Explore the foundations of, and cutting-edge developments in, statistics
Statistical Planning and Inference: Concepts and Applications delivers a robust introduction to statistical planning and inference, including classical and computer age developments in statistical science. The book examines the challenges faced in statistical planning and inference, exploring the optimum methods identifying limitations and commonly encountered pitfalls.
It addresses linear and non-linear statistical inference and discusses noise-effect reduction, error rates, balanced and unbalanced data, model selection, discrimination and classification, truncated and censored data, and experimental designs.
Each chapter offers readers problems and solutions and illustrative examples to introduce the concepts and methods discussed within.
The book offers:
- Analysis of both classical theory and modern developments in the field of statistical inference and planning
- Expansive discussions of linear and non-linear statistical inference
- Statistical problems and solutions to test the reader’s progress through and retention of the material contained within
Aimed at practitioners and researchers in the field of statistics, Statistical Planning and Inference: Concepts and Applications is also a must-read resource for graduate students, professors, and researchers in the life sciences, agriculture, psychology, education and measurement, sociology, computer and engineering sciences, and all other fields that rely on statistical concepts.
Table of Contents:
Preface xi
1 Foundation of Experiments 1
1.1 Uncertainties in Evidences 1
1.2 Examples 2
1.2.1 The Louis Pasteur Anthrax Vaccination Experiment 2
1.2.2 The Lanarkshire Milk Experiment: Milk Tests in Lanarkshire Schools 2
1.3 Replication, Randomization, Blocking, and Blinding 4
1.3.1 Replication 4
1.3.2 Randomization 4
1.3.3 Blocking 4
1.3.4 Blinding 4
1.4 Figuring It Out! 4
Questions and Answers 5
Bibliography 6
2 Completely Randomized Design 7
2.1 An Example 7
2.2 Analyses Using R and SAS 9
2.3 Figuring It Out! 12
Bibliography 16
3 Randomized Complete Block Design 17
3.1 Fixed Effects Model 18
3.2 Binomial Model for Signs 20
3.3 Randomization Model 20
3.4 Mixed Effects Model 25
3.5 General Mixed Effects Model 27
3.6 The REML Variance Components Estimates 28
3.7 BLUEs and BLUPs 31
3.7.1 The Conditional Model 32
3.7.2 The Unconditional Model 32
3.7.3 Computation—The Conditional Model 33
3.7.4 Computation—The Unconditional Model 34
3.8 Figuring It Out! 39
Bibliography 40
4 Randomized Incomplete Block Design 41
4.1 Model M1: Fixed-Effects Model 41
4.2 Model M2: Mixed-Effects Model 43
4.3 Research Questions 44
4.4 Figuring It Out! 45
4.5 Definitions 46
Exercises 46
Bibliography 51
5 Error Rates 53
5.1 Definitions of Error Rates 53
5.2 Single-Stage Methods 55
5.3 A Multistage Method 56
5.3.1 Benjamini and Hochberg Method 57
5.4 Figuring It Out 58
Questions 59
Bibliography 62
6 Nutrition Experiment 63
6.1 Figuring It Out! 63
Bibliography 75
7 The Pearson Dependence 77
7.1 Bivariate Normal Distribution 77
7.2 Estimation of Unknown Parameters 79
7.2.1 The Unconditional Model 79
7.2.2 The Conditional Model 81
7.2.3 Test of Significance 83
7.3 A Bayesian Estimation 84
7.4 Exercises 86
Bibliography 87
8 The Multivariate Dependence 89
8.1 The Multivariate Normal Distribution 90
8.2 Inference 91
8.3 Partial Dependence 96
8.4 Exercises 96
Bibliography 98
9 The Conditional Mean Dependence 99
9.1 LS Estimation 100
9.2 Ridge Estimation 101
9.2.1 A Bayesian Estimation 103
