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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