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
5 - Computational 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 present computational Monte Carlo methods to sample from probability distributions, including Bayesian posteriors, that do not permit direct sampling. In doing so, we introduce the basis for Monte Carlo and Markov chain Monte Carlo sampling schemes and delve into specific methods. These include, at first, samplers such as the Metropolis–Hastings algorithms and Gibbs samplers and discuss the interpretation of the output of these samplers including the concept of burn-in and sample correlation. We also discuss more advanced sampling schemes including auxiliary variable samplers, multiplicative random walk samplers, and Hamiltonian Monte Carlo.
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- Data Modeling for the SciencesApplications, Basics, Computations, pp. 163 - 212Publisher: Cambridge University PressPrint publication year: 2023