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# Introduction to probability and statistics for ecosystem managers : simulation and resampling / Timothy C. Haas, Sheldon B. Lubar School of Business, University of Wisconsin-Milwaukee, USA.

Material type: BookSeries: Statistics in practice: Publisher: Chichester, West Sussex, United Kingdom : Wiley, 2013Description: 1 online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9781118636237; 1118636236; 9781118636220; 1118636228; 9781118636244; 1118636244; 1118636201; 9781118636206.Genre/Form: Electronic books. | Electronic books.Additional physical formats: Print version:: Introduction to probability and statistics for ecosystem managers.DDC classification: 333.72 Online resources: Wiley Online Library
Contents:
1. Introduction -- 1.1. The textbook's purpose -- 1.1.1. The textbook's focus on ecosystem management -- 1.1.2. Reader level, prerequisites, and typical reader jobs -- 1.2. The textbook's pedagogical approach -- 1.2.1. General points -- 1.2.2. Use of this textbook for self-study -- 1.2.3. Learning resources -- 1.3. Chapter summaries -- 1.4. Installing and running R Commander -- 1.4.1. Running R -- 1.4.2. Starting an R Commander session -- 1.4.3. Terminating an R Commander session -- 1.5. Introductory R Commander session -- 1.6. Teaching probability through simulation -- 1.6.1. The frequentist statistical inference paradigm -- 1.7. Summary -- 2. Probability and simulation -- 2.1. Introduction -- 2.2. Basic probability -- 2.2.1. Definitions -- 2.2.2. Independence -- 2.3. Random variables -- 2.3.1. Definitions -- 2.3.2. Simulating random variables -- 2.3.3.A random variable's expected value (mean) and variance -- 2.3.4. Details of the normal (Gaussian) distribution.
2.3.5. Distribution approximations -- 2.4. Joint distributions -- 2.4.1. Definition -- 2.4.2. Mixed variables -- 2.4.3. Marginal distribution -- 2.4.4. Conditional distributions -- 2.4.5. Independent random variables -- 2.5. Influence diagrams -- 2.5.1. Definitions -- 2.5.2. Example of a Bayesian network in ecosystem management -- 2.5.3. Modeling causal relationships with an influence diagram -- 2.6. Advantages of influence diagrams in ecosystem management -- 2.7. Two ecosystem management Bayesian networks -- 2.7.1. Waterbody eutrophication -- 2.7.2. Wildlife population viability -- 2.8. Influence diagram sensitivity analysis -- 2.9. Drawbacks to influence diagrams -- 3. Application of probability: Models of political decision making in ecosystem management -- 3.1. Introduction -- 3.2. Influence diagram models of decision making -- 3.2.1. Ecosystem status perception nodes -- 3.2.2. Image nodes -- 3.2.3. Economic, militaristic, and institutional goal nodes.
3.2.4. Audience effect nodes -- 3.2.5. Resource nodes -- 3.2.6. Action and target nodes -- 3.2.7. Overall goal attainment node -- 3.2.8. How a group influence diagram reaches a decision -- 3.2.9. An advantage of this decision-making architecture -- 3.2.10. Evaluation dimensions -- 3.3. Rhino poachers: A simplified model -- 3.4. Policymakers: A simplified model -- 3.5. Conclusions -- 4. Statistical inference I: Basic ideas and parameter estimation -- 4.1. Definitions of some fundamental terms -- 4.2. Estimating the PDF and CDF -- 4.2.1. Histograms -- 4.2.2. Ogive -- 4.3. Measures of central tendency and dispersion -- 4.4. Sample quantiles -- 4.4.1. Sample quartiles -- 4.4.2. Sample deciles and percentiles -- 4.5. Distribution of a statistic -- 4.5.1. Basic setup in statistics -- 4.5.2. Sampling distributions -- 4.5.3. Normal quantile-quantile plot -- 4.6. The central limit theorem -- 4.7. Parameter estimation -- 4.7.1. Bias, variance, and efficiency -- 4.8. Interval estimates.
5.4.4. Testing for equal variances -- 5.5. Hypothesis tests on the regression model -- 5.5.1. Prediction and estimation confidence intervals -- 5.5.2. Multiple regression -- 5.5.3. Original scale prediction in regression -- 5.6. Brief introduction to vectors and matrices -- 5.6.1. Basic definitions -- 5.6.2. Inverse of a matrix -- 5.6.3. Random vectors and random matrices -- 5.7. Matrix form of multiple regression -- 5.7.1. Generalized least squares -- 5.8. Hypothesis testing with the delete-d jackknife -- 5.8.1. Background -- 5.8.2.A one-sample delete-d jackknife test -- 5.8.3. Testing classifier error rates -- 5.8.4. Important points about this test -- 5.8.5. Parameter confidence intervals -- 6. Introduction to spatial statistics -- 6.1. Overview -- 6.1.1. Types of spatial processes -- 6.2. Spatial statistics and GIS -- 6.2.1. Types of spatial data -- 6.3. QGIS -- 6.3.1. Capabilities -- 6.3.2. Installing QGIS -- 6.3.3. Documentation and tutorials -- 6.3.4. Installing plugins.
