Stage-Wise Adaptive Designs

by Zacks, Shelemyahu

• ISBN13: 9780470050958
• ISBN10: 0470050950
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-04-27
• Publisher: Wiley

Summary

Stage-Wise Adaptive Designs presents the theory and methodology of stage-wise adaptive design across various areas of study within the field of statistics, from sampling surveys and time series analysis to generalized linear models and decision theory. Providing the necessary background material along with illustrative S-PLUS functions, this book serves as a valuable introduction to the problems of adaptive designs.

Author Biography

Shelemyahu Zacks, PhD, is Professor of Statistics in the Department of Mathematical Sciences at Binghamton University. He has published several books and over 170 journal articles in the areas of design and analysis of experiments, statistical control of stochastic processes, statistical decision theory, statistical methods in logistics, and sampling from finite populations. Dr. Zacks is a Fellow of the American Statistical Association, Institute of Mathematical Sciences, and American Association for the Advancement of Sciences.

Table of Contents

Preface	p. xiii
Synopsis	p. 1
Multistage and Sequential Estimation	p. 1
Adaptive Designs for Generalized Linear Models	p. 3
Adaptive Methods for Sampling from Finite Populations	p. 5
Adaptive Prediction and Forecasting in Time Series Analysis	p. 6
Adaptive Search of an MTD in Cancer Phase I Clinical Trials	p. 7
Adaptive and Sequential Procedures in Phase III Clinical Trials	p. 9
Sequential Allocation of Resources	p. 10
Sequential Detection of Change Points	p. 12
Sequential Methods in Industrial Testing, Reliability, and Design of Experiments	p. 13
Multistage and Sequential Estimation	p. 15
Stein's Two-Stage Procedure	p. 15
Modifications to Attain Asymptotic Efficiency	p. 18
Two-Stage Sampling from Exponential Distributions	p. 20
Fixed-Width Confidence Interval for the Location Parameter of an Exponential Distribution	p. 20
Two-Stage Sampling for a Bounded Risk Point Estimation of the Exponential Parameter	p. 24
Sequential Fixed-Width Interval Estimation	p. 34
Distributions of Stopping Variables of Sequential Sampling	p. 37
General Theory	p. 38
Characteristics of Ray's Procedure	p. 40
Risk of Some Sequential Point Estimators	p. 41
Sequential Fixed-Width Intervals for the Log-Odds in Bernoulli Trials	p. 42
Problem	p. 42
Distribution of N (¿)	p. 43
Functionals of ¿&hat;N(¿)	p. 47
Bayesian Sequential Estimation	p. 49
General Theory	p. 49
Estimating the Scale Parameter of the Exponential Distribution	p. 51
Adaptive Designs for Generalized Linear Models	p. 55
Exponential Example	p. 55
Adaptive Designs for the Fisher Information	p. 57
Adaptive Bayesian Designs	p. 63
Adaptive Designs for Inverse Regression	p. 66
Non-Bayesian Adaptive Designs	p. 66
Bayesian Adaptive Designs, ¿ Known	p. 71
Stochastic Approximation	p. 73
Adaptive Methods for Sampling from Finite Populations	p. 75
Basic Theory	p. 75
Design Approach	p. 76
Modeling Approach	p. 79
Two-Stage and Sequential Estimation of the Population Mean	p. 81
Design Approach: SRSWR	p. 81
Design Approach: SRSWOR	p. 84
Modeling Approach	p. 86
Adaptive Allocation of Stratified SRS	p. 86
Basic Theory	p. 87
Two-Stage Procedure for a Fixed-Width Interval Estimation of &Ybar;n Under Stratified Sampling	p. 88
Adaptive Search for Special Units	p. 91
Adaptive Estimation of the Size of a Finite Population	p. 92
Applications in Software Reliability	p. 96
Sequential Stopping for Time Domain Models	p. 96
Sequential Stopping for Data Domain Models	p. 98
Sampling Inspection Schemes	p. 100
Two-Stage Sampling for Attributes	p. 100
Sequential Sampling for Attributes	p. 102
Dynamic Bayesian Prediction	p. 103
Adaptive Prediction and Forecasting in Time Series Analysis	p. 107
Basic Tools of Time Series Analysis	p. 107
Linear Predictors for Covariance Stationary T.S.	p. 113
Optimal Linear Predictors	p. 113
Minimal PMSE Predictors for AR(p) T.S.	p. 117
Prediction with Unknown Covariance Structure	p. 119
ARIMA Forecasting	p. 121
Quadratic LSE Predictors for Nonstationary T.S.	p. 124
