Zuluaga, C.D., Valencia, E.A., Álvarez, M.A. orcid.org/0000-0002-8980-4472 et al. (1 more author) (2015) A Parzen-based distance between probability measures as an alternative of summary statistics in Approximate Bayesian Computation. In: Image Analysis and Processing — ICIAP 2015. 18th International Conference, September 7-11, 2015, Genoa, Italy. Lecture Notes in Computer Science (9279). Springer , pp. 50-61. ISBN 978-3-319-23230-0
Abstract
Approximate Bayesian Computation (ABC) are likelihood-free Monte Carlo methods. ABC methods use a comparison between simulated data, using different parameters drew from a prior distribution, and observed data. This comparison process is based on computing a distance between the summary statistics from the simulated data and the observed data. For complex models, it is usually difficult to define a methodology for choosing or constructing the summary statistics. Recently, a nonparametric ABC has been proposed, that uses a dissimilarity measure between discrete distributions based on empirical kernel embeddings as an alternative for summary statistics. The nonparametric ABC outperforms other methods including ABC, kernel ABC or synthetic likelihood ABC. However, it assumes that the probability distributions are discrete, and it is not robust when dealing with few observations. In this paper, we propose to apply kernel embeddings using an smoother density estimator or Parzen estimator for comparing the empirical data distributions, and computing the ABC posterior. Synthetic data and real data were used to test the Bayesian inference of our method. We compare our method with respect to state-of-the-art methods, and demonstrate that our method is a robust estimator of the posterior distribution in terms of the number of observations.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Springer. This is an author produced version of a paper subsequently published in Lecture Notes in Computer Science. Uploaded in accordance with the publisher's self-archiving policy. The final publication is available at Springer via https://doi.org/10.1007/978-3-319-23231-7_5 |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 15 Aug 2017 15:51 |
Last Modified: | 21 Mar 2018 06:10 |
Published Version: | https://doi.org/10.1007/978-3-319-23231-7_5 |
Status: | Published |
Publisher: | Springer |
Series Name: | Lecture Notes in Computer Science |
Refereed: | Yes |
Identification Number: | 10.1007/978-3-319-23231-7_5 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:120154 |