Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions

M.H. Jansen

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Abstract

We present a continuous wavelet analysis of count data with timevarying intensities. The objective is to extract intervals with significant intensities from background intervals. This includes the precise starting point of the significant interval, its exact duration and the (average) level of intensity. We allow multiple change points in the intensity curve, without specifying the number of change points in advance. We extend the classical (discretised) continuous Haar wavelet analysis towards an unbalanced (i.e., asymmetric) version. This additional degree of freedom allows more powerful detection. Locations of intensity change points are identified as persistent local maxima in the wavelet analysis at the successive scales. We illustrate the approach with simulations on low intensity data. Although the method is presented here in thecnotext of Poisson (count) data, most ideas (apart from the specific Poisson normaluzation) apply for the detection of multiple change poits in other circumstances (such as additive Gaussian noise) as well.
Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004)
EditorsA. Di Bucchianico, R.M.M. Mattheij, M.A. Peletier
Place of PublicationBerlin
PublisherSpringer
Pages595-599
ISBN (Print)3-540-28073-1
DOIs
Publication statusPublished - 2006

Publication series

NameMathematics in Industry
Volume8
ISSN (Print)1612-3956

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wavelet analysis
wavelet
decomposition
simulation
analysis
detection

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Jansen, M. H. (2006). Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions. In A. Di Bucchianico, R. M. M. Mattheij, & M. A. Peletier (Eds.), Progress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004) (pp. 595-599). (Mathematics in Industry; Vol. 8). Berlin: Springer. https://doi.org/10.1007/3-540-28073-1_90
Jansen, M.H. / Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions. Progress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004). editor / A. Di Bucchianico ; R.M.M. Mattheij ; M.A. Peletier. Berlin : Springer, 2006. pp. 595-599 (Mathematics in Industry).
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abstract = "We present a continuous wavelet analysis of count data with timevarying intensities. The objective is to extract intervals with significant intensities from background intervals. This includes the precise starting point of the significant interval, its exact duration and the (average) level of intensity. We allow multiple change points in the intensity curve, without specifying the number of change points in advance. We extend the classical (discretised) continuous Haar wavelet analysis towards an unbalanced (i.e., asymmetric) version. This additional degree of freedom allows more powerful detection. Locations of intensity change points are identified as persistent local maxima in the wavelet analysis at the successive scales. We illustrate the approach with simulations on low intensity data. Although the method is presented here in thecnotext of Poisson (count) data, most ideas (apart from the specific Poisson normaluzation) apply for the detection of multiple change poits in other circumstances (such as additive Gaussian noise) as well.",
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Jansen, MH 2006, Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions. in A Di Bucchianico, RMM Mattheij & MA Peletier (eds), Progress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004). Mathematics in Industry, vol. 8, Springer, Berlin, pp. 595-599. https://doi.org/10.1007/3-540-28073-1_90

Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions. / Jansen, M.H.

Progress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004). ed. / A. Di Bucchianico; R.M.M. Mattheij; M.A. Peletier. Berlin : Springer, 2006. p. 595-599 (Mathematics in Industry; Vol. 8).

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

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AB - We present a continuous wavelet analysis of count data with timevarying intensities. The objective is to extract intervals with significant intensities from background intervals. This includes the precise starting point of the significant interval, its exact duration and the (average) level of intensity. We allow multiple change points in the intensity curve, without specifying the number of change points in advance. We extend the classical (discretised) continuous Haar wavelet analysis towards an unbalanced (i.e., asymmetric) version. This additional degree of freedom allows more powerful detection. Locations of intensity change points are identified as persistent local maxima in the wavelet analysis at the successive scales. We illustrate the approach with simulations on low intensity data. Although the method is presented here in thecnotext of Poisson (count) data, most ideas (apart from the specific Poisson normaluzation) apply for the detection of multiple change poits in other circumstances (such as additive Gaussian noise) as well.

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Jansen MH. Multiscale change-point analysis of inhomogeneous Poisson processes using unbalanced wavelet decompositions. In Di Bucchianico A, Mattheij RMM, Peletier MA, editors, Progress in Industrial Mathematics at ECMI 2004 (Proceedings 13th European Conference on Mathematics for Industry, Eindhoven, The Netherlands, June 21-25, 2004). Berlin: Springer. 2006. p. 595-599. (Mathematics in Industry). https://doi.org/10.1007/3-540-28073-1_90