Moving Average Predictors for Nonstationary T.S.	p. 128
Linear MAS Predictors	p. 130
Predictors for General Trends with Exponential Discounting	p. 132
Recursive Computations with Shifted Origin	p. 133
Linear Trend	p. 136
Linear Trend with Cyclical Components	p. 137
Dynamic Linear Models	p. 141
Recursive Computations for the Normal Random Walk DLM, Constant Variances	p. 143
Incorporating External Information	p. 146
General DLM with Applications	p. 147
DLM for ARMA(p,q) T.S.	p. 153
Asymptotic Behavior of DLM	p. 157
Linear Control of DLM	p. 163
Deterministic Linear Control	p. 163
Stochastic Linear Control	p. 166
Adaptive Search of an MTD in Cancer Phase I Clinical Trials	p. 171
Up-and-Down Adaptive Designs	p. 171
Bayesian Adaptive Search: The Continuous Reassessment Method	p. 177
Efficient Dose Escalation with Overdose Control	p. 179
Patient-Specific Dosing	p. 181
Toxicity versus Efficacy	p. 182
Adaptive and Sequential Procedures in Clinical Trials, Phases II and III	p. 185
Randomization in Clinical Trials	p. 185
Adaptive Randomization Procedures	p. 187
Random Allocation Rule	p. 187
Truncated Binomial Design	p. 189
Efron's Biased Coin Design	p. 190
Wei's Urn Design	p. 192
Response Adaptive Designs	p. 192
Fixed-Width Sequential Estimation of the Success Probability in Bernoulli Trials	p. 193
Sequential Procedure for Estimating the Probability of Success in Bernoulli Trials	p. 197
Sequential Comparison of Success Probabilities	p. 198
Group Sequential Methods	p. 200
Dynamic Determination of Stage-Wise Sample Size	p. 205
Truncated Three-Stage Procedure for Power (TTSP)	p. 205
Bartoff-Lai GLR Procedure	p. 208
Sequential Allocation of Resources	p. 211
Bernoulli Bandits	p. 211
Gittins Dynamic Allocation Indices	p. 216
Sequential Allocations in Clinical Trials	p. 218
Bernoulli Bandits with Change Point	p. 221
Introduction	p. 221
Optimizing the Final Cycle	p. 222
Surveillance Cycle	p. 224
Multiple Surveillance Cycles	p. 230
Sequential Designs for Estimating the Common Mean of Two Normal Distributions: One Variance Known	p. 233
Sequential Detection of Change Points	p. 237
Bayesian Detection When the Distributions Before and After the Change Are Known	p. 237
Problem	p. 237
Bayesian Framework	p. 238
Application in System Reliability	p. 241
Optimal Stopping for Detecting a Change Point in the intensity of a Poisson Process	p. 243
Bayesian Detection When the Distributions Before and After the Change Are Unknown	p. 245
Bayesian Framework	p. 246
Optimal Stopping Rules	p. 247
Detecting a Change in the Success Probabilities of Binomial Trials: An Example	p. 248
CUSUM Procedures for Sequential Detection	p. 250
Structure of CUSUM Procedures	p. 250
Asymptotic Minimaxity of CUSUM Procedures	p. 251
Exact Distribution of Stopping Variables in CUSUM Procedures	p. 253
Tracking Algorithms for Processes with Change Points	p. 258
General Comments	p. 258
Tracking a Process with Change Points	p. 259
Recursive Nonlinear Estimation with Moving Windows	p. 260
Specific Cases	p. 263
Case Studies	p. 269
Recursive Estimation with Change Points	p. 272
Reaction of Recursive Estimators to Change Points	p. 272
Recursive Estimation with the Kalman Filter	p. 276
Detecting Change Points in Recursive Estimation	p. 278
Adjustment of the Kalman Filter for Change Points	p. 279
Special Case	p. 282
Additional Theoretical Contributions	p. 283
Sequential Methods In Industrial Testing	p. 285
Sequential Testing (SPRT)	p. 285
Wald Sequential Probability Ratio Test	p. 286
Exact Distributions of N in the Exponential Case	p. 294
Characteristics of Sequential Procedures in Reliability Estimation and Testing	p. 298
Reliability Estimation	p. 299
Reliability Testing	p. 302
Total Operating Time of Repairable System	p. 304
Some Comments on Sequential Design of Experiments	p. 305
Sequential Testing of Software Reliability	p. 308
Complete Bayesian Model	p. 309
Empirical Bayes: Adaptive Approach When ¿ and ¿ Are Unknown	p. 310
Bibliography	p. 313
Appendix: SPLUS/R Programs	p. 336
Author Index	p. 375
Topic Index	p. 382
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