Smoothing and filtering with a class of outer measures

Houssineau, J; Bishop, AN

Smoothing and filtering with a class of outer measures

Houssineau, J Bishop, AN

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Publication Type:: Journal Article
Citation:: SIAM-ASA Journal on Uncertainty Quantification, 2018, 6 (2), pp. 845 - 866
Issue Date:: 2018-01-01

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Field	Value	Language
dc.contributor.author	Houssineau, J	en_US
dc.contributor.author	Bishop, AN https://orcid.org/0000-0001-8581-8562	en_US
dc.date.issued	2018-01-01	en_US
dc.identifier.citation	SIAM-ASA Journal on Uncertainty Quantification, 2018, 6 (2), pp. 845 - 866	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132695
dc.description.abstract	© 2018 Society for Industrial and Applied Mathematics and American Statistical Association. Filtering and smoothing with a generalized representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using outer-measure-type versions of Markov kernels and generalized Bayesian-like update equations. This leads to a system of generalized smoothing and filtering equations where integrals are replaced by supremums and probability density functions are replaced by positive functions with supremum equal to one. Interestingly, these equations retain most of the structure found in the classical Bayesian filtering framework. It is additionally shown that the Kalman filter recursion can be recovered from weaker assumptions on the available information on the corresponding hidden Markov model.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DE120102873
dc.relation.ispartof	SIAM-ASA Journal on Uncertainty Quantification	en_US
dc.relation.isbasedon	10.1137/17M1124383	en_US
dc.rights	info:eu-repo/semantics/openAccess
dc.title	Smoothing and filtering with a class of outer measures	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	6	en_US
utslib.for	0104 Statistics	en_US
utslib.for	0103 Numerical and Computational Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Biomedical Engineering
pubs.organisational-group	/University of Technology Sydney/Strength - CHT - Health Technologies
utslib.copyright.status	open_access	*
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	6	en_US

Abstract:

© 2018 Society for Industrial and Applied Mathematics and American Statistical Association. Filtering and smoothing with a generalized representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using outer-measure-type versions of Markov kernels and generalized Bayesian-like update equations. This leads to a system of generalized smoothing and filtering equations where integrals are replaced by supremums and probability density functions are replaced by positive functions with supremum equal to one. Interestingly, these equations retain most of the structure found in the classical Bayesian filtering framework. It is additionally shown that the Kalman filter recursion can be recovered from weaker assumptions on the available information on the corresponding hidden Markov model.

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http://hdl.handle.net/10453/132695