Curve Registration of Functional Data for Approximate Bayesian Computation

Anthony Ebert, Kerrie Mengersen, Fabrizio Ruggeri and Paul Wu
Additional contact information
Anthony Ebert: Mathematics and Statistics for Medical Science, Queensland University of Technology, Brisbane, QLD 4000, Australia
Kerrie Mengersen: Mathematics and Statistics for Medical Science, Queensland University of Technology, Brisbane, QLD 4000, Australia
Fabrizio Ruggeri: ARC Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS), Parkville, VIC 3052, Australia
Paul Wu: Mathematics and Statistics for Medical Science, Queensland University of Technology, Brisbane, QLD 4000, Australia

Stats, 2021, vol. 4, issue 3, 1-14

Abstract: Approximate Bayesian computation is a likelihood-free inference method which relies on comparing model realisations to observed data with informative distance measures. We obtain functional data that are not only subject to noise along their y axis but also to a random warping along their x axis, which we refer to as the time axis. Conventional distances on functions, such as the L 2 distance, are not informative under these conditions. The Fisher–Rao metric, previously generalised from the space of probability distributions to the space of functions, is an ideal objective function for aligning one function to another by warping the time axis. We assess the usefulness of alignment with the Fisher–Rao metric for approximate Bayesian computation with four examples: two simulation examples, an example about passenger flow at an international airport, and an example of hydrological flow modelling. We find that the Fisher–Rao metric works well as the objective function to minimise for alignment; however, once the functions are aligned, it is not necessarily the most informative distance for inference. This means that likelihood-free inference may require two distances: one for alignment and one for parameter inference.

Keywords: approximate Bayesian computation; functional data; Fisher–Rao metric; hydrological flow; likelihood-free inference; curve registration (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2571-905X/4/3/45/pdf (application/pdf)
https://www.mdpi.com/2571-905X/4/3/45/ (text/html)

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:gam:jstats:v:4:y:2021:i:3:p:45-775:d:630469

Access Statistics for this article

Stats is currently edited by Mrs. Minnie Li

More articles in Stats from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().