A unique introduction to the innovative methodology of statistical flowgraphsThis book offers a practical, application-based approach to flowgraph models for time-to-event data. It clearly shows how this innovative new methodology can be used to analyze data from semi-Markov processes without prior knowledge of stochastic processes--opening the door to interesting applications in survival analysis and reliability as well as stochastic processes.Unlike other books on multistate time-to-event data, this work emphasizes reliability and not just biostatistics, illustrating each method with medical and engineering examples. It demonstrates how flowgraphs bring together applied probability techniques and combine them with data analysis and statistical methods to answer questions of practical interest. Bayesian methods of data analysis are emphasized. Coverage includes:* Clear instructions on how to model multistate time-to-event data using flowgraph models* An emphasis on computation, real data, and Bayesian methods for problem solving* Real-world examples for analyzing data from stochastic processes* The use of flowgraph models to analyze complex stochastic networks* Exercise sets to reinforce the practical approach of this volumeFlowgraph Models for Multistate Time-to-Event Data is an invaluable resource/reference for researchers in biostatistics/survival analysis, systems engineering, and in fields that use stochastic processes, including anthropology, biology, psychology, computer science, and engineering.
Author(s): Aparna V. Huzurbazar
Edition: 1
Publisher: Wiley-Interscience
Year: 2004
Language: English
Pages: 293
Contents......Page 10
Preface......Page 14
1 Multistate Models and Flowgraph Models......Page 16
1.1 Multistate Models......Page 17
1.2 Flowgraphs as Multistate Models......Page 20
1.3 Organization of the Book......Page 22
1.4 Computational Aspects......Page 24
2 Flowgraph Models......Page 25
2.1 Flowgraph Basics: Models for Series Structures......Page 26
2.1.1 Series Flowgraph Models versus Series Engineering Systems......Page 28
2.2 Flowgraph Models for Parallel Structures......Page 29
2.3 Combinations of Series and Parallel Flowgraphs......Page 31
2.3.1 Loop Flowgraph Model......Page 32
2.4.1 Solving the Simple Series Flowgraph......Page 34
2.4.2 General Results for Convolution......Page 38
2.4.4 Solving Combinations of Series and Parallel Flowgraphs......Page 39
2.4.5 Solving Flowgraphs with Feedback Loops......Page 43
2.4.6 Combining Series, Parallel, and Loop Flowgraphs......Page 47
2.5 Systematic Procedure for Solving Flowgraphs......Page 50
2.6 Flowgraphs for Counts......Page 54
Exercises......Page 56
3.1 Exact Inversion of Flowgraph MGFs......Page 58
3.1.1 Comments on Exact Inversion......Page 62
3.2 Approximate Inversion of Flowgraph MGFs: Saddlepoint Approximation......Page 63
3.3 Using Saddlepoint Approximations with Flowgraph Models......Page 72
3.4 Inversion of Complex Flowgraphs......Page 75
3.5 General Saddlepoint Program......Page 79
Exercises......Page 84
4.1 Censored Data......Page 86
4.2 Survivor and Reliability Functions......Page 87
4.3 Hazard and Cumulative Hazard Functions......Page 89
4.4 Kaplan–Meier Estimator......Page 93
4.5 Histogram for Censored Data......Page 96
Exercises......Page 102
5.1 Bayesian Predictive Density......Page 104
5.2.1 Rejection Sampling......Page 118
5.2.2 Gibbs Sampling......Page 122
5.2.3 Laplace’s Method......Page 125
5.2.4 Slice Sampling......Page 128
5.3 Using Slice Sampling with Flowgraphs......Page 133
Exercises......Page 143
6.1 Code for Censored Data Histograms......Page 144
6.2 Saddlepoint Approximation Code......Page 148
6.3 Code for Bayesian Analysis......Page 149
6.4 Code for Maximum Likelihood Analysis......Page 153
6.5 Code for post.c......Page 156
6.6 Code for transform.c......Page 158
Exercises......Page 159
7 Semi-Markov Processes......Page 160
7.1 Birth and Death Processes......Page 162
7.2 Application to a Markov Model of HIV Infection......Page 165
7.3.1 Flowgraph Model for Diabetic Retinopathy......Page 169
7.3.2 Flowgraph Model for a Construction Engineering Project......Page 184
7.4 Phase Type Distributions......Page 190
Exercises......Page 199
8 Incomplete Data......Page 202
8.1 Constructed Likelihood......Page 203
8.2 Simulations of Unrecognized Incomplete Data......Page 215
Exercises......Page 220
9 Flowgraph Models for Queuing Systems......Page 221
9.1 Review of Queuing Terminology......Page 222
9.2 M/M/1 Queue......Page 224
9.3 Cellular Telephone Network: M/M/c Queue......Page 231
9.3.1 Cellular Telephone Network: Complete Data......Page 234
9.4 Startup Cells and Incomplete Data......Page 240
9.5 Cellular Telephone Network: M/G/1 Queue......Page 244
9.6 Infinite-State M/M/c Queue......Page 253
Exercises......Page 260
Appendix: Moment Generating Functions......Page 262
References......Page 266
Author Index......Page 276
Subject Index......Page 280