Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists - Hardcover

Stauffer, Howard B.

Hardcover

ISBN 10: 0470165049 ISBN 13: 9780470165041

Publisher: Wiley-Interscience, 2007

Synopsis

The first all-inclusive introduction to modern statistical research methods in the natural resource sciences

The use of Bayesian statistical analysis has become increasingly important to natural resource scientists as a practical tool for solving various research problems. However, many important contemporary methods of applied statistics, such as generalized linear modeling, mixed-effects modeling, and Bayesian statistical analysis and inference, remain relatively unknown among researchers and practitioners in this field. Through its inclusive, hands-on treatment of real-world examples, Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists successfully introduces the key concepts of statistical analysis and inference with an accessible, easy-to-follow approach.

The book provides case studies illustrating common problems that exist in the natural resource sciences and presents the statistical knowledge and tools needed for a modern treatment of these issues. Subsequent chapter coverage features:

• An introduction to the fundamental concepts of Bayesian statistical analysis, including its historical background, conjugate solutions, Bayesian hypothesis testing and decision-making, and Markov Chain Monte Carlo solutions

• The relevant advantages of using Bayesian statistical analysis, rather than the traditional frequentist approach, to address research problems

• Two alternative strategiesā€”the a posteriori model selection strategy and the a priori parsimonious model selection strategy using AIC and DICā€”to model selection and inference

• The ideas of generalized linear modeling (GLM), focusing on the most popular GLM of logistic regression

• An introduction to mixed-effects modeling in S-PlusĀ® and R for analyzing natural resource data sets with varying error structures and dependencies

Each statistical concept is accompanied by an illustration of its frequentist application in S-PlusĀ® or R as well as its Bayesian application in WinBUGS. Brief introductions to these software packages are also provided to help the reader fully understand the concepts of the statistical methods that are presented throughout the book. Assuming only a minimal background in introductory statistics, Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists is an ideal text for natural resource students studying statistical research methods at the upper-undergraduate or graduate level and also serves as a valuable problem-solving guide for natural resource scientists across a broad range of disciplines, including biology, wildlife management, forestry management, fisheries management, and the environmental sciences.

About this title

About the Author

Howard B. Stauffer, PhD, is Professor of Applied Statistics and former chairperson of the Mathematics Department at Humboldt State University. Dr. Stauffer has over thirty-five years of experience in academia, government, and industry specializing in sampling and experimental design and analysis, in addition to the current methodologies in statistical analysis, such as generalized linear modeling, mixed-effects modeling, Bayesian statistical analysis, and capture-recapture analysis.

The use of Bayesian statistical analysis has become increasingly important to natural resource scientists as a practical tool for solving various research problems. However, many important contemporary methods of applied statistics, such as generalized linear modeling, mixed-effects modeling, and Bayesian statistical analysis and inference, remain relatively unknown among researchers and practitioners in this field. Through its inclusive, hands-on treatment of real-world examples, Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists successfully introduces the key concepts of statistical analysis and inference with an accessible, easy-to-follow approach.

The book provides case studies illustrating common problems that exist in the natural resource sciences and presents the statistical knowledge and tools needed for a modern treatment of these issues. Subsequent chapter coverage features:

• An introduction to the fundamental concepts of Bayesian statistical analysis, including its historical background, conjugate solutions, Bayesian hypothesis testing and decision-making, and Markov Chain Monte Carlo solutions

• The relevant advantages of using Bayesian statistical analysis, rather than the traditional frequentist approach, to address research problems

• Two alternative strategiesā??the a posteriori model selection strategy and the a priori parsimonious model selection strategy using AIC and DICā??to model selection and inference

• The ideas of generalized linear modeling (GLM), focusing on the most popular GLM of logistic regression

• An introduction to mixed-effects modeling in S-PlusĀ® and R for analyzing natural resource data sets with varying error structures and dependencies

Each statistical concept is accompanied by an illustration of its frequentist application in S-PlusĀ® or R as well as its Bayesian application in WinBUGS. Brief introductions to these software packages are also provided to help the reader fully understand the concepts of the statistical methods that are presented throughout the book. Assuming only a minimal background in introductory statistics, Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists is an ideal text for natural resource students studying statistical research methods at the upper-undergraduate or graduate level and also serves as a valuable problem-solving guide for natural resource scientists across a broad range of disciplines, including biology, wildlife management, forestry management, fisheries management, and the environmental sciences.

The use of Bayesian statistical analysis has become increasingly important to natural resource scientists as a practical tool for solving various research problems. However, many important contemporary methods of applied statistics, such as generalized linear modeling, mixed-effects modeling, and Bayesian statistical analysis and inference, remain relatively unknown among researchers and practitioners in this field. Through its inclusive, hands-on treatment of real-world examples, Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists successfully introduces the key concepts of statistical analysis and inference with an accessible, easy-to-follow approach.

