Book contents
- Frontmatter
- Dedication
- Epigraph
- Contents
- Preface
- Acknowledgements
- Expanded Note for Instructors
- Part I Concepts from Modeling, Inference, and Computing
- Part II Statistical Models
- 6 Regression Models
- 7 Mixture Models
- 8 Hidden Markov Models
- 9 State-Space Models
- 10 Continuous Time Models
- Part III Appendices
- Index
- Back Cover
6 - Regression Models
from Part II - Statistical Models
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
- Part II Statistical Models
- 6 Regression Models
- 7 Mixture Models
- 8 Hidden Markov Models
- 9 State-Space Models
- 10 Continuous Time Models
- Part III Appendices
- Index
- Back Cover
Summary
In this chapter we formulate the general regression problem relevant to function estimation. We begin with simple frequentist methods and quickly move to regression within the Bayesian paradigm. We then present two complementary mathematical formulations: one that relies on Gaussian process priors, appropriate for the regression of continuous quantities, and one that relies on Beta–Bernoulli process priors, appropriate for the regression of discrete quantities. In the context of the Gaussian process, we discuss more advanced topics including various admissible kernel functions, inducing point methods, sampling methods for nonconjugate Gaussian process prior-likelihood pairs, and elliptical slice samplers. For Beta–Bernoulli processes, we address questions of posterior convergence in addition to applications. Taken together, both Gaussian processes and Beta–Bernoulli processes constitute our first foray into Bayesian nonparametrics. With end of chapter projects, we explore more advanced modeling questions relevant to optics and microscopy.
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- Data Modeling for the SciencesApplications, Basics, Computations, pp. 215 - 244Publisher: Cambridge University PressPrint publication year: 2023