9.3 Dependence of Ridge Estimator on the Tuning Parameter 103
9.4 LASSO Estimation 104
9.5 Dependence of LASSO Estimators on the Tuning Parameter 105
Bibliography 116
10 More Parameters Than Observations 119
10.1 Learning by Doing—Exercises 122
Exercises 123
Bibliography 125
11 Eigenvalues, Eigenvectors, and Applications 127
11.1 Eigenvalues and Eigenvectors 127
11.2 Second-Order Response Surface 129
Exercises 132
Bibliography 133
12 Covariance Estimation 135
12.1 Model 1 135
12.1.1 Characterization of the Covariance Matrix and Its Estimators 135
12.1.2 Likelihood Function 136
12.1.3 Properties 137
12.2 Model 2 137
12.2.1 Characterization of the Covariance Matrix and Its Estimators 138
12.3 Model 3 138
12.4 Model 4 139
12.5 Model 5 140
12.6 Exercises 141
Bibliography 142
13 Discriminant Analysis 145
13.1 Learning from the Univariate Data—Two Normal Populations with Equal Variances 145
13.1.1 Discriminant Analysis for the Univariate Data 147
13.1.2 Example—Univariate Discriminant Analysis 148
13.2 Learning from the Univariate Data—Two Normal Populations with Unequal Variances 151
13.2.1 Classification of 25 Versicolor Iris Flowers 153
13.2.2 Classification of 25 Setosa Iris Flowers 154
13.2.3 Test of Homogeneity of Variances 154
13.3 Learning from the Multivariate Data 155
13.3.1 Classification of Versicolor and Setosa 156
13.3.2 Classification of Versicolor and Virginica 158
13.4 Logistic Regression 159
13.5 Exercises 160
Bibliography 162
14 Optimizing the Variance–Bias Trade-Off 163
14.1 Variance–Bias Trade-Off 163
14.1.1 Example 1 164
14.1.2 Example 2 165
14.1.3 Example 3 166
14.2 Information in Data 167
14.3 Information and Design in Presence of a Covariate 169
14.3.1 Information 169
14.3.2 Optimum Design for a Covariate 170
14.4 Information and Design in Presence of Multiple Covariates 171
14.4.1 Information 171
14.4.2 Exponential Model 175
14.4.3 Exponential Regression Model with Multiple Covariates 176
14.4.4 Poisson Log-Linear Model 177
14.4.5 Non-parametric Regression Model 180
14.5 Exercises 183
Bibliography 187
15 Specification, Discrimination, Robustness, and Sensitivity 189
15.1 The Global and Local Optimal Models 189
15.2 The T-Optimal Design 190
15.3 Convex and Concave Functions 192
15.4 The Kullback–Leibler (KL) Divergence 194
15.5 The KL Design Optimality 197
15.6 The Differential Entropy 198
15.7 Lindley Information Measure 200
15.8 Joint Entropy, Conditional Entropy, and Mutual Information 202
15.9 Maximum Entropy Sampling 204
15.10 Search Linear Models and Search Designs 207
15.10.1 Factorial Experiments 209
15.10.2 Search Probability Matrix 210
15.11 Robustness Against Unavailable Data 210
15.12 Influential Sets of Observations 212
15.13 Exercises 213
Bibliography 214
Data Index 217
Subject Index 219
About the Author :
Subir Ghosh is a Professor of Statistics at the University of California, Riverside, USA. He is known for his research work in Statistical Design and Analysis of Experiments and Modeling. He is an elected fellow of the American Statistical Association, the American Association of the Advancement of Science, and an elected member of the International Statistical Institute. He received the awards at the University of California, Riverside:
2012-2016 Distinguished Teaching Professor and a member of the UCR Academy of Distinguished Teachers.
2003 Graduate Council Dissertation Advisor/Mentoring Award, and 1993 Academic Senate Distinguished Teaching Award.
He also served as the 2000-2003 executive editor of the Journal of Statistical Planning and Inference.
