Introduction to Probability and Statistics for Ecosystem Managers Simulation and Resampling

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  • Edition: 1st
  • Format: eBook
  • Copyright: 2013-06-04
  • Publisher: Wiley

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Explores computer-intensive probability and statistics for ecosystem management decision making

Simulation is an accessible way to explain probability and stochastic model behavior to beginners. This book introduces probability and statistics to future and practicing ecosystem managers by providing a comprehensive treatment of these two areas. The author presents a self-contained introduction for individuals involved in monitoring, assessing, and managing ecosystems and features intuitive, simulation-based explanations of probabilistic and statistical concepts. Mathematical programming details are provided for estimating ecosystem model parameters with Minimum Distance, a robust and computer-intensive method.

The majority of examples illustrate how probability and statistics can be applied to ecosystem management challenges. There are over 50 exercises – making this book suitable for a lecture course in a natural resource and/or wildlife management department, or as the main text in a program of self-study.

Key features:

  • Reviews different approaches to wildlife and ecosystem management and inference.
  • Uses simulation as an accessible way to explain probability and stochastic model behavior to beginners.
  • Covers material from basic probability through to hierarchical Bayesian models and spatial/ spatio-temporal statistical inference.
  • Provides detailed instructions for using R, along with complete R programs to recreate the output of the many examples presented.
  • Provides an introduction to Geographic Information Systems (GIS) along with examples from Quantum GIS, a free GIS software package.
  • A companion website featuring all R code and data used throughout the book.
  • Solutions to all exercises are presented along with an online intelligent tutoring system that supports readers who are using the book for self-study.

Table of Contents


List of Abbreviations

List of Tables

List of Figures

1 Introduction

1.1 This 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 This 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

4.8.1 A Confidence Interval for μ When σ2 is Known

4.9 Basic Regression Analysis

4.9.1 Definitions and Fundamental Characteristics

4.9.2 The Regression Model

4.9.3 Correlation

4.9.4 Sampling Distributions

4.9.5 Prediction and Estimation

4.9.6 Misuse of Regression Models

4.10 General Methods of Parameter Estimation

4.10.1 Maximum Likelihood

4.10.2 Minimum Hellinger Distance

4.10.3 Consistency Analysis

5 Statistical Inference II: Hypothesis Tests

5.1 Introduction

5.2 Hypothesis Tests: General Definitions and Properties

5.2.1 Definitions and Procedure

5.2.2 Confidence Intervals and Hypothesis Tests

5.2.3 Types of Mistakes

5.2.4 One Way to Set the Test’s Level

5.2.5 The z-Test for Hypotheses About μ

5.2.6 P-values

5.3 Power

5.3.1 Power Curves

5.4 t-Tests and a Test for Equal Variances

5.4.1 The t-Test

5.4.2 Two-Sample t-Tests

5.4.3 Tests for Paired Data

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

8.3 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 Inuence 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


A Simpson's Rule in Two Dimensions



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