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E-raamat: Predictive Statistics: Analysis and Inference beyond Models

(University of Nebraska, Lincoln), (University of Nebraska, Lincoln)
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Predictive Statistics: Analysis and Inference beyond ModelsSuurem pilt
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Aimed at statisticians and machine learners, this retooling of statistical theory asserts that high-quality prediction should be the guiding principle of modeling and learning from data, then shows how. The fully predictive approach to statistical problems outlined embraces traditional subfields and 'black box' settings, with computed examples.

All scientific disciplines prize predictive success. Conventional statistical analyses, however, treat prediction as secondary, instead focusing on modeling and hence estimation, testing, and detailed physical interpretation, tackling these tasks before the predictive adequacy of a model is established. This book outlines a fully predictive approach to statistical problems based on studying predictors; the approach does not require predictors correspond to a model although this important special case is included in the general approach. Throughout, the point is to examine predictive performance before considering conventional inference. These ideas are traced through five traditional subfields of statistics, helping readers to refocus and adopt a directly predictive outlook. The book also considers prediction via contemporary 'black box' techniques and emerging data types and methodologies where conventional modeling is so difficult that good prediction is the main criterion available for evaluating the performance of a statistical method. Well-documented open-source R code in a Github repository allows readers to replicate examples and apply techniques to other investigations.

Arvustused

'Prediction, one of the most important practical applications of statistical analysis, has rarely been treated as anything more than an afterthought in most formal treatments of statistical inference. This important book aims to counter this neglect by a wholehearted emphasis on prediction as the primary purpose of the analysis. The authors cut a broad swathe through the statistical landscape, conducting thorough analyses of numerous traditional, recent, and novel techniques, to show how these are illuminated by taking the predictive perspective.' Philip Dawid, University of Cambridge 'The prime focus in statistics has always been on modeling rather than prediction; as a result, different prediction methods have arisen within different subfields of statistics, and a general, all-encompassing account has been lacking. For the first time, this book provides such an account and, as such, it convincingly argues for the primacy of prediction. The authors consider a wide range of topics from a predictive point of view and I am impressed by both the breadth and depth of the topics addressed and by the unifying story the authors manage to tell.' Peter Grünwald, Centrum Wiskunde & Informatica and Universiteit Leiden 'The book Predictive Statistics by Bertrand S. and Jennifer L. Clarke provides for an interesting and thought-provoking read. The underlying idea is that much of current statistical thinking is focused on model building instead of taking prediction seriously.' Harald Binder, Biometrical Journal

