文章基本信息

标题：Curve Registration of Functional Data for Approximate Bayesian Computation
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作者：Anthony Ebert ; Kerrie Mengersen ; Fabrizio Ruggeri 等
期刊名称：Stats
电子版ISSN：2571-905X
出版年度：2021
卷号：4
期号：3
页码：762-775
DOI：10.3390/stats4030045
语种：English
出版社：MDPI AG
摘要：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.