Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Preface
- Acknowledgements
- Expanded Note for Instructors
- Part I Concepts from Modeling, Inference, and Computing
- 1 Probabilistic Modeling and Inference
- 2 Dynamical Systems and Markov Processes
- 3 Likelihoods and Latent Variables
- 4 Bayesian Inference
- 5 Computational Inference
- Part II Statistical Models
- Part III Appendices
- Index
- Back Cover
4 - Bayesian Inference
from Part I - Concepts from Modeling, Inference, and Computing
Published online by Cambridge University Press: 17 August 2023
- Frontmatter
- Dedication
- Epigraph
- Contents
- Preface
- Acknowledgements
- Expanded Note for Instructors
- Part I Concepts from Modeling, Inference, and Computing
- 1 Probabilistic Modeling and Inference
- 2 Dynamical Systems and Markov Processes
- 3 Likelihoods and Latent Variables
- 4 Bayesian Inference
- 5 Computational Inference
- Part II Statistical Models
- Part III Appendices
- Index
- Back Cover
Summary
In this chapter we introduce Bayesian inference and use it to extend the frequentist models of the previous chapters. To do this, we describe the concept of model priors, informative priors, uninformative priors, and conjugate prior-likelihood pairs . We then discuss Bayesian updating rules for using priors and likelihoods to obtain posteriors. Building upon priors and posteriors, we then describe more advanced concepts including predictive distributions, Bayes factors, expectation maximization to obtain maximum posterior estimators, and model selection. Finally, we present hierarchical Bayesian models, Markov blankets, and graphical representations. We conclude with a case study on change point detection.
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- Data Modeling for the SciencesApplications, Basics, Computations, pp. 131 - 162Publisher: Cambridge University PressPrint publication year: 2023