The book provides case studies illustrating common problems that exist in the natural resource sciences and presents the statistical knowledge and tools needed for a modern treatment of these issues. Subsequent chapter coverage features:

• An introduction to the fundamental concepts of Bayesian statistical analysis, including its historical background, conjugate solutions, Bayesian hypothesis testing and decision-making, and Markov Chain Monte Carlo solutions

• The relevant advantages of using Bayesian statistical analysis, rather than the traditional frequentist approach, to address research problems

• Two alternative strategiesā??the a posteriori model selection strategy and the a priori parsimonious model selection strategy using AIC and DICā??to model selection and inference

• The ideas of generalized linear modeling (GLM), focusing on the most popular GLM of logistic regression

• An introduction to mixed-effects modeling in S-PlusĀ® and R for analyzing natural resource data sets with varying error structures and dependencies

Each statistical concept is accompanied by an illustration of its frequentist application in S-PlusĀ® or R as well as its Bayesian application in WinBUGS. Brief introductions to these software packages are also provided to help the reader fully understand the concepts of the statistical methods that are presented throughout the book. Assuming only a minimal background in introductory statistics, Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists is an ideal text for natural resource students studying statistical research methods at the upper-undergraduate or graduate level and also serves as a valuable problem-solving guide for natural resource scientists across a broad range of disciplines, including biology, wildlife management, forestry management, fisheries management, and the environmental sciences.

Excerpt. © Reprinted by permission. All rights reserved.

Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists

By Howard B. Stauffer

John Wiley & Sons

Copyright © 2008 John Wiley & Sons, Inc.
All right reserved.
ISBN: 978-0-470-16504-1

Chapter One

Introduction

We will begin this initial chapter by introducing three case studies that illustrate some of the fundamental general statistical problems challenging the contemporary natural resource scientist. We will then present a review and preview of some solution strategies to these general problems. The first solution strategies that we will review are traditional frequentist approaches: parameter estimation from sample surveys, hypothesis testing from experiments, and linear regression modeling. Each of these methods is summarized using a frequentist approach to statistical analysis. We will then preview some more contemporary solution strategies: an alternative Bayesian approach to statistical analysis and other more advanced solutions to the case studies, generalized linear modeling, and mixed-effects modeling using both frequentist and Bayesian approaches to statistical analysis. We will also preview a more contemporary approach to model selection and inference using information-theoretic criteria such as Akaike's information criterion for frequentist statistical analysis and the deviance information criterion for Bayesian statistical analysis. All of these contemporary methods will be discussed in greater detail throughout the remainder of this book and illustrated with examples.

In this initial chapter we include a reminder of the importance of project management in natural resource studies with statistical components. Project management consists of organizing projects into three phases: a planning phase, a data collection phase, and a concluding phase. The planning phase includes an identification of the problem and the objectives of the project, along with a statistical design for the collection of the dataset. The concluding phase includes a statistical analysis of the dataset, along with interpretation and conclusions drawn from the analysis. All of these statistical components-the statistical design, the collection of the dataset, and the statistical analysis-provide essential tools for the solutions to the objectives of the project.

We conclude this initial chapter with an introduction to the frequentist statistical analysis software used throughout the book: the proprietary software S-Plus and its freeware "equivalent" R. The Bayesian statistical analysis software WinBUGS will be introduced in Chapters 2-4 when Bayesian ideas are discussed.

1.1 INTRODUCTION

In recent years there have been major advances in the methods of statistics used for research in the natural resource sciences. Yet, little of this is known outside selected research circles. Students and scientists in the natural resource sciences have continued to use traditional frequentist methods, such as the estimation of parameters from sample surveys, t tests and ANOVA hypothesis testing from experiments, and linear regression modeling. However, extraordinary newer methods are now available that enhance, complement, and extend these basic techniques, methods such as Bayesian statistical inference, information-theoretic approaches to model selection, generalized linear modeling, and mixed-effects modeling. It is the primary objective of this book to introduce these newer contemporary methods to natural resource students and scientists.

This book must begin by emphasizing critical statistical issues that have too often been neglected in natural resource studies in the past. We stress the importance of the planning and concluding phases in a data collection project. We particularly highlight the essential role of statistical design and analysis that help ensure the efficient, powerful, and effective use of data. Our approach throughout the book will be "hands-on," illustrating concepts with examples using the software languages of S-Plus or R for frequentist statistical analysis and WinBUGS for Bayesian statistical analysis.

Let's begin with a description of several case studies that illustrate problems of fundamental interest to contemporary natural resource scientists.

