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, Vol.2011).

Preview

PDF WRAP_Johansen_11-19w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader Download (467Kb)

Abstract

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
Date:	31 May 2011
Volume:	Vol.2011
Number:	No.19
Status:	Not Peer Reviewed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)
References:	Albert, J. and S. Chib (1993). Bayes inference via gibbs sampling of autoregressive time series subject to Markov mean and variance shifts. Journal of Business & Economic Statistics 11 (1), 1{15. Albert, P. S. (1991). A two-state Markov mixture model for a time series of epileptic seizure counts. Biometrics 47 (4), pp. 1371{1381. Andrieu, C., A. Doucet, and R. Holenstein (2010). Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (3), 269{342. Ashburner, J., K. Friston, A. P. Holmes, and J. B. Poline (1999). Statistical Parametric Mapping (SPM2 ed.). website(http://www.fil.ion.ucl.ac.uk/spm): Wellcome Department of Cognitive Neurology. Aston, J. A. and D. E. K. Martin (2007). Distributions associated with general runs and patterns in hidden Markov models. The Annals of Applied Statistics 1 (2), 585{611. Aston, J. A. D., J. Y. Peng, and D. E. K. Martin (2009). Implied distributions in multiple change point problems. CRiSM Research Report 08-26, University of Warwick. Baum, L. E., T. Petrie, G. Soules, and N.Weiss (1970). A maximization technique occurring in the statis- tical analysis of probabilistic functions of Markov chains. The Annals of Mathematical Statistics 41 (1), pp. 164{171. Cappe, O., E. Moulines, and T. Ryden (2005). Inference in Hidden Markov Models. Springer Series in Statistics. Carpenter, J., P. Clifford, and P. Fearnhead (1999). An improved particle filter for non-linear problems. IEEE Proceedings on Radar, Sonar and Navigation 146 (1), 2{7. Chen, J. and A. K. Gupta (2000). Parametric Statistical Change Point Analysis. Birkhauser. Chib, S. (1998). Estimation and comparison of multiple change-point models. Journal of Economet- rics 86, 221{241. Chopin, N. (2007). Inference and model choice for sequentially ordered hidden Markov models. Journal of the Royal Statistical Society Series B 69 (2), 269. Chopin, N. and F. Pelgrin (2004). Bayesian inference and state number determination for hidden Markov models: an application to the information content of the yield curve about in ation. Journal of Econometrics 123 (2), 327 { 344. Recent advances in Bayesian econometrics. Davis, R. A., T. C. M. Lee, and G. A. Rodriguez-Yam (2006). Structural break estimation for nonsta- tionary time series models. Journal of the American Statistical Association 101, 223{239. Del Moral, P., A. Doucet, and A. Jasra (2006). Sequential Monte Carlo samplers. Journal of the Royal Statistical Society Series B 68 (3), 411{436. Del Moral, P., A. Doucet, and A. Jasra (2011). On Adaptive Resampling Procedures for Sequential Monte Carlo Methods. Bernoulli To appear. Douc, R. and O. Cappe (2005). Comparison of resampling schemes for particle filtering. In Image and Signal Processing and Analysis, 2005. ISPA 2005. Proceedings of the 4th International Symposium on, pp. 64{69. IEEE. Doucet, A. and A. M. Johansen (2011). A tutorial on particle filtering and smoothing: Fifteen years later. In D. Crisan and B. Rozovski (Eds.), The Oxford Handbook of Nonlinear Filtering. Oxford University Press. Durbin, R., S. Eddy, A. Krogh, and G. Mitchinson (1998). Biological Sequence Analysis: Probabilistic Models of Proteins and Nucleic Acids. Cambridge University Press. Eckley, I., P. Fearnhead, and R. Killick (2011). Analysis of changepoint models. In D. Barber, A. Cemgil, and S. Chiappa (Eds.), Probabilistic Methods for Time-Series Analysis, pp. 215{238. Cambridge Uni- versity Press. To appear. Fearnhead, P. (2006). Exact and efficient Bayesian inference for multiple changepoint problems. Statistical Computing 16, 203{213. Fearnhead, P. and Z. Liu (2007). On-line