Introduction to Probability and Statistics for Ecosystem Managers E-Book

Timothy C. Haas

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Serie: Statistics in Practice
• Sprache: Englisch

Seitenzahl: 365

Veröffentlichungsjahr: 2013

Beschreibung

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.

Leseprobe

Table of Contents

Statistics in Practice

Title Page

Copyright

Dedication

List of figures

List of tables

Preface

Acknowledgments

List of abbreviations

Chapter 1: Introduction

1.1 The textbook's purpose

1.2 The textbook's pedagogical approach

1.3 Chapter summaries

1.4 Installing and running R Commander

1.5 Introductory R Commander session

1.6 Teaching probability through simulation

1.7 Summary

Chapter 2: Probability and simulation

2.1 Introduction

2.2 Basic probability

2.3 Random variables

2.4 Joint distributions

2.5 Influence diagrams

2.6 Advantages of influence diagrams in ecosystem management

2.7 Two ecosystem management Bayesian networks

2.8 Influence diagram sensitivity analysis

2.9 Drawbacks to influence diagrams

Chapter 3: Application of probability: Models of political decision making in ecosystem management

3.1 Introduction

3.2 Influence diagram models of decision making

3.3 Rhino poachers: A simplified model

3.4 Policymakers: A simplified model

3.5 Conclusions

Chapter 4: Statistical inference I: Basic ideas and parameter estimation

4.1 Definitions of some fundamental terms

4.2 Estimating the PDF and CDF

4.3 Measures of central tendency and dispersion

4.4 Sample quantiles

4.5 Distribution of a statistic

4.6 The central limit theorem

4.7 Parameter estimation

4.8 Interval estimates

4.9 Basic regression analysis

4.10 General methods of parameter estimation

Chapter 5: Statistical inference II: Hypothesis tests

5.1 Introduction

5.2 Hypothesis tests: General definitions and properties

5.3 Power

5.4 t-Tests and a test for equal variances

5.5 Hypothesis tests on the regression model

5.6 Brief introduction to vectors and matrices

5.7 Matrix form of multiple regression

5.8 Hypothesis testing with the delete-d jackknife

Chapter 6: Introduction to spatial statistics

6.1 Overview

6.2 Spatial statistics and GIS

6.3 QGIS

6.4 Continuous spatial processes

6.5 Spatial point processes

6.6 Continuously valued multivariate processes

Chapter 7: Introduction to spatio-temporal statistics

7.1 Introduction

7.2 Representing time in a GIS

7.3 Spatio-temporal prediction: MCSTK

7.4 Multivariate processes

7.5 Spatio-temporal point processes

7.6 Marked spatio-temporal point processes

Chapter 8: Application of statistical inference: Estimating the parameters of an individual-based model

8.1 Overview

8.2 A simple IBM and its estimation

8.3 Fitting IBMs with MSHD

8.4 Further properties of parameter estimators

8.5 Parameter confidence intervals for a nonergodic model

8.6 Rhino-supporting ecosystem influence diagram

8.7 Estimation of rhino IBM parameters

Chapter 9: Guiding an influence diagram's learning

9.1 Introduction

9.2 Online learning of Bayesian network parameters

9.3 Learning an influence diagram's structure

9.4 Feedback-based learning for group decision-making diagrams

9.5 Summary and conclusions

Chapter 10: Fitting and testing a political–ecological simulator

10.1 Introduction

10.2 EMT simulator construction

10.3 Consistency analysis estimates of simulator parameters

10.4 MPEMP computation

10.5 Conclusions

Appendix

Simpson's rule in two dimensions

References

Index

Statistics in Practice

Statistics in Practice

Series Advisors

Human and Biological Sciences

Stephen Senn

CRP-Santé, Luxembourg

Earth and Environmental Sciences

Marian Scott

University of Glasgow, UK

Industry, Commerce and Finance

Wolfgang Jank

University of Maryland, USA

Founding Editor

Vic Barnett

Nottingham Trent University, UK

Statistics in Practice is an important international series of texts which provide detailed coverage of statistical concepts, methods and worked case studies in specific fields of investigation and study.

