EconPapers    
Economics at your fingertips  
 

A Partition Dirichlet Process Model for Functional Data Analysis

Christoph Hellmayr () and Alan E. Gelfand ()
Additional contact information
Christoph Hellmayr: Duke University
Alan E. Gelfand: Duke University

Sankhya B: The Indian Journal of Statistics, 2021, vol. 83, issue 1, No 3, 30-65

Abstract: Abstract Recently, extensions of the Dirichlet process to the functional domain have been presented in the literature. These processes can be classified based on the type of labeling they induce across different arguments in the domain, i.e., marginal or joint labeling. We show that marginal labeling processes have undesirable properties if functional observations are assumed to be almost surely continuous. Joint labeling processes avoid this undesirable behavior. They are specified through finite dimensional distributions for locations across the entire domain. They range from a common label for all arguments (relatively easy to fit) to joint local label selection at every argument (computationally very demanding). Here, we offer a middle ground - a joint labeling process which partitions the domain of the stochastic process and assign labels to individual partition elements. We call the proposed model a partition functional Dirichlet process and show that it can outperform both of the foregoing extremes of joint labeling. Given data that is a sample from each function in a collection of independent functions over the given domain, we employ this process as a prior for the true functions. We show results from simulation studies as well as a dataset arising from reflectance curves to demonstrate the performance of this process and make comparison with the two extreme labeling models.

Keywords: Gaussian process; Labeling process; Markov chain Monte Carlo; Stick-breaking; Primary 62C10; Secondary 62F15, 62G99 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://link.springer.com/10.1007/s13571-019-00221-x Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-019-00221-x

Ordering information: This journal article can be ordered from
http://www.springer.com/statistics/journal/13571

DOI: 10.1007/s13571-019-00221-x

Access Statistics for this article

Sankhya B: The Indian Journal of Statistics is currently edited by Dipak Dey

More articles in Sankhya B: The Indian Journal of Statistics from Springer, Indian Statistical Institute
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2021-05-29
Handle: RePEc:spr:sankhb:v:83:y:2021:i:1:d:10.1007_s13571-019-00221-x