1.2 THREE CASE STUDIES

1.2.1 Case Study 1: Maintenance of a Population Parameter Above a Critical Threshold Level

A fundamental problem of interest to contemporary natural resource scientists is to assess whether a critical population parameter, such as a proportion parameter p, has been maintained above (or below) a specified critical threshold level: p [greater than or equal to] [p.sub.c] (or p [less than or equal to] [p.sub.c])?

Many examples in natural resource science illustrate this problem:

1. A timber company is required to maintain the proportion p of its timberlands occupied by nesting Northern Spotted Owl pairs above a specified threshold level [p.sub.c]. The threshold [p.sub.c] is a level determined by biologists to ensure the viability of the local population of owls.

2. Federal managers of a national forest are interested in maintaining the proportion p of forest covered by dense undergrowth below a specified threshold level [p.sub.c], to limit the risk of fire.

3. The managers of a national park are interested in maintaining the proportion p of a disease or insect infestation below a specified threshold level [p.sub.c] to control its spread.

4. Fishery biologists managing a watershed are interested in maintaining the proportional abundance p of a fishery above a specified threshold level [p.sub.c] of its carrying capacity to ensure its long-term sustainability.

5. A government agency implementing a natural resource conservation policy is interested in ensuring that the proportion p of the public in favor of one of its controversial policies is maintained above a certain threshold level [p.sub.c].

Besides the proportion parameter p in the examples presented above, there are many other biological parameters of interest to natural resource managers with similar threshold issues, such as the mean abundance [mu], survival rate [phi] from year i to year i + 1, fitness [[lambda].sub.i] = [N.sub.i+1]/[N.sub.i] (where [N.sub.i] and [N.sub.i+1] are the population abundances in years i and i + 1), ecological diversity index such as the Shannon-Wiener diversity index H, and population total [tau].

The failure to maintain the population parameter p above (or below) the threshold level [p.sub.c] might suggest the need for a "corrective action" decision in the examples listed above, such as

1. Reducing the timber harvesting

2. Applying fire suppression treatment

3. Applying disease or insect treatment

4. Increasing the watershed river flow by releasing more water from a dam

5. Altering the natural resource conservation policy

Alternatively, success at maintaining the population parameter p above (or below) the threshold [p.sub.c] might suggest a decision of "no action."

In such circumstances, a common approach employed by natural resource scientists is to begin monitoring the population and collecting sample data, say, on an annual basis, in order to assess the status of the population parameter. The intent is to conduct statistical analysis on the sample data and make inferences about the population parameter to determine whether it is above (or below) the threshold, and thus whether corrective action or no action is needed at the management level.

1.2.2 Case Study 2: Estimation of the Abundance of a Discrete Population

Our second case study focuses on the analysis of population count data. Often biological populations, such as birds, amphibians, or mammals, are sampled with discrete measurements such as plot counts, in fixed-area plots called quadrants. The intent is to estimate population size or density in an area using total count estimates of abundance or mean estimates of density.

The analysis consists of estimates of total or mean. Traditional estimates of total or mean are based on the assumption of the normal distribution of the population measurements. For plot counts, however, measurements are discrete and noncontinuous, consisting of nonnegative integers in a skewed distribution. If the biological population is randomly dispersed spatially, a proper model for the analysis should be based on the Poisson distribution rather than the normal distribution for the plot counts. If, however, the population is spatially aggregated or clumped, the analysis should be based on a more general model for the population measurements, such as a negative binomial distribution. Furthermore, the plot counts will likely be sampled without complete certainty of detection. Animals may be within the plot and yet be undetected by the sample surveyor. A rigorous analysis of the population therefore must factor in the Poisson or negative binomial distribution of the plot measurements, sampled with an uncertainty of detection. We will examine such analyses in Chapters 2-4 with Bayesian statistical analysis and Chapters 6-7 with generalized linear models and mixed-effects models.

1.2.3 Case Study 3: Habitat Selection Modeling of a Wildlife Population

In general, it can be quite difficult to estimate the presence or abundance of a wildlife population. Many important biological populations whose presence or abundance needs to be estimated are endangered or locally threatened wildlife species, such as the Northern Spotted Owl and Marbled Murrelet bird populations, Del Norte salamander amphibian population, and grizzly bear mammal population. These endangered species are often of particular importance because they are associated with old-growth ecosystems that are also in danger of extinction. Therefore it is important to monitor these populations, estimating their presence or abundance over time, to assess the status of the old-growth ecosystems. A particularly effective approach to estimating these mobile populations is to model their relationship with habitat.

With habitat selection modeling, the presence or abundance of a mobile population species is treated as a dependent response variable. Its relationship with "independent" predictor explanatory habitat variables such as vegetation, geologic, and meteorologic attributes can be assessed with statistical modeling. The intent of the habitat selection modeling is to analyze the relationship between the mobile wildlife population variable and the habitat variables and use it to describe or predict the presence or abundance of the endangered species as a function of the habitat variables. The idea behind the modeling is that many habitat variables can be more easily and less expensively sampled than can the mobile wildlife population.

