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1 results

  • 6 - Regression Models

  • from Part II - Statistical Models
  • Steve Pressé, Arizona State University, Ioannis Sgouralis, University of Tennessee, Knoxville
  • Book:
    Data Modeling for the Sciences
    Published online:
    17 August 2023
    Print publication:
    31 August 2023, pp 215-244

  • 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.