With sound motivation and many worked practical examples, the books show in down-to-earth terms how to select and use an appropriate range of statistical techniques in a particular practical field within each title's special topic area.

The books provide statistical support for professionals and research workers across a range of employment fields and research environments. Subject areas covered include medicine and pharmaceutics; industry, finance and commerce; public services; the earth and environmental sciences, and so on.

The books also provide support to students studying statistical courses applied to the above areas. The demand for graduates to be equipped for the work environment has led to such courses becoming increasingly prevalent at universities and colleges.

It is our aim to present judiciously chosen and well-written workbooks to meet everyday practical needs. Feedback of views from readers will be most valuable to monitor the success of this aim.

A complete list of titles in this series appears at the end of the volume.

This edition first published 2013

© 2013 John Wiley & Sons, Ltd

Registered office

John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988.

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher.

Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books.

Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trademarks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book.

Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. It is sold on the understanding that the publisher is not engaged in rendering professional services and neither the publisher nor the author shall be liable for damages arising herefrom. If professional advice or other expert assistance is required, the services of a competent professional should be sought.

Library of Congress Cataloging-in-Publication Data

Haas, Timothy C.

Introduction to probability and statistics for ecosystem managers : simulation and resampling / Timothy C. Haas, Sheldon B. Lubar.

pages cm

Includes bibliographical references and index.

ISBN 978-1-118-35768-2 (cloth)

1. Ecosystem management – Statistical methods. I. Lubar, Sheldon B. II. Title.

QH77.3.S73H33 2013

333.72 – dc23

2013002861

A catalogue record for this book is available from the British Library.

ISBN: 978-1-118-35768-2

List of figures

List of tables

Preface

This textbook will be useful for readers who are either in training for or are in positions having to do with the management of environmental systems and/or wildlife populations wherein one of the decreed management goals is the protection of some part of the ecosystem, for example, wildlife that is at threat from anthropogenic forces. Examples of such positions include being a member of a forestry, fish and game, national parks, or environmental protection agency—or a wildlife advocacy organization such as the African Wildlife Foundation or the World Wildlife Fund. The prerequisites needed for grasping the ideas presented in this textbook are some familiarity with natural resources and a precalculus course.

This textbook has the following pedagogical features:

1. Explanations of probabilistic and statistical concepts are intuitive. Probability is explained through simulations rather than mathematical derivations and statistics is presented through computer-based resampling methods rather than methods based on large sample approximations.

2. Almost all examples show how probability and statistics can be applied to ecosystem management challenges.

3. Exercises are plentiful and appear just after the associated content—making the textbook 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.

4. Detailed instructions for using the statistical program R are provided along with many complete R programs that generate the output of the textbook's many examples.

5. Enough mathematical programming details are given so that the reader can estimate statistical model parameters with minimum distance methods.

6. An introduction to Geographic Information Systems (GIS) appears that includes examples from quantum GIS (QGIS), a free GIS software package.

7. Spatial and spatio-temporal statistics are introduced and illustrated with examples from ecosystem management that make use of R's spatial statistics capabilities and JAVA® programs written by the author. The language of vectors and matrices is introduced in enough detail to allow the reader to grasp spatial and spatio-temporal models that are expressed in this language.

8. A capstone case study is presented of how one might manage the rhino meta-population kept on private land in South Africa. This case study puts to use the textbook's material on probability, statistics, ecosystem stakeholder models, and individual-based models of wildlife populations.

9. An accompanying website (www4.uwm.edu/people/haas/introtext) contains all R and JAVA codes used in this textbook. It also contains all datasets used in the textbook's examples, a web-based ecosystem management tool (EMT) developed by the author in his previous book, Improving Natural Resource Management: Ecological and Political Models (Wiley-Blackwell), and answers to all of the textbook's exercises.

Several items are original to this textbook:

1. A new function to transform non-normal data to near-normality.

2. R codes to compute a spatial median filter, spatial cumulants, and spatial neural networks; along with codes that implement a probabilistic model of the spatial diffusion of an invasive species and an algorithm for constrained random search.

