Stage-Wise Adaptive Designs

by Shelemyahu Zacks (Binghamton University )

• ISBN13: 9780470466940
• ISBN10: 0470466944
• Format: eBook
• Copyright: 2009-05-01
• Publisher: Wiley

Summary

Adaptive methods can be found in all fields of statistics. Written by an eminent statistician who has a strong working knowledge of all the key areas in statistics that make use of adaptive designs, this book presents the theory and methodology of stagewise adaptive designs in all applicable fields of statistics. The book includes such novel content as Bayesian dynamic adaptive techniques (for finance), adaptive decision making and sequential analysis (for survey sampling), and adaptive filtering (for engineering). This extensively class-tested text is ideal for researchers, practitioners, and students.

Table of Contents

Preface

Synopsis

Multi-Stage and Sequential Estimation

Adaptive Designs for Generalized Linear Models

Adaptive Methods for Sampling from Finite Populations

Adaptive Prediction and Forecasting in Time Series Analysis

Adaptive Search of an MTD in Cancer Phase I Clinical Trials

Adaptive and Sequential Procedures in Phase III of Clinical Trials

Sequential Allocation of Resources: The One-Armed and Multi-Armed Bandits Applied to Clinical Trials

Sequential Detection of Change-Points

Sequential Methods in Industrial Testing, Reliability and Design of Experiments

Multi-Stage and Sequential Estimation

Stein's Two-Stage Procedure

Modifications to Attain Asymptotic Efficiency

Two-Stage Sampling From Exponential Distributions

Fixed-Width Confidence Interval For The Location Parameter of An Exponential Distribution

Two-Stage Sampling For a Bounded Risk Point Estimation of The Exponential Parameter

Sequential Fixed-Width Interval Estimation

The Distributions of Stopping Variables of Sequential Sampling From Exponential Distributions

General Theory

The Characteristics of Ray's Procedure

The Risk of Some Sequential Point Estimators

Sequential Fixed-Width Intervals for the Log-Odds In Bernoulli Trials

The Problem

The Distribution of N(ë)

Functionals of æN(ë)

Bayesian Sequential Estimation

General Theory

Estimating the Scale Parameter of the Exponential Distribution

Adaptive Designs For Generalized Linear Models

Exponential Example

Adaptive Designs For The Fisher Information

Adaptive Bayesian Designs

Adaptive Designs For Inverse Regression

Non-Bayesian Adaptive Designs

Bayesian Adaptive Designs, å Known

Stochastic Approximation

Adaptive Methods For Sampling From Finite Populations

Basic Theory

The Design Approach

The Modeling Approach

Two-Stage and Sequential Estimation of the Population Mean

Design Approach: SRSWR

Design Approach: SRSWOR

Modeling Approach

Adaptive Allocation of Stratified SRS

Basic Theory

A Two-Stage Procedure For a Fixed-Width Interval Estimation of Y N Under Stratified Sampling

Adaptive Search For Special Units

Adaptive Estimation Of The Size of A Finite Population

Applications In Software Reliability

Sequential Stopping For Time Domain Models

Sequential Stopping For Data Domain Models

Sampling Inspection Schemes

Two-Stage Sampling For Attributes

Sequential Sampling For Attributes

Dynamic Bayesian Prediction

Adaptive Prediction and Forecasting in Time Series Analysis

Basic Tools of T.S. Analysis

Linear Predictors for Covariance Stationary T.S

Optimal Linear Predictors

Minimal PMSE Predictors For AR(p) T.S

Prediction With Unknown Covariance Structure

ARIMA Forecasting

Quadratic LSE Predictors For Non-Stationary T.S

Moving Averages Predictors For Non-Stationary T.S

Linear MAS Predictors

Predictors For General Trends With Exponential Discounting

Recursive Computations With Shifted Origin

Linear Trend

Linear Trend With Cyclical Components

Smoothing Model For Seasonal Data: The Winter Multiplicative Model

Dynamic Linear Models

Recursive Computations for The Normal Random Walk DLM, Constant Variances

Incorporating External Information

The General DLM With Applications

DLM for ARMA(p, q) T.S

Asymptotic Behavior of DLM

Linear Control of DLM

Deterministic Linear Control

Stochastic Linear Control

Adaptive Search of an MTD in Cancer Phase I Clinical Trials

Up-And-Down Adaptive Designs

Bayesian Adaptive Search: The Continuous Reassessment Method

Efficient Dose Escalation With Overdose Control

Patient Specific Dosing

Toxicity Versus Efficacy

Adaptive and Sequential Procedures In Clinical Trials, Phases II and III

Randomization In Clinical Trials

Adaptive Randomization Procedures

Random Allocation Rule

Truncated Binomial Design

Efron's Biased Coin Design

Wei's Urn Design

Response Adaptive Designs

Fixed Width Sequential Estimation of the Success Probability in Bernoulli Trials

Sequential Procedure For Estimating The Probability of Success in Bernoulli Trials With Prescribed Proportional Closeness

Sequential Comparison of Success Probabilities

Group Sequential Methods

Dynamic Determination of Stage-Wise Samples Size

A Truncated Three-Stage Procedure for Power (TTSP)

The Bartoff-Lai GLR Procedure

Sequential Allocation of Resources

Bernoulli Bandits

Gittins Dynamic Allocation Indices

Sequential Allocations In Clinical Trials

Bernoulli Bandits With Change-Point

Introduction

Optimizing The Final Cycle

The Surveillance Cycle

Multiple Surveillance Cycles

Sequential Designs for Estimating The Common Mean of Two Normal Distributions: One Variance Known

Sequential Detection of Change-Points

Bayesian Detection When The Distribution Before and After The Change Are Known

The Problem

The Bayesian Framework

Application in System Reliability

Optimal Stopping For Detecting A Change-Point In The Intensity of A Poisson Process

Bayesian Detection When The Distributions Before and After The Change Are Unknown

The Bayesian Framework

Optimal Stopping Rules

Detecting A Change In The Success Probabilities of Binomial Trials: An Example

CUSUM Procedures For Sequential Detection

The Structure of CUSUM Procedures

Asymptotic Minimaxity of CUSUM Procedures

Exact Distribution Of Stopping Variables In CUSUM Procedures

Tracking Algorithms For Processes With Change-Points

General Comments

Tracking a Process With Change-Points

Recursive Non-Linear Estimation With Moving Windows

Specific Cases

Case Studies

Recursive Estimation With Change-Points

The Reaction of Recursive Estimators to Change-Points

Recursive Estimation With The Kalman Filter

Detecting Change-Points in Recursive Estimation

Adjustment of the Kalman-Filter For Change-Points

A Special Case

Additional Theoretical Contributions

Sequential Methods In Industrial Testing

Sequential Testing (SPRT)

The Wald Sequential Probability Ratio Test

Exact Distributions of N in The Exponential Case

The Characteristics of Sequential Procedures In Reliability Estimation and Testing

Reliability Estimation

Reliability Testing

The Total Operating Time of Repairable System

Some Comments On Sequential Design of Experiments

Sequential Testing of Software Reliability

The Complete Bayesian Model

Empirical Bayes: Adaptive Approach When -and à are Unknown

Bibliography

Appendix: SPLUS/R Programs

Author Index

Subject Index

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