Curve Registration of Functional Data for Approximate Bayesian Computation

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, wh...

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Bibliographic Details
Published in:Stats (Basel, Switzerland) Vol. 4; no. 3; pp. 762 - 775
Main Authors: Ebert, Anthony, Mengersen, Kerrie, Ruggeri, Fabrizio, Wu, Paul
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.09.2021
Subjects:
approximate Bayesian computation
curve registration
Data analysis
Fisher–Rao metric
functional data
hydrological flow
likelihood-free inference
Mathematical functions
Random variables
Registration
Simulation
Spectrum analysis
ISSN:2571-905X, 2571-905X
Online Access:Get full text
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Summary: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 L2 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.
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ISSN:2571-905X
2571-905X
DOI:10.3390/stats4030045