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| Titel |
Bayesian multiple change-points and segmentation: application to homogenization of climatic series homogenization of climatic series |
| VerfasserIn |
A. Hannart, P. Naveau |
| Konferenz |
EGU General Assembly 2009
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| Medientyp |
Artikel
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| Sprache |
Englisch
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| Digitales Dokument |
PDF |
| Erschienen |
In: GRA - Volume 11 (2009) |
| Datensatznummer |
250028870
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| Zusammenfassung |
| We describe a new multiple change-point detection technique based on segmenting the time
series under study into subsequences. These segments correspond to the episodes that
are likely to contain at most a unique jump. They are found by applying Bayesian
decision theory through the minimization of simple cost functions. To perform this
task, we recall that a change-point is universally defined as an abrupt shift. In our
view, this characterization makes change-point a local concept and problem. Abrupt
changes are only apparent with respect to their immediate surroundings. By contrast,
values that are remote from the change-points are irrelevant to the detection process.
In this context, our main assumption is that the whole time series does not have
to be treated globally but can be segmented into shorter subsequences that may
contain one change-point and can be treated with a single change-point algorithm.
Concerning the computational cost, we no longer need to work with a complex
multiple change-point model and a high number of interrelated parameters, leading to
inextricable inference procedures - especially in the Bayesian context. Rather,
two tools are required: a criterion capable of quickly quantifying the amount of
evidence in favour of the existence of a single change-point in a particular subsequence
and a fast and single change-point model to infer change-point characteristics in
each subsequence. This plan can be implemented because basic Bayesian single
change-points with explicit solutions are already available (Lee and Heghinian,
1977) and can be modified in a decision and cost minimization framework. As a
result of this simplifying scheme, calculations can be performed explicitly, without
falling back on MCMC methods and resulting in particularly light implementation.
Through prior distributions derived from a stochastic renewal process description
of jump occurrences, past knowledge on jump amplitude and frequency is also
introduced in our decision process. Results on simulated series lead to improved
speeds and inferences compared to past penalized likelihood methods. At a low
computational cost, the method therefore benefits from the strengths of the Bayesian
framework, which mainly consist in introducing expert knowledge through prior
distributions, and in quantifying the uncertainty on changepoints characteristics
through posterior distributions. In applications to homogenization, those benefits
could be leveraged in two foreseeable ways. Posteriors of jumps position can be
found useful to help objectivize a decision on the existence of jumps when they are
detected simultaneously on multiple series of pairwise station comparison, a process
which is currently performed visually. Also, joint posteriors of jumps position and
amplitude can be used to derive confidence intervals on the corrected series, and to
quantify the uncertainty introduced by homogenization in climatic trends further
obtained. |
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