6.3.5. How to convert a text file to a shapefile -- 6.4. Continuous spatial processes -- 6.4.1. Definitions -- 6.4.2. Graphical tools for exploring continuous spatial data -- 6.4.3. Third- and fourth-order cumulant minimization -- 6.4.4. Best linear unbiased predictor -- 6.4.5. Kriging variance -- 6.4.6. Model-fitting diagnostics -- 6.4.7. Kriging within a window -- 6.5. Spatial point processes -- 6.5.1. Definitions -- 6.5.2. Marked spatial point processes -- 6.5.3. Conclusions -- 6.6. Continuously valued multivariate processes -- 6.6.1. Fitting multivariate covariance functions -- 6.6.2. Cokriging: The MWRCK procedure -- 7. Introduction to spatio-temporal statistics -- 7.1. Introduction -- 7.2. Representing time in a GIS -- 7.2.1. The QGIS Time Manager plugin -- 7.2.2.A Clifford algebra-based spatio-temporal data structure -- 7.2.3.A raster- and event-based spatio-temporal data model -- 7.2.4. Application of ESTDM to a land cover study.
7.3. Spatio-temporal prediction: MCSTK -- 7.3.1. Algorithms -- 7.3.2. Covariogram model and its estimator -- 7.4. Multivariate processes -- 7.4.1. Definitions -- 7.4.2. Transformations -- 7.4.3. Covariograms and cross-covariograms -- 7.4.4. Parameter estimation -- 7.4.5. Prediction algorithms -- 7.4.6. Cross-validation -- 7.4.7. Summary -- 7.5. Spatio-temporal point processes -- 7.6. Marked spatio-temporal point processes -- 7.6.1.A mark semivariogram estimator -- 8. Application of statistical inference: Estimating the parameters of an individual-based model -- 8.1. Overview -- 8.2.A simple IBM and its estimation -- 8.2.1. Simple IBM -- 8.2.2. Parameter estimation -- 8.3. Fitting IBMs with MSHD -- 8.3.1. Ergodicity -- 8.3.2. Observable random variables from IBM output -- 8.4. Further properties of parameter estimators -- 8.4.1. Consistency -- 8.4.2. Robustness -- 8.5. Parameter confidence intervals for a nonergodic model -- 8.6. Rhino-supporting ecosystem influence diagram.
8.6.1. Spatial effects on poaching -- 8.6.2. IBM variables -- 8.6.3. Initial conditions and hypothesis values of parameters -- 8.6.4. Mapping functions -- 8.6.5. Realism of ecosystem influence diagram output -- 8.7. Estimation of rhino IBM parameters -- 8.7.1. Parameter confidence intervals -- 9. Guiding an influence diagram's learning -- 9.1. Introduction -- 9.2. Online learning of Bayesian network parameters -- 9.2.1. Basic algorithm using simulation -- 9.2.2. Updating influence diagrams -- 9.3. Learning an influence diagram's structure -- 9.3.1. Minimum description length score function -- 9.3.2. Description length of an edge -- 9.3.3. Random generation of DAGs -- 9.3.4. Algorithm to detect and delete cycles -- 9.3.5. Mutate functions -- 9.3.6. MDLEP algorithm -- 9.3.7. Using MDLEP to learn influence diagram structure -- 9.4. Feedback-based learning for group decision-making diagrams -- 9.4.1. Definitions and algorithm -- 9.5. Summary and conclusions.
10. Fitting and testing a political-ecological simulator -- 10.1. Introduction -- 10.1.1. Background on rhino poaching -- 10.1.2. Scenarios wherein rhino poaching is reduced -- 10.2. EMT simulator construction -- 10.2.1. Modeled groups -- 10.2.2. Rhino-supporting ecosystem influence diagram -- 10.3. Consistency analysis estimates of simulator parameters -- 10.4. MPEMP computation -- 10.4.1. Setup -- 10.4.2. Solution -- 10.5. Conclusions.
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1. Introduction -- 1.1. The textbook's purpose -- 1.1.1. The textbook's focus on ecosystem management -- 1.1.2. Reader level, prerequisites, and typical reader jobs -- 1.2. The textbook's pedagogical approach -- 1.2.1. General points -- 1.2.2. Use of this textbook for self-study -- 1.2.3. Learning resources -- 1.3. Chapter summaries -- 1.4. Installing and running R Commander -- 1.4.1. Running R -- 1.4.2. Starting an R Commander session -- 1.4.3. Terminating an R Commander session -- 1.5. Introductory R Commander session -- 1.6. Teaching probability through simulation -- 1.6.1. The frequentist statistical inference paradigm -- 1.7. Summary -- 2. Probability and simulation -- 2.1. Introduction -- 2.2. Basic probability -- 2.2.1. Definitions -- 2.2.2. Independence -- 2.3. Random variables -- 2.3.1. Definitions -- 2.3.2. Simulating random variables -- 2.3.3.A random variable's expected value (mean) and variance -- 2.3.4. Details of the normal (Gaussian) distribution.

