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Case Studies in Bayesian Statistical Modelling and Analysis

Book Description

Provides an accessible foundation to Bayesian analysis using real world models

This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches.

Case Studies in Bayesian Statistical Modelling and Analysis:

  • Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems.

  • Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods.

  • Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing.

Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.

Table of Contents

  1. Cover
  2. Wiley Series in Probability and Statistics
  3. Title Page
  4. Copyright
  5. Preface
  6. List of contributors
  7. Chapter 1: Introduction
    1. 1.1 Introduction
    2. 1.2 Overview
    3. 1.3 Further Reading
    4. References
  8. Chapter 2: Introduction to MCMC
    1. 2.1 Introduction
    2. 2.2 Gibbs Sampling
    3. 2.3 Metropolis–Hastings Algorithms
    4. 2.4 Approximate Bayesian Computation
    5. 2.5 Reversible Jump MCMC
    6. 2.6 MCMC for some Further Applications
    7. References
  9. Chapter 3: Priors: Silent or active Partners of Bayesian Inference?
    1. 3.1 Priors in the very Beginning
    2. 3.2 Methodology I: Priors Defined by Mathematical Criteria
    3. 3.3 Methodology II: Modelling Informative Priors
    4. 3.4 Case Studies
    5. 3.5 Discussion
    6. Acknowledgements
    7. References
  10. Chapter 4: Bayesian Analysis of the Normal Linear Regression Model
    1. 4.1 Introduction
    2. 4.2 Case Studies
    3. 4.3 Matrix Notation and the Likelihood
    4. 4.4 Posterior Inference
    5. 4.5 Analysis
    6. References
  11. Chapter 5: Adapting ICU Mortality Models for Local Data: A Bayesian Approach
    1. 5.1 Introduction
    2. 5.2 Case Study: Updating a known Risk-Adjustment Model for Local Use
    3. 5.3 Models and Methods
    4. 5.4 Data Analysis and Results
    5. 5.5 Discussion
    6. References
  12. Chapter 6: A Bayesian Regression Model with Variable Selection for Genome-Wide Association Studies
    1. 6.1 Introduction
    2. 6.2 Case Study: Case–Control of Type 1 Diabetes
    3. 6.3 Case Study: GENICA
    4. 6.4 Models and Methods
    5. 6.5 Data Analysis and Results
    6. 6.6 Discussion
    7. Acknowledgements
    8. References
    9. 6.A Appendix: SNP IDs
  13. Chapter 7: Bayesian Meta-Analysis
    1. 7.1 Introduction
    2. 7.2 Case Study 1: Association between Red Meat Consumption and Breast Cancer
    3. 7.3 Case study 2: Trends in Fish Growth Rate and Size
    4. Acknowledgements
    5. References
  14. Chapter 8: Bayesian Mixed Effects Models
    1. 8.1 Introduction
    2. 8.2 Case Studies
    3. 8.3 Models and Methods
    4. 8.4 Data Analysis and Results
    5. 8.5 Discussion
    6. References
  15. Chapter 9: Ordering of Hierarchies in Hierarchical Models: Bone Mineral Density Estimation
    1. 9.1 Introduction
    2. 9.2 Case Study
    3. 9.3 Models
    4. 9.4 Data Analysis and Results
    5. 9.5 Discussion
    6. References
    7. 9.A Appendix: Likelihoods
  16. Chapter 10: Bayesian Weibull Survival Model for Gene Expression Data
    1. 10.1 Introduction
    2. 10.2 Survival Analysis
    3. 10.3 Bayesian Inference for the Weibull Survival Model
    4. 10.4 Case Study
    5. 10.5 Discussion
    6. References
  17. Chapter 11: Bayesian Change Point Detection in Monitoring Clinical Outcomes
    1. 11.1 Introduction
    2. 11.2 Case Study: Monitoring Intensive Care Unit Outcomes
    3. 11.3 Risk-Adjusted Control Charts
    4. 11.4 Change Point Model
    5. 11.5 Evaluation
    6. 11.6 Performance Analysis
    7. 11.7 Comparison of Bayesian Estimator with Other Methods
    8. 11.8 Conclusion
    9. References
  18. Chapter 12: Bayesian Splines
    1. 12.1 Introduction
    2. 12.2 Models and Methods
    3. 12.3 Case Studies
    4. 12.4 Conclusion
    5. References
