Degree Type
Dissertation
Date of Award
2005
Degree Name
Doctor of Philosophy
Department
Statistics
First Advisor
Michael J. Daniels
Abstract
This dissertation, composed of three papers to be submitted for publication in scholarly journals, focuses on Bayesian methods in function estimation. Chapter 2 specifically discusses spectral density estimation. The semiparametric estimator derived in this chapter combines a smoothed version of the periodogram with a parametric estimator of the spectral density. This semiparametric estimator, which shrinks towards the parametric form provided it is correct, is derived from a hierarchical model. This estimator is consistent, it is competitive with other estimators (as seen through simulation studies), and ultimately does not require the specification of a parametric form.;The third and fourth chapters begin by modeling longitudinal data with linear mixed regression splines. The knots associated with the fixed and random effect curves (in the mixed model) are identified using Bayesian methods. In Chapter 3, reversible jump MCMC methods are used to sample from the marginal posterior of the knots associated with these two curves. Sampling from such a posterior, however, requires evaluation of the marginal likelihood of the knots. This marginal likelihood can not be calculated. Two sampling methods are thus considered in this chapter; these two methods correspond to two different approximations of this likelihood and are compared on how effectively they penalize models with unnecessarily large values of random effect knots.;In the fourth chapter, a similar posterior is considered. This posterior, however, relies on the decomposition of the random effect curve into orthogonal principal component curves, and restricts the random effect curves to have the same knots as the fixed effect curve. The knots associated with the fixed and random effect curves and the number of significant principal component curves is identified by sampling from their joint posterior distribution of knots.
DOI
https://doi.org/10.31274/rtd-180813-16439
Publisher
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Copyright Owner
Carsten Holm Botts
Copyright Date
2005
Language
en
Proquest ID
AAI3184588
File Format
application/pdf
File Size
95 pages
Recommended Citation
Botts, Carsten Holm, "Bayesian methods in single and multiple curve fitting " (2005). Retrospective Theses and Dissertations. 1834.
https://lib.dr.iastate.edu/rtd/1834