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4 - Bayesian Inference

from Part I - Concepts from Modeling, Inference, and Computing

Published online by Cambridge University Press:  17 August 2023

Steve Pressé
Affiliation:
Arizona State University
Ioannis Sgouralis
Affiliation:
University of Tennessee, Knoxville
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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.

Type
Chapter
Information
Data Modeling for the Sciences
Applications, Basics, Computations
, pp. 131 - 162
Publisher: Cambridge University Press
Print publication year: 2023

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  • Bayesian Inference
  • Steve Pressé, Arizona State University, Ioannis Sgouralis, University of Tennessee, Knoxville
  • Book: Data Modeling for the Sciences
  • Online publication: 17 August 2023
  • Chapter DOI: https://doi.org/10.1017/9781009089555.006
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  • Bayesian Inference
  • Steve Pressé, Arizona State University, Ioannis Sgouralis, University of Tennessee, Knoxville
  • Book: Data Modeling for the Sciences
  • Online publication: 17 August 2023
  • Chapter DOI: https://doi.org/10.1017/9781009089555.006
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bayesian Inference
  • Steve Pressé, Arizona State University, Ioannis Sgouralis, University of Tennessee, Knoxville
  • Book: Data Modeling for the Sciences
  • Online publication: 17 August 2023
  • Chapter DOI: https://doi.org/10.1017/9781009089555.006
Available formats
×