2.3.5. Distribution approximations -- 2.4. Joint distributions -- 2.4.1. Definition -- 2.4.2. Mixed variables -- 2.4.3. Marginal distribution -- 2.4.4. Conditional distributions -- 2.4.5. Independent random variables -- 2.5. Influence diagrams -- 2.5.1. Definitions -- 2.5.2. Example of a Bayesian network in ecosystem management -- 2.5.3. Modeling causal relationships with an influence diagram -- 2.6. Advantages of influence diagrams in ecosystem management -- 2.7. Two ecosystem management Bayesian networks -- 2.7.1. Waterbody eutrophication -- 2.7.2. Wildlife population viability -- 2.8. Influence diagram sensitivity analysis -- 2.9. Drawbacks to influence diagrams -- 3. Application of probability: Models of political decision making in ecosystem management -- 3.1. Introduction -- 3.2. Influence diagram models of decision making -- 3.2.1. Ecosystem status perception nodes -- 3.2.2. Image nodes -- 3.2.3. Economic, militaristic, and institutional goal nodes.

3.2.4. Audience effect nodes -- 3.2.5. Resource nodes -- 3.2.6. Action and target nodes -- 3.2.7. Overall goal attainment node -- 3.2.8. How a group influence diagram reaches a decision -- 3.2.9. An advantage of this decision-making architecture -- 3.2.10. Evaluation dimensions -- 3.3. Rhino poachers: A simplified model -- 3.4. Policymakers: A simplified model -- 3.5. Conclusions -- 4. Statistical inference I: Basic ideas and parameter estimation -- 4.1. Definitions of some fundamental terms -- 4.2. Estimating the PDF and CDF -- 4.2.1. Histograms -- 4.2.2. Ogive -- 4.3. Measures of central tendency and dispersion -- 4.4. Sample quantiles -- 4.4.1. Sample quartiles -- 4.4.2. Sample deciles and percentiles -- 4.5. Distribution of a statistic -- 4.5.1. Basic setup in statistics -- 4.5.2. Sampling distributions -- 4.5.3. Normal quantile-quantile plot -- 4.6. The central limit theorem -- 4.7. Parameter estimation -- 4.7.1. Bias, variance, and efficiency -- 4.8. Interval estimates.

5.4.4. Testing for equal variances -- 5.5. Hypothesis tests on the regression model -- 5.5.1. Prediction and estimation confidence intervals -- 5.5.2. Multiple regression -- 5.5.3. Original scale prediction in regression -- 5.6. Brief introduction to vectors and matrices -- 5.6.1. Basic definitions -- 5.6.2. Inverse of a matrix -- 5.6.3. Random vectors and random matrices -- 5.7. Matrix form of multiple regression -- 5.7.1. Generalized least squares -- 5.8. Hypothesis testing with the delete-d jackknife -- 5.8.1. Background -- 5.8.2.A one-sample delete-d jackknife test -- 5.8.3. Testing classifier error rates -- 5.8.4. Important points about this test -- 5.8.5. Parameter confidence intervals -- 6. Introduction to spatial statistics -- 6.1. Overview -- 6.1.1. Types of spatial processes -- 6.2. Spatial statistics and GIS -- 6.2.1. Types of spatial data -- 6.3. QGIS -- 6.3.1. Capabilities -- 6.3.2. Installing QGIS -- 6.3.3. Documentation and tutorials -- 6.3.4. Installing plugins.

