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
1 - Probabilistic Modeling and 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 provide an overview of data modeling and describe the formulation of probabilistic models. We introduce random variables, their probability distributions, associated probability densities, examples of common densities, and the fundamental theorem of simulation to draw samples from discrete or continuous probability distributions. We then present the mathematical machinery required in describing and handling probabilistic models, including models with complex variable dependencies. In doing so, we introduce the concepts of joint, conditional, and marginal probability distributions, marginalization, and ancestral sampling.
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- Data Modeling for the SciencesApplications, Basics, Computations, pp. 3 - 39Publisher: Cambridge University PressPrint publication year: 2023
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