. Facing ecological data sets of unprecedented size and complexity, environmental scientists are struggling to understand and exploit powerful new statistical tools for making sense of ecological processes.

In "Models for Ecological Data," James Clark introduces ecologists to these modern methods in modeling and computation. Assuming only basic courses in calculus and statistics, the text introduces readers to basic maximum likelihood and then works up to more advanced topics in Bayesian modeling and computation. Clark covers both classical statistical approaches and powerful new computational tools and describes how complexity can motivate a shift from classical to Bayesian methods. Through an available lab manual, the book introduces readers to the practical work of data modeling and computation in the language R. Based on a successful course at Duke University and National Science Foundation-funded institutes on hierarchical modeling, "Models for Ecological Data" will enable ecologists and other environmental scientists to develop useful models that make sense of ecological data.Consistent treatment from classical to modern Bayes Underlying distribution theory to algorithm development Many examples and applications Does not assume statistical background Extensive supporting appendixes Accompanying lab manual in R

"In summary, Models for Ecological Data is an important text for those interested in ecological problems, which require computationally intensive methods. The level of the text is such that the reader should have a strong quantitative background (masters degree or higher in a quantitative discipline). The accompanying lab manual is a must for those who have this text and want to put the material to practice. The text and accompanying lab manual would serve as a good textbook for a graduate course in quantitative ecology provided that the students have the necessary mathematical background."--Timothy J. Robinson, Journal of the American Statistical Association

Prefacep. ix
Introductionp. 1
Models in Contextp. 3
Complexity and Obscurity in Nature and in Modelsp. 3
Making the Connections: Data, Inference, and Decisionp. 5
Two Elements of Models: Known and Unknownp. 13
Learning with Models: Hypotheses and Quantificationp. 19
Estimation versus Forward Simulationp. 23
Statistical Pragmatismp. 24
Model Elements: Application to Population Growthp. 27
A Model and Data Examplep. 27
Model State and Timep. 30
Stochasticity for the Unknownp. 42
Additional Background on Process Modelsp. 44
Elements of Inferencep. 45
Point Estimation: Maximum Likelihood and the Method of Moments
Introductionp. 47
Likelihoodp. 47
A Binomial Modelp. 53
Combining the Binomial and Exponentialp. 54
Maximum Likelihood Estimates for the Normal Distributionp. 56
Population Growthp. 57
Application: Fecundityp. 60
Survival Analysis Using Maximum Likelihoodp. 62
Design Matrixesp. 68
Numerical Methods for MLEp. 71
Moment Matchingp. 71
Common Sampling Distributions and Dispersionp. 74
Assumptions and Next Stepsp. 76
Elements of the Bayesian Approachp. 77
The Bayesian Approachp. 78
The Normal Distributionp. 84
Subjective Probability and the Role of the Priorp. 91
Confidence Envelopes and Prediction Intervalsp. 93
Classical Interval Estimationp. 95
Bayesian Credible Intervalsp. 115
Likelihood Profile for Multiple Parametersp. 120
Confidence Intervals for Several Parameters: Linear Regressionp. 122
Which Confidence Envelope to Usep. 130
Predictive Intervalsp. 133
Uncertainty and Variabilityp. 141
When Is It Bayesian?p. 142
Model Assessment and Selectionp. 143
Using Statistics to Evaluate Modelsp. 143
The Role of Hypothesis Testsp. 144
Nested Modelsp. 144
Additional Considerations for Classical Model Selectionp. 151
Bayesian Model Assessmentp. 154
Additional Thoughts on Bayesian Model Assessmentp. 159
Larger Modelsp. 161
Computational Bayes: Introduction to Tools Simulationp. 163
Simulation to Obtain the Posteriorp. 163
Some Basic Simulation Techniquesp. 164
Markov Chain Monte Carlo Simulationp. 173
Application: Bayesian Analysis for Regressionp. 189
Using MCMCp. 202
Computation for Bayesian Model Selectionp. 205
Priors on the Responsep. 209
The Basics Are Now Behind Usp. 212
A Closer Look at Hierarchical Structuresp. 213
Hierarchical Models for Contextp. 213
Mixed and Generalized Linear Modelsp. 216
Application: Growth Responses to CO2p. 230
Thinking Conditionallyp. 235
Two Applications to Treesp. 241
Noninformative Priors in Hierarchical Settingsp. 249
From Simple Models to Graphsp. 249
More Advance Methodsp. 251
Time
Why Is Time Important?p. 253
Time Series Terminologyp. 254
Descriptive Elements of Time Series Modelsp. 255
The Frequency Domainp. 264
Application: Detecting Density Dependence in Population Time Seriesp. 264
Bayesian State Space Modelsp. 272
Application: Black Noddy on Heron Islandp. 282
Nonlinear State Space Modelsp. 289
Lagsp. 297
Regime Changep. 298
Constraints on Time Series Datap. 300
Additional Sources of Variablityp. 301
Alternatives to the Gibbs Samplerp. 302
More on Longitudinal Data Structuresp. 302
Intervention and Treatment Effectsp. 309
Capture-Recapture Studiesp. 318
Structured Models as Matrixesp. 329
Structure as Systems of Difference Equationsp. 336
Time Series, Population Regulation, and Stochasticityp. 347
Space-Timep. 353
A Deterministic Model for a Stochastic Spa
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780691121789
ISBN-10: 0691121788
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 632
Published: 15th April 2007
Publisher: Princeton University Press
Country of Publication: US
Dimensions (cm): 25.4 x 20.3  x 4.09
Weight (kg): 1.63