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by David Fletcher (Author)
About the Author
David Fletcher is an Associate Professor of Statistics at the University of Otago in Dunedin, New Zealand. His research interests developed primarily from collaboration with other scientists, particularly ecologists. He has developed new methods in a range of areas, including experimental design, mark-recapture, meta-regression, model averaging, population dynamics, overdispersion and zero-inflated data.
About this book
This book provides a concise and accessible overview of model averaging, with a focus on applications. Model averaging is a common means of allowing for model uncertainty when analysing data, and has been used in a wide range of application areas, such as ecology, econometrics, meteorology and pharmacology. The book presents an overview of the methods developed in this area, illustrating many of them with examples from the life sciences involving real-world data. It also includes an extensive list of references and suggestions for further research. Further, it clearly demonstrates the links between the methods developed in statistics, econometrics and machine learning, as well as the connection between the Bayesian and frequentist approaches to model averaging. The book appeals to statisticians and scientists interested in what methods are available, how they differ and what is known about their properties. It is assumed that readers are familiar with the basic concepts of statistical theory and modelling, including probability, likelihood and generalized linear models.
Brief contents
1 Why Model Averaging? 1
1.1 Country Fairs and the Size of the Universe 1
1.2 Benefits of Model Averaging 2
1.3 Examples 4
1.3.1 Sea Lion Bycatch 4
1.3.2 Ecklonia Density 6
1.3.3 Water-Uptake in Amphibia. 8
1.3.4 Toxicity of a Pesticide 10
1.3.5 Assessing the Risk of a Stroke 13
1.4 When Is Model Averaging Useful? 14
1.5 Aim of This Book 16
1.6 Related Literature 18
References 19
2 Bayesian Model Averaging 31
2.1 Introduction 31
2.2 Classical BMA 32
2.2.1 Posterior Model Probabilities 34
2.2.2 Choice of Priors 35
2.3 Prediction-Based BMA 37
2.3.1 DIC and WAIC 38
2.3.2 Bayesian Stacking 39
2.4 Examples 41
2.4.1 Ecklonia Density 41
2.4.2 Toxicity of a Pesticide 42
2.5 Discussion 45
2.6 Related Literature 46
References 48
3 Frequentist Model Averaging 57
3.1 Introduction 57
3.2 Point Estimation 57
3.2.1 Information-Criterion Methods 58
3.2.2 Bagging 61
3.2.3 Optimal Weights 62
3.3 Examples 66
3.3.1 Sea Lion Bycatch 66
3.3.2 Ecklonia Density 66
3.3.3 Water-Uptake in Amphibia. 68
3.3.4 Toxicity of a Pesticide 69
3.4 Interval Estimation 71
3.4.1 Wald Interval 71
3.4.2 Percentile-Bootstrap Interval 74
3.4.3 MATA Interval 74
3.5 Examples 77
3.5.1 Sea Lion Bycatch 77
3.5.2 Ecklonia Density 77
3.5.3 Water-Uptake in Amphibia. 78
3.5.4 Toxicity of a Pesticide 79
3.6 Discussion 80
3.6.1 Choice of Scale 80
3.6.2 Choice of Model Set 80
3.6.3 Confidence Intervals 81
3.6.4 Mixed Models 82
3.6.5 Missing Data 83
3.6.6 Summing Model Weights 83
3.7 Related Literature 84
3.7.1 Information-Criterion Methods 84
3.7.2 Constraints on Optimal Weights 84
3.7.3 AIC(w) 86
3.7.4 Machine Learning Methods 86
3.7.5 Focussed Methods 87
3.7.6 Miscellanea 87
3.7.7 Software 88
References 89
4 Summary and Future Directions 99
4.1 Summary of Key Points 99
4.2 Future Directions 100
References 101
Index 103
Series: SpringerBriefs in Statistics
Pages: 120 pages
Publisher: Springer; 1st ed. 2018 edition (January 17, 2019)
Language: English
ISBN-10: 3662585405
ISBN-13: 978-3662585405
PDF version
Springer__Model Averaging .pdf
(2.11 MB, 需要: 15 个论坛币)
EPUB version
Springer__Model Averaging .epub
(1.68 MB, 需要: 15 个论坛币)
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