Quantifying the uncertainty in change points
Nam, Christopher F. H., Aston, John A. D. and Johansen, Adam M. (2011) Quantifying the uncertainty in change points. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. Working papers, Volume 2011 (Number 19).
WRAP_Johansen_11-19w.pdf - Published Version
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
Quantifying the uncertainty in the location and nature of change points in time series is important
in a variety of applications. Many existing methods for estimation of the number and location of
change points fail to capture fully or explicitly the uncertainty regarding these estimates, whilst
others require explicit simulation of large vectors of dependent latent variables.
This paper proposes methodology for approximating the full posterior distribution of various
change point characteristics in the presence of parameter uncertainty. The methodology combines
recent work on evaluation of exact change point distributions conditional on model parameters via
Finite Markov Chain Imbedding in a Hidden Markov Model setting, and accounting for parameter
uncertainty and estimation via Bayesian modelling and Sequential Monte Carlo. The combination of
the two leads to a
exible and computationally efficient procedure, which does not require estimates
of the underlying state sequence.
We illustrate that good estimation of posterior distributions regarding change point characteristics
is provided for simulated and functional magnetic resonance imaging data. We use the methodology
to show that the modelling of relevant physical properties of the scanner can in
uence detection of
change points and their uncertainty.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Change-point problems|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Official Date:||31 May 2011|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|Funder:||Engineering and Physical Sciences Research Council (EPSRC), Higher Education Funding Council for England (HEFCE)|
|Grant number:||EP/H016856/1 (EPSRC), EP/I017984/1 (EPSRC)|
|Version or Related Resource:||Nam, Christopher F. H., Aston, John A. D. and Johansen, Adam M. (2012). Quantifying the uncertainty in change points. Journal of Time Series Analysis, Volume 33 (Number 5). pp. 807-823. ISSN 0143-9782 http://wrap.warwick.ac.uk/id/eprint/44378|
Albert, J. and S. Chib (1993). Bayes inference via gibbs sampling of autoregressive time series subject
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