Flowgraph Models for Multistate Time-to-Event DataA unique introduction to the innovative methodology of statistical flowgraphs This 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 volume Flowgraph 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. |
Contents
| 1 | |
| 10 | |
3 Inversion of Flowgraph Moment Generating Functions | 43 |
4 Censored Data Histograms | 71 |
5 Bayesian Prediction for Flowgraph Models | 89 |
6 Computational Implementation of Flowgraph Models | 129 |
7 SemiMarkov Processes | 145 |
8 Incomplete Data | 187 |
9 Flowgraph Models for Queuing Systems | 206 |
Appendix Moment Generating Functions | 247 |
| 251 | |
Author Index | 261 |
| 265 | |
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Common terms and phrases
Applications Bayes predictive density Bayesian birth and death cell censored data histograms compute dashed line death process Define denote derivatives diabetic retinopathy ensit equivalent transmittance exact Example exponential distributions exponential waiting failed pump feedback loop flowgraph flowgraph analysis flowgraph model flowgraph of Figure gamma distribution Gibbs sampling given in Figure gives hazard function Huzurbazar hydraulic pump system interval inverse Gaussian Kaplan–Meier kidney likelihood function MAPLE code Markov model Markov process Mason’s rule maximum likelihood multistate models overall waiting parameters parametric models path patient posterior distribution posterior samples predictive distribution present prior problem queuing radios random variables random waiting rejection sampling retinopathy data saddlepoint approximation saddlepoint density approximation Second Edition semi-Markov processes simulated slice sampling solid line solve Statistical survival analysis survivor function total failure total waiting uncensored observations values waiting time distribution Weibull