6.3.5. How to convert a text file to a shapefile -- 6.4. Continuous spatial processes -- 6.4.1. Definitions -- 6.4.2. Graphical tools for exploring continuous spatial data -- 6.4.3. Third- and fourth-order cumulant minimization -- 6.4.4. Best linear unbiased predictor -- 6.4.5. Kriging variance -- 6.4.6. Model-fitting diagnostics -- 6.4.7. Kriging within a window -- 6.5. Spatial point processes -- 6.5.1. Definitions -- 6.5.2. Marked spatial point processes -- 6.5.3. Conclusions -- 6.6. Continuously valued multivariate processes -- 6.6.1. Fitting multivariate covariance functions -- 6.6.2. Cokriging: The MWRCK procedure -- 7. Introduction to spatio-temporal statistics -- 7.1. Introduction -- 7.2. Representing time in a GIS -- 7.2.1. The QGIS Time Manager plugin -- 7.2.2.A Clifford algebra-based spatio-temporal data structure -- 7.2.3.A raster- and event-based spatio-temporal data model -- 7.2.4. Application of ESTDM to a land cover study.

7.3. Spatio-temporal prediction: MCSTK -- 7.3.1. Algorithms -- 7.3.2. Covariogram model and its estimator -- 7.4. Multivariate processes -- 7.4.1. Definitions -- 7.4.2. Transformations -- 7.4.3. Covariograms and cross-covariograms -- 7.4.4. Parameter estimation -- 7.4.5. Prediction algorithms -- 7.4.6. Cross-validation -- 7.4.7. Summary -- 7.5. Spatio-temporal point processes -- 7.6. Marked spatio-temporal point processes -- 7.6.1.A mark semivariogram estimator -- 8. Application of statistical inference: Estimating the parameters of an individual-based model -- 8.1. Overview -- 8.2.A simple IBM and its estimation -- 8.2.1. Simple IBM -- 8.2.2. Parameter estimation -- 8.3. Fitting IBMs with MSHD -- 8.3.1. Ergodicity -- 8.3.2. Observable random variables from IBM output -- 8.4. Further properties of parameter estimators -- 8.4.1. Consistency -- 8.4.2. Robustness -- 8.5. Parameter confidence intervals for a nonergodic model -- 8.6. Rhino-supporting ecosystem influence diagram.

8.6.1. Spatial effects on poaching -- 8.6.2. IBM variables -- 8.6.3. Initial conditions and hypothesis values of parameters -- 8.6.4. Mapping functions -- 8.6.5. Realism of ecosystem influence diagram output -- 8.7. Estimation of rhino IBM parameters -- 8.7.1. Parameter confidence intervals -- 9. Guiding an influence diagram's learning -- 9.1. Introduction -- 9.2. Online learning of Bayesian network parameters -- 9.2.1. Basic algorithm using simulation -- 9.2.2. Updating influence diagrams -- 9.3. Learning an influence diagram's structure -- 9.3.1. Minimum description length score function -- 9.3.2. Description length of an edge -- 9.3.3. Random generation of DAGs -- 9.3.4. Algorithm to detect and delete cycles -- 9.3.5. Mutate functions -- 9.3.6. MDLEP algorithm -- 9.3.7. Using MDLEP to learn influence diagram structure -- 9.4. Feedback-based learning for group decision-making diagrams -- 9.4.1. Definitions and algorithm -- 9.5. Summary and conclusions.

10. Fitting and testing a political-ecological simulator -- 10.1. Introduction -- 10.1.1. Background on rhino poaching -- 10.1.2. Scenarios wherein rhino poaching is reduced -- 10.2. EMT simulator construction -- 10.2.1. Modeled groups -- 10.2.2. Rhino-supporting ecosystem influence diagram -- 10.3. Consistency analysis estimates of simulator parameters -- 10.4. MPEMP computation -- 10.4.1. Setup -- 10.4.2. Solution -- 10.5. Conclusions.

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