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
2 - Dynamical Systems and Markov Processes
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 dynamical systems and their probabilistic description. We distinguish between system descriptions with discrete and continuous state-spaces as well as discrete and continuous time. We formulate examples of statistical models including Markov models, Markov jump processes, and stochastic differential equations. In doing so, we describe fundamental equations governing the evolution of the probability of dynamical systems. These equations include the master equation, Langevin equation, and Fokker–Plank equation. We also present sampling methods to simulate realizations of a stochastic dynamical process such as the Gillespie algorithm. We end with case studies relevant to chemistry and physics.
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- Data Modeling for the SciencesApplications, Basics, Computations, pp. 40 - 107Publisher: Cambridge University PressPrint publication year: 2023