Statistics in Practice

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University of Maryland, USA

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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

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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

Dedicated to the next generation of ecosystem managers

List of figures

1.1 | R Commander's window just after the fish toxic chemical data strip chart has been drawn
1.2 | Strip chart of fish toxic chemical data as drawn by R Commander
1.3 | Entering R commands from R Commander's Script Window
2.1 | Outcomes in the sample space map to values of a random variable
2.2 | The first three values of the geometric random variable's PMF
2.3 | Standard normal PDF
2.4 | Standard normal CDF
2.5 | Standard normal quantile function
2.6 | A directed acyclic graph
2.7 | Example of the back-door criterion
2.8 | Example of the front-door criterion
3.1 | Simplified rhino poacher decision-making diagram
3.2 | Sensitivity of poaching behavior to risk perception parameters
3.3 | A simplified policymaker decision-making diagram
4.1 | Histogram of plant biodiversity index sample
4.2 | Normal Q-Q plot
4.3 | Scatterplot and fitted line when plant biodiversity index is regressed onto road density
4.4 | Scatterplot of reading ability versus shoe size
4.5 | Influence diagram of age, reading ability, and shoe size
4.6 | Catch as a function of the number of fishing boat-days (effort)
5.1 | PMF and rejection region for the population viability hypothesis test
5.2 | Critical regions for the two-sided z-test at α = 0.05
5.3 | A one-sided z-test critical region (upper tail)
5.4 | Two-sided test p-value that is not significant
5.5 | Shift in T(X₁,...,Xn)'s distribution under Ha
5.6 | Power curves for n = 25 and 100
5.7 | Two-tailed t-test critical region at α = 0.05
5.8 | 2,5-distribution PDF
5.9 | Positive relationship
5.10 | No relationship
5.11 | Negative relationship
5.12 | Illustration of SST
5.13 | Illustration of SSR
5.14 | Illustration of SSE
5.15 | Perfect straight line relationship
6.1 | QGIS display of a river reach drawn from a vector dataset expressed in WKT format
6.2 | A raster map of a hill displayed with QGIS
6.3 | QGIS display of total sulfate (SO₄) deposition (kg/ha) for the year 1987 over the conterminous United States
6.4 | Exploratory analysis of 1987 sulfate deposition using R: quilt plot of sulfate observations (top), plot of residuals from a 2-NN median filter (middle), and empirical semivariogram of these residuals (bottom)
6.5 | Predictions of 1987 sulfate deposition using the implementation of OK contained in the R package gstat
6.6 | Cross-validation normal Q-Q plots for the MWRRK predictions of total 1987 sulfate deposition
6.7 | Surface of MWRRK predictions of total 1987 sulfate deposition across the conterminous United States
6.8 | Surface of kriging standard deviations of the MWRRK predictions of total 1987 sulfate deposition across the conterminous United States
6.9 | Quilt plot of work cessation dates on temples in the Mayan Lowlands during the eighth and ninth centuries AD
6.10 | R computation of Ripley's K function for the Mayan temple work cessation dataset
6.11 | Fitted semivariograms and cross-covariogram of the MWRCK residuals at a selected location in the conterminous United States
6.12 | Cross-validation normal Q-Q plots for the MWRCK predictions of total 1987 sulfate deposition
7.1 | Snapshot of active Mayan temple sites through the year 731 AD
7.2 | Snapshot of active Mayan temple sites through the year 775 AD
7.3 | Snapshot of active Mayan temple sites through the year 820 AD
7.4 | Snapshot of active Mayan temple sites through the year 864 AD
7.5 | Snapshot of active Mayan temple sites through the year 909 AD
7.6 | An MCSTK cylinder spatially centered at the point (x₀, y₀)
7.7 | Cross-validation of normal Q-Q plots for the MCSTK predictions of summer 1989 sulfate deposition across the conterminous United States
7.8 | Normal Q-Q plots of the MCSTK one-step-ahead prediction errors of summer 1989 sulfate deposition across the conterminous United States
7.9 | Histogram of 10,000 deviates from a random variable W with τ₁ = 0.8, τ₂ = 1.2, and σ = 1
7.10 | Histogram of deviates back-transformed from W to Z using the estimated parameter values found by minimizing the Cramér–von Mises distance
7.11 | Normal Q-Q plots of the LOMAP one-step-ahead prediction errors of Lake Saki mud thickness for the years 1000 AD through 1895 AD using a long-memory covariogram model
7.12 | Normal Q-Q plots of the LOMAP one-step-ahead prediction errors of Lake Saki mud thickness for the years 1000 AD through 1895 AD using a short-memory covariogram model
7.13 | Normal Q-Q plots of the LOMAP cross-validation predictions of the spatio-temporal data exhibiting an asymmetric residual distribution
7.14 | A bumblebee invasion observed over a 5 × 4 lattice
8.1 | One deviate of the biofilm bacterial growth IBM on a 41 × 41 grid with b = d = 0.1 and w = 1.1
8.2 | Empirical semivariogram computed from the deviate displayed in Figure 8.1
8.3 | Rhino ecosystem influence diagram
8.4 | Patch layout of a rhino-hosting ranch used in the rhino IBM
8.5 | Simulated weekly available vegetation (g/m²)
8.6 | Mean rhino abundance under (a) no poaching and (b) the poaching of four randomly chosen mature rhinos each week
10.1 | Policymaker decision-making diagram
10.2 | Judicial system decision-making diagram
10.3 | Wildlife ranch owner decision-making diagram
10.4 | Antipoaching unit decision-making diagram
10.5 | Poacher decision-making diagram
10.6 | Rhino horn consumer decision-making diagram
10.7 | Simulator output under consistent parameter values
10.8 | Simulator output over the time period 2012–2052 using MPEMP parameter values

List of tables

3.1 | Nodes that represent evaluation dimensions
3.2 | A truth table to relate Situation Change and Scenario Change node value combinations to values of a Scenario Goal node
3.3 | Situation subdiagram to scenario subdiagram relationships that produce three unique out-combinations
3.4 | CPT for the Goal: Make Money node
3.5 | CPT for the Goal: Avoid Prosecution node
3.6 | Relative importance weights for the OGA node
5.1 | Possible decisions and mistakes when performing a hypothesis test
5.2 | PMF of test statistic under H₀: p = 0.1
5.3 | Power calculations for Example 5.8
5.4 | Power calculations when n = 100
5.5 | Phosphorus concentration data
5.6 | ANOVA table for simple linear regression
8.1 | Rhino IBM parameters and their hypothesis values
8.2 | Delete-d jackknife parameter confidence intervals at 95% confidence for the life expectancy, maturation age, and intercalving interval parameters of the rhino IBM
9.1 | Parameter values of the Scenario Imminent Interaction With Police node before and after the Voting EM algorithm update computation with forgetting parameter set to 0.5
10.1 | Group output actions and associated targets
10.2 | A portion of the political–ecological dataset used to find the consistent values of the simulator's parameters (Table 10.4)
10.3 | Parameters fitted by the consistency analysis computation
10.4 | Parameter values of distributions most changed between their hypothesis and consistent values

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 .

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