Skip to main content Accessibility help
×
Hostname: page-component-788cddb947-tr9hg Total loading time: 0 Render date: 2024-10-10T11:54:41.650Z Has data issue: false hasContentIssue false

6 - Regression Models

from Part II - Statistical Models

Published online by Cambridge University Press:  17 August 2023

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

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.

Type
Chapter
Information
Data Modeling for the Sciences
Applications, Basics, Computations
, pp. 215 - 244
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Regression Models
  • 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/10.1017/9781009089555.009
Available formats
×

Save book to Dropbox

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 Dropbox.

  • Regression Models
  • 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/10.1017/9781009089555.009
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.

  • Regression Models
  • 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/10.1017/9781009089555.009
Available formats
×