3. A learning algorithm that models how ecosystem stakeholders learn from experience as they reach ecosystem-affecting decisions.

4. Complete coverage of how to build and evaluate an individual-based model of a wildlife population that is to be managed.

5. An Online Intelligent Tutoring System (OITS) tied to the text that uses a learned model of a reader to deliver explanations that are focused on just those topics the reader is having difficulty with. This tutoring system can be found at the above-mentioned website.

Acknowledgments

The author appreciates comments made on an early version of Chapter 10 by the participants of the 7th International Wildlife Ranching Symposium, Kimberley, South Africa, October 10–13, 2011.

List of abbreviations

m

-NN

m

-nearest-neighbor

AER

actual error rate

ANOVA

analysis of variance

BLUP

best linear unbiased predictor

CDF

cumulative distribution function

CPT

conditional probability table

CRS

coordinate reference system

CSR

complete spatial randomness

d.o.f.

degrees of freedom

DAG

directed acyclic graph

DL

description length

DM-group

decision-making group

EMAT

ecosystem management actions taxonomy

EMT

ecosystem management tool

EPA

Environment Protection Agency

ESA/NASA

European Space Agency/National Aeronautics and Space Administration

ESTDM

event-based spatio-temporal data model

FBLGDMD

feedback-based learning for group decision-making diagrams

FFT

fast Fourier transform

GIS

geographic information system

GLS

generalized least squares

GUI

graphical user interface

i.i.d.

independently and identically distributed

IBM

individual-based model

ICBEMP

Interior Columbia Basin Ecosystem Management Project

INTERCALV

intercalving interval

IQR

inter-quartile range

IUCN

International Union for Conservation of Nature

KECs

Key environmental correlates

LE

life expectancy

LOMAP

Local Model And Predictor

MA

maturation age

MCSTK

moving cylinder spatio-temporal kriging

MDLEP

minimum description length-evolutionary programming

MDL

minimum description length

MHD

minimum Hellinger distance

MLE

maximum likelihood estimate

MPEMP

most practical ecosystem management plan

MSHD

minimum simulated Hellinger distance

MSL

maximum simulated likelihood

MWRCK

moving window residual cokriging

MWRRK

moving window, regression, residual kriging

NEMBA

National Environmental Management: Biodiversity Act

NEMPAA

National Environmental Management: Protected Areas Act

NGO

nongovernmental organization

NP-hard

non-polynomial time hard

OC

operating characteristic

OGA

overall goal attainment

OITS

online intelligent tutoring system

OK

ordinary kriging

OLS

ordinary least squares

PAC

protected area complex

PA

protected area

PDF

probability density function

PDPF

probability density–probability function

PMF

probability mass function

POM

pattern-oriented modeling

Q-Q

Quantile–Quantile

QGIS

quantum GIS

SPPP

spatial Poisson point process

SSE

error sum of squares

SSR

regression sum of squares

SST

total sum of squares

TOPS

Threatened and Protected Species

USDA

US Department of Agriculture

WKT

well-known text

Chapter 1

Introduction

1.1 The textbook's purpose

The book Improving Natural Resource Management: Ecological and Political Models (Haas, 2011), in pages 206–207, provides a list of areas that ecosystem managers need stronger training in. This textbook provides such instruction in probability, statistics, simulation, and resampling methods. It is designed to be used either as a classroom textbook or as the main text supporting a self-study regime (with web-based aids) by practicing ecosystem managers who are unable to attend an instructor-led course.

Topics salient to ecosystem management, but rarely covered in introductory statistics textbooks, are introduced. These include

1. basics of Bayesian networks and influence diagrams;

2. minimum simulated Hellinger distance (MSHD) parameter estimation;

3. resampling-based hypothesis tests and confidence intervals that can be applied to spatio-temporal data;

4. spatial and spatio-temporal statistics;

5. learning algorithms for influence diagrams; and

6. individual-based models (IBMs) of wildlife populations.

Influence diagrams are Bayesian networks that have decision and utility nodes. IBMs are also called .