Muu info

A bold retooling of statistics to focus directly on predictive performance with traditional and contemporary data types and methodologies.
Preface xi
Part I: The Predictive View 1(122)
1 Why Prediction?
3(31)
1.1 Motivating the Predictive Stance
4(7)
1.2 Some Examples
11(21)
1.2.1 Prediction with Ensembles rather than Models
12(9)
1.2.2 Hypothesis Testing as Prediction
21(5)
1.2.3 Predicting Classes
26(6)
1.3 General Issues
32(2)
2 Defining a Predictive Paradigm
34(33)
2.1 The Sunrise Problem
34(7)
2.2 Parametric Families
41(6)
2.2.1 Frequentist Parametric Case
41(2)
2.2.2 Bayesian Parametric Case
43(3)
2.2.3 Interpretation
46(1)
2.3 The Abstract Version
47(16)
2.3.1 Frequentism
48(3)
2.3.2 Bayes Approach
51(5)
2.3.3 Survey Sampling
56(2)
2.3.4 Predictivist Approach
58(5)
2.4 A Unified Framework for Predictive Analysis
63(4)
3 What about Modeling?
67(19)
3.1 Problem Classes for Models and Predictors
68(5)
3.2 Interpreting Modeling
73(2)
3.3 The Dangers of Modeling
75(3)
3.4 Modeling, Inference, Prediction, and Data
78(2)
3.5 Prequentialism
80(6)
4 Models and Predictors: A Bickering Couple
86(37)
4.1 Simple Nonparametric Cases
87(7)
4.2 Fixed Effects Linear Regression
94(7)
4.3 Quantile Regression
101(3)
4.4 Comparisons: Regression
104(4)
4.5 Logistic Regression
108(3)
4.6 Bayes Classifiers and LDA
111(4)
4.7 Nearest Neighbors
115(1)
4.8 Comparisons: Classification
116(3)
4.9 A Look Ahead to Part II
119(4)
Part II: Established Settings for Prediction 123(236)
5 Time Series
125(36)
5.1 Classical Decomposition Model
125(3)
5.2 Box-Jenkins: Frequentist SARIMA
128(11)
5.2.1 Predictor Class Identification
129(3)
5.2.2 Estimating Parameters in an ARMA(p,q) Process
132(1)
5.2.3 Validation in an ARMA(p,q) Process
133(2)
5.2.4 Forecasting
135(4)
5.3 Bayes SARIMA
139(3)
5.4 Computed Examples
142(8)
5.5 Stochastic Modeling
150(6)
5.6 Endnotes: Variations and Extensions
156(5)
5.6.1 Regression with an ARMA(p,q) Error Term
157(2)
5.6.2 Dynamic Linear Models
159(2)
6 Longitudinal Data
161(45)
6.1 Predictors Derived from Repeated-Measures ANOVA
167(5)
6.2 Linear Models for Longitudinal Data
172(8)
6.3 Predictors Derived from Generalized Linear Models
180(4)
6.4 Predictors Using Random Effects
184(10)
6.4.1 Linear Mixed Models
184(9)
6.4.2 Generalized Linear Mixed Models
193(1)
6.4.3 Nonlinear Mixed Models
194(1)
6.5 Computational Comparisons
194(7)
6.6 Endnotes: More on Growth Curves
201(5)
6.6.1 A Fixed Effect Growth Curve Model
203(1)
6.6.2 Another Fixed Effect Technique
204(2)
7 Survival Analysis
206(43)
7.1 Nonparametric Predictors of Survival
208(18)
7.1.1 The Kaplan-Meier predictor
208(8)
7.1.2 Median as a Predictor
216(3)
7.1.3 Bayes Version of the Kaplan-Meier Predictor
219(2)
7.1.4 Discrimination and Calibration
221(1)
7.1.5 Predicting with Medians
222(4)
7.2 Proportional Hazards Predictors
226(13)
7.2.1 Frequentist Estimates of h0 and beta in PH Models
228(3)
7.2.2 Frequentist PH Models as Predictors
231(2)
7.2.3 Bayes PH Models
233(3)
7.2.4 Continuing the Example
236(3)
7.3 Parametric Models
239(6)
7.4 Endnotes: Other Models
245(4)
7.4.1 Accelerated Failure Time (AFT) Models
245(1)
7.4.2 Competing Risks
246(3)
8 Nonparametric Methods
249(58)
8.1 Predictors Using Orthonormal Basis Expansions
252(8)
8.2 Predictors Based on Kernels
260(15)
8.2.1 Kernel Density Estimation
260(6)
8.2.2 Kernel Regression: Deterministic Designs
266(4)
8.2.3 Kernel Regression: Random Design
270(5)
8.3 Predictors Based on Nearest Neighbors
275(11)
8.3.1 Nearest Neighbor Density Estimation
275(6)
8.3.2 Nearest Neighbor Regression
281(4)
8.3.3 Beyond the Independence Case
285(1)
8.4 Predictors from Nonparametric Bayes
286(8)
8.4.1 Polya Tree Process Priors for Distribution Estimation
288(3)
8.4.2 Gaussian Process Priors for Regression
291(3)
8.5 Comparing Nonparametric Predictors
294(8)
8.5.1 Description of the Data, Methods, and Results
295(5)
8.5.2 M-Complete or M-Open?
300(2)
8.6 Endnotes