The relationship in such circumstances is assumed to be associative rather than causal; thus, the modeling is descriptive, based on population monitoring with sample survey data, and not on experimental manipulation to establish evidence for cause and effect. The mobile wildlife population may have access to only a limited amount of habitat attributes and be able to express a restricted preference among what remains. Other habitat attributes that the mobile wildlife population most prefers may no longer be available for selection. Hence the habitat "selection" relationship must be interpreted within this context.

Habitat selection modeling is often based on regression analysis. For continuous-abundance response variables such as biomass, multiple linear regression analysis may indeed be applicable. For discrete-abundance response variables such as population counts, however, Poisson regression or negative binomial regression may be more appropriate. For binary response variables, such as the presence or absence, or occupancy versus nonoccupancy, of a population, logistic regression analysis or some other form of generalized linear modeling may be more appropriate. We will examine these methods of analysis, along with strategies for model selection, in Chapters 5 and 6. Traditional multiple linear regression analysis is discussed in Chapter 5. Logistic regression analysis, Poisson regression analysis, negative binomial regression analysis, and other forms of generalized linear modeling are discussed in Chapter 6.

1.2.4 Case Studies Summary

This book presents various contemporary statistical options available to the natural resource scientist to analyze and interpret sample data for these case studies and other general statistical problems of current interest to natural resource scientists. We will first review more familiar traditional statistical methods of sample survey parameter estimation, experimental hypothesis testing, and multiple linear regression modeling, and then describe the less familiar contemporary methods of Bayesian statistical inference, model selection strategies, generalized linear modeling, and mixed-effects modeling. These methods provide contemporary natural resource scientists with an up-to-date statistical toolbox of methods to tackle many important challenging problems of current interest.

1.3 OVERVIEW OF SOME SOLUTION STRATEGIES

In this section we present both a review of traditional statistical methods and a preview of contemporary statistical methods that provide solutions to the case studies that were presented in the previous section: assessing whether a population parameter has been maintained above (or below) a critical threshold level, the estimation of abundance of a discrete population, and habitat selection modeling. Further details on the contemporary methods will follow in later chapters.

1.3.1 Sample Surveys and Parameter Estimation

A first traditional statistical approach to addressing the fundamental case study problems of Section 1.2 is to conduct a sample survey of the population and collect sample data using a rigorous sampling design. The aim of the survey in case study 1 is to estimate a proportion parameter p or mean parameter [mu] from the sample data and compare it with a critical threshold level [p.sub.c] or [[micro].sub.c]. The aim of the survey in case study 2 is to estimate the mean abundance parameter [mu] of a discrete population. The aim of the survey in case study 3 is to model a mobile wildlife population as a function of habitat attributes and estimate the proportion parameter p or abundance parameter mean of the species in the habitat or at a specific site. Ideally, a natural resource scientist would like to use an approximately unbiased estimator [??] = [??] or [??] for the estimate of the parameter [??] = p or [mu], respectively, of minimum sampling error E, with a specified level of confidence P (or level of significance [alpha] = 1 - P).

If simple randomly sampled measurements {[y.sub.i]} are continuous and normally distributed with sample size n, the mean estimator is given by

[??] = [n.summation over (i=1)] [y.sup.i]/n,

with standard deviation

s = [square root of [n.summation over (i=1)] [([y.sub.1] - [??]).sup.2] / n - 1],

standard error

se = s / [square root of n],

and sampling error

E = [t.sub.(1 - [alpha]/2), n - 1] x se = [t.sub.(1 - [alpha]/ 2), n - 1] x s / [square root of n],

where [t.sub.(1 - [alpha]/2), n - 1 is the t value with (n - 1) degrees of freedom at the (1 - [alpha]/2) percentile with a level of significance.

If simple randomly sampled measurements {[y.sub.i]} are binary and binomially distributed with sample size n [greater than or equal to] 30, the proportion estimator is given by

[??] = y / n, where y = [n.summation over (i=1)] [y.sub.i]

with standard error

se = [square root of [??] x (1 - [??]) / n - 1]

and sampling error

E = [t.sub.(1 - [alpha]/2-1), n - 1] x se,

where [t.sub/(1 - [alpha]/2), n - 1] is the t value with (n - 1) degrees of freedom at the (1 - [alpha] /2) percentile with [alpha] level of significance.

(Continues...)

Excerpted from Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientistsby Howard B. Stauffer Copyright © 2008 by John Wiley & Sons, Inc.. Excerpted by permission.
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Edition details

• Publisher: Wiley-Interscience
• Publication date: 2007
• Language: English
• ISBN 10: 0470165049
• ISBN 13: 9780470165041
• Binding: Hardcover
• Edition number: 1
• Number of pages: 416