Contemporary Bayesian and Frequentist Statistical Research Methods for Natural Resource Scientists

417 Pages·2007·20.28 MB·English

by  Howard B. Stauffer

CONTEMPORARY
BAYESIAN AND
FREQUENTIST
STATISTICAL RESEARCH
METHODS FOR NATURAL
RESOURCE SCIENTISTS

CONTEMPORARY
BAYESIAN AND
FREQUENTIST
STATISTICAL RESEARCH
METHODS FOR NATURAL
RESOURCE SCIENTISTS
Howard B. Stauffer
Mathematics Department, Humboldt State University, Arcata, California
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LibraryofCongressCataloging-in-PublicationData:
Stauffer,HowardB.,1941-
ContemporaryBayesianandfrequentiststatisticalresearchmethodsfornaturalresource
scientists/HowardB.Stauffer.
p.cm.
ISBN978-0-470-16504-1(cloth)
1. Bayesianstatisticaldecisiontheory. 2. Mathematicalstatistics. I. Title.
QA279.5.S762008
519.5’42—dc22
2007015575
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
To my parents,
Howard Hamilton Staufferand Elizabeth Boyer Stauffer,
and to my family,
wife Rebecca Ann Stauffer,
daughter Sarah Elizabeth Stauffer,
and son Noah Hamilton Stauffer.
Their love and support has sustained me and provided
meaning and joy in my life.

CONTENTS
Preface xiii
1 Introduction 1
1.1 Introduction 2
1.2 Three Case Studies 2
1.2.1 Case Study 1: Maintenanceof a Population Parameter
above a Critical Threshold Level 2
1.2.2 Case Study 2: Estimation of the Abundance of a Discrete
Population 3
1.2.3 Case Study 3: Habitat Selection Modeling of a Wildlife
Population 4
1.2.4 Case Studies Summary 5
1.3 Overviewof Some Solution Strategies 5
1.3.1 Sample Surveys and Parameter Estimation 5
1.3.2 Experiments and Hypothesis Testing 8
1.3.3 Multiple Linear Regression, GeneralizedLinear Modeling,
and Model Selection 9
1.3.4 A Preview of Bayesian Statistical Inference 10
1.3.5 A Preview of Model Selection Strategies and
Information-Theoretic Criteriafor Model Selection 11
1.3.6 A Preview of Mixed-Effects Modeling 14
1.4 Review: Principles of Project Management 14
1.5 Applications 15
1.6 S-Pluswand ROrientation I: Introduction 16
1.6.1 Orientation I 16
1.6.2 Simple Manipulations 17
1.6.3 Data Structures 21
1.6.4 RandomNumbers 21
1.6.5 Graphs 21
1.6.6 Importingand Exporting Files 22
1.6.7 Saving and Restoring Objects 22
vii
viii CONTENTS
1.6.8 Directory Structures 22
1.6.9 Functions and Control Structures 22
1.6.10 Linear Regression Analysis in S-Plus and R 23
1.7 S-Plus and ROrientation II:Distributions 23
1.7.1 Uniform Distribution 23
1.7.2 Normal Distribution 24
1.7.3 Poisson Distribution 26
1.7.4 BinomialDistributions 27
1.7.5 Simple Random Sampling 33
1.8 S-Plus and ROrientation III: Estimation of Mean and
Proportion, Sampling Error, andConfidence Intervals 34
1.8.1 Estimation of Mean 34
1.8.2 Estimation of Proportion 36
1.9 S-Plus and ROrientation IV: Linear Regression 36
1.10 Summary 39
Problems 40
2 Bayesian Statistical AnalysisI: Introduction 47
2.1 Introduction 47
2.1.1 Historical Background 47
2.1.2 Limitationsto the Use of Frequentist Statistical Inference for
Natural Resource Applications: An Example 49
2.2 ThreeMethods for Fitting Modelsto Datasets 50
2.2.1 Least-Squares (LS) Fit—Minimizinga
Goodness-of-Fit Profile 51
2.2.2 Maximum-Likelihood (ML)Fit—Maximizing the
LikelihoodProfile 52
2.2.3 Bayesian Fit—Bayesian Statistical Analysis and Inference 54
2.2.4 Examples 56
2.3 The Bayesian Paradigm for Statistical Inference: Bayes Theorem 61
2.4 Conjugate Priors 63
2.4.1 Continuous Datawith the Normal Model 64
2.4.2 Count Datawith the Poisson Model 66
2.4.3 Binary Datawith the BinomialModel 69
2.4.4 Conjugate Priors for Other Datasets 71
2.5 OtherPriors 72
2.5.1 Noninformative,Uniform, and Properor Improper Priors 73
2.5.2 Jeffreys Priors 73
2.5.3 Reference Priors, Vague Priors, andElicitedPriors 74
CONTENTS ix
2.5.4 Empirical Bayes Methods 74
2.5.5 SensitivityAnalysis: An Example 74
2.6 Summary 77
Problems 77
3 Bayesian Statistical Inference II: Bayesian Hypothesis Testing
and Decision Theory 81
3.1 Bayesian Hypothesis Testing: Bayes Factors 81
3.1.1 Proportion Estimation of Nesting Northern
Spotted Owl Pairs 83
3.1.2 Medical Diagnostics 83
3.2 Bayesian Decision Theory 88
3.3 Preview: More Advanced Methodsof Bayesian Statiscal
Analysis—MarkovChain Monte Carlo (MCMC)
Alogrithms and WinBUGS Software 90
3.4 Summary 91
Problems 91
4 Bayesian Statistical Inference III: MCMCAlgorithms and
WinBUGS Software Applications 93
4.1 Introduction 93
4.2 MarkovChain Theory 94
4.3 MCMCAlgorithms 96
4.3.1 Gibbs Sampling 96
4.3.2 The Metropolis–Hastings Algorithm 98
4.4 WinBUGS Applications 101
4.4.1 The Normal Mean Model for Continuous Data 106
4.4.2 Models for Count Data:The Poisson Model, Poisson–Gamma
Negative Binomial Model, andOverdispersed
Mixed-Effects Poisson Model 110
4.4.3 The Linear RegressionModel 112
4.5 Summary 115
Problems 115
5 Alternative Strategies for Model Selection and Inference Using
Information-Theoretic Criteria 121
5.1 Alternative Strategies for Model Selection and Inference:
Descriptive and Predictive ModelSelection 121
5.1.1 Introduction 121
5.1.2 The Metaphorof the Race 123