302(5)
8.6.1 Smoothing Splines
303(1)
8.6.2 Nearest Neighbor Classification
304(1)
8.6.3 Test-Based Prediction
304(3)
9 Model Selection
307(52)
9.1 Linear Models
312(8)
9.2 Information Criteria
320(7)
9.3 Bayes Model Selection
327(7)
9.4 Cross-Validation
334(5)
9.5 Simulated Annealing
339(5)
9.6 Markov Chain Monte Carlo and the Metropolis-Hastings Algorithm
344(4)
9.7 Computed Examples: SA and MCMC-MH
348(5)
9.8 Endnotes
353(8)
9.8.1 DIC
354(1)
9.8.2 Posterior Predictive Loss
354(1)
9.8.3 Information-Theoretic Model Selection Procedures
355(1)
9.8.4 Scoring Rules and BFs Redux
356(3)
Part III: Contemporary Prediction 359(246)
10 Blackbox Techniques
361(88)
10.1 Classical Nonlinear Regression
364(4)
10.2 Trees
368(18)
10.2.1 Finding a Good Tree
371(8)
10.2.2 Pruning and Selection
379(4)
10.2.3 Bayes Trees
383(3)
10.3 Neural Nets
386(19)
10.3.1 'Fitting' a Good NN
388(5)
10.3.2 Choosing an Architecture for an NN
393(1)
10.3.3 Bayes NNs
394(3)
10.3.4 NN Heuristics
397(2)
10.3.5 Deep Learning, Convolutional NNs, and All That
399(6)
10.4 Kernel Methods
405(17)
10.4.1 Bayes Kernel Predictors
409(7)
10.4.2 Frequentist Kernel Predictors
416(6)
10.5 Penalized Methods
422(7)
10.6 Computed Examples
429(14)
10.6.1 Doppler Function Example
429(4)
10.6.2 Predicting a Vegetation Greenness Index
433(10)
10.7 Endnotes
443(6)
10.7.1 Projection Pursuit
443(2)
10.7.2 Logic Trees
445(1)
10.7.3 Hidden Markov Models
446(1)
10.7.4 Errors-in-Variables Models
447(2)
11 Ensemble Methods
449(75)
11.1 Bayes Model Averaging
454(8)
11.2 Bagging
462(9)
11.3 Stacking
471(9)
11.4 Boosting
480(9)
11.4.1 Boosting Classifiers
481(5)
11.4.2 Boosting and Regression
486(3)
11.5 Median and Related Methods
489(8)
11.5.1 Different Sorts of 'Median'
489(5)
11.5.2 Median and Other Components
494(1)
11.5.3 Heuristics
495(2)
11.6 Model Average Prediction in Practice
497(22)
11.6.1 Simulation Study
497(10)
11.6.2 Reanalyzing the Vegout Data
507(11)
11.6.3 Mixing It Up
518(1)
11.7 Endnotes
519(5)
11.7.1 Prediction along a String
520(2)
11.7.2 No Free Lunch
522(2)
12 The Future of Prediction
524(81)
12.1 Recommender Systems
526(11)
12.1.1 Collaborative Filtering Recommender Systems
526(4)
12.1.2 Content-Based (CB) Recommender Systems
530(3)
12.1.3 Other Methods
533(3)
12.1.4 Evaluation
536(1)
12.2 Streaming Data
537(19)
12.2.1 Key Examples of Procedures for Streaming Data
538(9)
12.2.2 Sensor Data
547(4)
12.2.3 Streaming Decisions
551(5)
12.3 Spatio-Temporal Data
556(14)
12.3.1 Spatio-Temporal Point Data
559(3)
12.3.2 Remote Sensing Data
562(3)
12.3.3 Spatio-Temporal Point Process Data
565(3)
12.3.4 Areal Data
568(2)
12.4 Network Models
570(15)
12.4.1 Static Networks
572(9)
12.4.2 Dynamic Networks
581(4)
12.5 Multitype Data
585(14)
12.5.1 &aposOmics Data
586(6)
12.5.2 Combining Data Types
592(7)
12.6 Topics that Might Have Been Here...But Are Not
599(1)
12.7 Predictor Properties that Remain to be Studied
600(2)
12.8 Whither Prediction?
602(3)
References 605(30)
Index 635
Bertrand S. Clarke is Chair of the Department of Statistics at the University of Nebraska, Lincoln. His research focuses on predictive statistics and statistical methodology in genomic data. He is a fellow of the American Statistical Association, serves as editor or associate editor for three journals, and has published numerous papers in several statistical fields as well as a book on data mining and machine learning. Jennifer Clarke is Professor of Food Science and Technology, Professor of Statistics, and Director of the Quantitative Life Sciences Initiative at the University of Nebraska, Lincoln. Her current interests include statistical methodology for metagenomics and prediction, statistical computation, and multitype data analysis. She serves on the steering committee of the Midwest Big Data Hub and is co-PI on an award from the NSF focused on data challenges in digital agriculture.
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