  19. Chapter 13: Disease Mapping using Bayesian Hierarchical Models
    1. 13.1 Introduction
    2. 13.2 Case Studies
    3. 13.3 Models and Methods
    4. 13.4 Data Analysis and Results
    5. 13.5 Discussion
    6. References
  20. Chapter 14: Moisture, Crops and Salination: An Analysis of a Three-Dimensional Agricultural Data Set
    1. 14.1 Introduction
    2. 14.2 Case Study
    3. 14.3 Review
    4. 14.4 Case Study Modelling
    5. 14.5 Model Implementation: Coding Considerations
    6. 14.6 Case Study Results
    7. 14.7 Conclusions
    8. References
  21. Chapter 15: A Bayesian Approach to Multivariate State Space Modelling: A Study of a Fama–French Asset-Pricing Model with Time-Varying Regressors
    1. 15.1 Introduction
    2. 15.2 Case Study: Asset Pricing in Financial Markets
    3. 15.3 Time-varying Fama–French Model
    4. 15.4 Bayesian Estimation
    5. 15.5 Analysis
    6. 15.6 Conclusion
    7. References
  22. Chapter 16: Bayesian Mixture Models: When the Thing you need to know is the Thing you cannot Measure
    1. 16.1 Introduction
    2. 16.2 Case Study: CT Scan Images of Sheep
    3. 16.3 Models and Methods
    4. 16.4 Data Analysis and Results
    5. 16.5 Discussion
    6. References
  23. Chapter 17: Latent Class Models in Medicine
    1. 17.1 Introduction
    2. 17.2 Case Studies
    3. 17.3 Models and Methods
    4. 17.4 Data Analysis and Results
    5. 17.5 Discussion
    6. References
  24. Chapter 18: Hidden Markov Models for Complex Stochastic Processes: A Case Study in Electrophysiology
    1. 18.1 Introduction
    2. 18.2 Case Study: Spike Identification and Sorting of Extracellular Recordings
    3. 18.3 Models and Methods
    4. 18.4 Data Analysis and Results
    5. 18.5 Discussion
    6. References
  25. Chapter 19: Bayesian Classification and Regression Trees
    1. 19.1 Introduction
    2. 19.2 Case Studies
    3. 19.3 Models and Methods
    4. 19.4 Computation
    5. 19.5 Case Studies – Results
    6. 19.6 Discussion
    7. References
  26. Chapter 20: Tangled Webs: Using Bayesian Networks in the Fight Against Infection
    1. 20.1 Introduction to Bayesian Network Modelling
    2. 20.2 Introduction to Case Study
    3. 20.3 Model
    4. 20.4 Methods
    5. 20.5 Results
    6. 20.6 Discussion
    7. References
  27. Chapter 21: Implementing Adaptive Dose Finding Studies using Sequential Monte Carlo
    1. 21.1 Introduction
    2. 21.2 Model and Priors
    3. 21.3 SMC for Dose Finding Studies
    4. 21.4 Example
    5. 21.5 Discussion
    6. References
    7. 21.A Appendix: Extra Example
  28. Chapter 22: Likelihood-Free Inference for Transmission Rates of Nosocomial Pathogens
    1. 22.1 Introduction
    2. 22.2 Case Study: Estimating Transmission Rates of Nosocomial Pathogens
    3. 22.3 Models and Methods
    4. 22.4 Data Analysis and Results
    5. 22.5 Discussion
    6. References
  29. Chapter 23: Variational Bayesian Inference for Mixture Models
    1. 23.1 Introduction
    2. 23.2 Case Study: Computed Tomography (CT) Scanning of a Loin Portion of a Pork Carcase
    3. 23.3 Models and Methods
    4. 23.4 Data Analysis and Results
    5. 23.5 Discussion
    6. References
    7. 23.A Appendix: Form of the Variational Posterior for a Mixture of Multivariate Normal Densities
  30. Chapter 24: Issues in Designing Hybrid Algorithms
    1. 24.1 Introduction
    2. 24.2 Algorithms and Hybrid Approaches
    3. 24.3 Illustration of Hybrid Algorithms
    4. 24.4 Discussion
    5. References
  31. Chapter 25: A Python Package for Bayesian Estimation using Markov Chain Monte Carlo
    1. 25.1 Introduction
    2. 25.2 Bayesian Analysis
    3. 25.3 Empirical Illustrations
    4. 25.4 Using PyMCMC Efficiently
    5. 25.5 PyMCMC Interacting with R
    6. 25.6 Conclusions
    7. 25.7 Obtaining PyMCMC
    8. References
  32. Index
  33. Wiley Series in Probability and Statistics