inference for multiple changepoint problems. Journal of the Royal Statistical Society Series B 69, 589{605. Fu, J. C. and M. V. Koutras (1994). Distribution theory of runs: A Markov chain approach. Journal of the American Statistical Association 89 (427), 1050{1058. Fu, J. C. and W. Y. W. Lou (2003). Distribution Theory of Runs and Patterns and its Applications: A Finite Markov Chain Imbedding Approach. World Scientific. Gilks, W. R., S. Richardson, and D. J. Spiegelhalter (Eds.) (1996). Markov Chain Monte Carlo In Practice (first ed.). Chapman and Hall. Gordon, N. J., D. J. Salmond, and A. F. M. Smith (1993). Novel approach to nonlinear/non-Gaussian Bayesian state estimation. Radar and Signal Processing, IEEE Proceedings F 140 (2), 107{113. Hamilton, J. D. (1989, March). A new approach to the economic analysis of nonstationary time series and the business cycle. Econometrica 57 (2), 357{384. Huerta, G. and M. West (1999). Priors and component structures in autoregressive time series models. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 61 (4), 881{899. Kong, A., J. S. Liu, and W. H. Wong (1994, March). Sequential imputations and Bayesian missing data problems. Journal of the American Statistical Association 89 (425), 278{288. Lehmann, E. L. and G. Casella (1998). Theory of Point Estimation (Second ed.). Springer. Lindquist, M. (2008). The statistical analysis of fMRI data. Statistical Science 23, 439{464. Lindquist, M. A., C. Waugh, and T. D. Wager (2007). Modeling state-related fMRI activity using change-point theory. NeuroImage 35 (3), 1125{1141. MacDonald, I. L. and W. Zucchini (1997). Monographs on Statistics and Applied Probability 70: Hidden Markov and Other Models for Discrete-valued Time Series. Chapman & Hal/CRC. Neal, R. (2001). Annealed importance sampling. Statistics and Computing 11 (2), 125{139. Ogawa, S., T. M. Lee, A. R. Kay, and D. W. Tank (1990). Brain magnetic resonance imaging with contrast dependent on blood oxygenation. Proc Natl Acad Sci U S A 87 (24), 9868{72. Page, E. S. (1954). Continuous inspection schemes. Biometrika 41, 100{115. Peng, J.-Y. (2008). Pattern Statistics in Time Series Analysis. Ph. D. thesis, Department of Computer Science and Information Engineering College of Electrical Engineering and Computer Science, National Taiwan University. Peng, J.-Y., J. A. D. Aston, and C.-Y. Liou (2011). Modeling time series and sequences using Markov chain embedded finite automata. International Journal of Innovative Computing Information and Control 7, 407{431. Roberts, G., A. Gelman, and W. Gilks (1997). Weak convergence and optimal scaling of random walk Metropolis algorithms. The Annals of Applied Probability 7 (1), 110{120. Robinson, L. F., T. D. Wager, and M. A. Lindquist (2010). Change point estimation in multi-subject fMRI studies. NeuroImage 49, 1581{1592. Scott, S. (2002). Bayesian methods for hidden Markov models: Recursive computing in the 21st century. Journal of the American Statistical Association 97 (457), 337{351. Stephens, D. A. (1994). Bayesian retrospective multiple-changepoint identification. Journal of the Royal Statistical Society Series C (Applied Statistics) 43, 159{578. Viterbi, A. (1967, April). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. Information Theory, IEEE Transactions on 13 (2), 260 { 269. Whiteley, N., C. Andrieu, and A. Doucet (2009). Particle MCMC for multiple changepoint models. Research report, University of Bristol. Worsley, K. J., C. Liao, J. A. D. Aston, V. Petre, G. Duncan, and A. C. Evans (2002). A general statistical analysis for fMRI data. Neuroimage 15 (1), 1{15. Yao, Y.-C. (1988). Estimating the number of change-points via Schwarz' criterion. Statistics and Prob- abilitiy Letters 6, 181{189. Yu, S.-Z. (2010). Hidden semi-Markov models. Artificial Intelligence 174 (2), 215 { 243. Special Review Issue.
URI:	http://wrap.warwick.ac.uk/id/eprint/37291

Request changes to a record

Actions (login required)

View Item