Bayesian Analysis

Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments

Jason Wyse, Nial Friel, and Håvard Rue

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This paper proposes approaches for the analysis of multiple changepoint models when dependency in the data is modelled through a hierarchical Gaussian Markov random field. Integrated nested Laplace approximations are used to approximate data quantities, and an approximate filtering recursions approach is proposed for savings in compuational cost when detecting changepoints. All of these methods are simulation free. Analysis of real data demonstrates the usefulness of the approach in general. The new models which allow for data dependence are compared with conventional models where data within segments is assumed independent.

Article information

Bayesian Anal., Volume 6, Number 4 (2011), 501-528.

First available in Project Euclid: 13 June 2012

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Changepoints Gaussian Markov random field Integrated Nested Laplace Approximation (INLA) approximate inference model selection


Wyse, Jason; Friel, Nial; Rue, Håvard. Approximate simulation-free Bayesian inference for multiple changepoint models with dependence within segments. Bayesian Anal. 6 (2011), no. 4, 501--528. doi:10.1214/11-BA620.

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  • Boys, R. J. and Henderson, D. A. (2004). "A Bayesian Approach to DNA Sequence Segmentation." Biometrics, 60: 573–588.
  • Carlin, B. P., Gelfand, A. E., and Smith, A. F. M. (1992). "Hierarchical Bayesian Analysis of Changepoint Problems." Applied Statistics, 2: 389–405.
  • Chib, S. (1998). "Estimation and comparison of multiple change-point models." Journal of Econometrics, 86: 221–241.
  • Cox, D. R. and Lewis, P. A. W. (1966). The Statistical Analysis of Series of Events. London: Methuen.
  • Fearnhead, P. (2005). "Exact Bayesian Curve Fitting and Signal Segmentation." IEEE Transactions on Signal Processing, 53: 2160–2166.
  • –- (2006). "Exact and efficient Bayesian inference for multiple changepoint problems." Statistics and Computing, 16: 203–213.
  • Fearnhead, P. and Clifford, P. (2003). "On-Line Inference for Hidden Markov Models via Particle Filters." Journal of the Royal Statistical Society, Series B, 65: 887–899.
  • Fearnhead, P. and Liu, Z. (2011). "Efficient Bayesian analysis of multiple changepoint models with dependence across segments." Statistics and Computing, 21: 217–229.
  • Green, P. J. (1995). "Reversible Jump Markov Chain Monte Carlo Computation and Bayesian Model Determination." Biometrika, 82: 711–732.
  • Jarrett, R. G. (1979). "A note on the intervals between coal-mining disasters." Biometrika, 66: 191–193.
  • Ó Ruanaidh, J. J. K. and Fitzgerald, W. J. (1996). Numerical Bayesian Methods applied to Signal Processing. New York: Springer.
  • Raftery, A. E. and Akman, V. E. (1986). "Bayesian Analysis of a Poisson Process with a Change-Point." Biometrika, 73: 85–89.
  • Rue, H. and Held, L. (2005). Gaussian Markov Random Fields: Theory and Applications, volume 104 of Monographs on Statistics and Applied Probability. London: Chapman & Hall.
  • Rue, H., Martino, S., and Chopin, N. (2009). "Approximate Bayesian Inference for Latent Gaussian Models Using Integrated Nested Laplace Approximations (with discussion)." Journal of the Royal Statistical Society, Series B, 71: 319–392.
  • Scott, S. L. (2002). "Bayesian Methods for Hidden Markov Models: Recursive Computing in the 21st Century." Journal of the American Statistical Association, 97: 337–351.
  • Wyse, J. and Friel, N. (2010). "Simulation-based Bayesian analysis for multiple changepoints." arXiv:1011.2932v1 [stat.CO].
  • Yang, T. Y. and Kuo, L. (2001). "Bayesian Binary Segmentation Procedure for a Poisson Process with Multiple Changepoints." Journal of Computational and Graphical Statistics, 10: 772–785.

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